 exciting in among the participants. Yeah, I can imagine. So I think that as soon as, okay, I think that the live streaming has started, great. So welcome everybody for this day of lectures. So the first speaker of today is Vishweshwara Guttal, who is giving the second lecture on instability in Socasticity in Ecological Science. So please Vishu, share the screen when you are ready. Okay, hold on for a second. I don't see the screen yet. Okay. Do you see my? Okay, hold on. I think I made a mistake one second. Is it fine now? Can you see my slides? Excellent. Thank you. So welcome back everyone. So yesterday Simon gave a very broad overview that incidentally included ideas of by stability, tipping points, and also early warning signals. So I'm sort of going to continue on those themes today. As I as I had mentioned in the first talk, so have this, this is the plan for the three talks I have. So I've sort of sort of talked about basic by stable dynamics, resilience and tipping points and how can we anticipate these using the ideas of early warning signals. And then today the main focus will be on spatial models, you know, everything I spoke on the last talk assume actually there was no reference to space. All the mathematical techniques I used was basically simple ordinary differential equations with some noise superimposed on it and then I had to walk away. So but today, let us look at what happens if there is space. Now, how do we understand by stable systems? Basically the one question that one can try to which I try to focus on today would be, can spatial patterns in ecosystems be used to infer resilience of ecosystems? That's the main question I'm going to ask. So the last one, which I'm hoping will be as planned will be to look at that. Okay, so today I'll just do a brief recap. I'm going to go over this somewhat quickly before I move into the terms of tipping points. So I give this example of large scale continental drift that is a classic example. This is not the only one. There are many other examples of ecosystems for gradual changes in the driver. Okay. And of course, this has been observed in many, many, many systems and to my own list of Simon added a whole bunch of other systems yesterday in the stock. So how do we, so here is the simple ecosystem model I demonstrated the first term in this ecosystem model where we represents the total biomass density in the system actually compares to the classic ecological model which is logistic growth to which we add a grazing term, which is sort of, you know, which could be intrinsic to the system could also be extrinsic such as livestock grazing. Okay. So this is a non-linear term and interestingly, the ones who add this and for a whole range of parameter values, you get a bistability. There's a region of this grazing rate for which two alternative stable states exist and which state current and there could be these switches, shifts, critical transitions, tipping points, abrupt changes at these two points which are critical points or the bifurcation points of the, of this simple model. So the question, you know, the nice thing about this simple model was that we could think of the dynamics of ecosystems with bistability as a ball rolling in this landscape. So for example, the minima in these landscapes correspond to correspond to the stable branches in the bifurcation diagram. So depending on the initial condition, the system could be either in this state or this state. And, and this, you know, this helps us understand concepts of basin of attraction and resilience. And, you know, this concept of potentials was not just for heuristics, it was also useful for arriving at, you know, arriving at quantitative metrics that helps us may make some forecasts about tipping points. For example, if the system is far away from the critical point, as in this, the leftmost point here, these potentials are symmetric. Whereas, when you're very close to the tipping points, potentials are shallow with the low curvature and asymmetric. And this led to the phenomenon of critical slowing down and asymmetric fluctuations. Critical slowing down means that systems take now longer to return back to the equilibrium, they exhibit more fluctuations, and they also exhibit asymmetric fluctuations. Put these things together, we could, you know, come up with some metrics from the time series. And that could actually forecast in this example, we found that if the system were to undergo a transition at this point, if we had this time series before the 1000 time minutes, if we could, if I could calculate simple quantities like autocorrelation at lag 1, this measures the critical slowing down, it's increasing with time as one is approaching a critical point or the abrupt transition. Standard deviation and measure of fluctuation is increasing. The skewness, the strength of skewness, again, which is a measure of asymmetric fluctuation is also increasing. Now, these metrics, if you had no, you know, if you were somewhere around 800 or the time 100, time in it, so these combined metrics give us a hint that the system might be going towards tipping point. So that's the sort of, you know, summary of where we were. I also spoke to you about how there have been many empirical studies, experimental studies, field studies, sometimes they work, sometimes they don't work, as I also showed you when there is huge amount of stochasticity, you know, some of these classic signatures can be masked. Okay, so now, so now of course, ecosystems are really spatial, right? Now they also exhibit really fascinating patterns. These are, you know, some of the classic examples of the fairy rings are found in African deserts. And these are, again, you know, patches of laborentine patterns of vegetation. And then, you know, one can go on, there are more types of vegetation. Many of these vegetation patterns are often found in resource constrained systems or systems which actually have a relatively higher amount of ecological stress. Therefore, this sort of prompted many people to think, can these spatial patterns provide some signatures of abrupt regime shifts that might happen in the future. So this is an example of clustering in the muscles, muscles. And this is an example of clustering of vegetation on the seabed. So there are many, many examples, plenty of examples. So now to understand these kinds of state systems, there are three classic approaches. One is called, so the first two of them are actually both reaction diffusion systems. However, the distinction between the first and second comes from the fact that in the first system, there are no regular patterns, there are no patterning in the ecosystem. Systems sort of roughly appears homogeneous. There are second class of systems are regular patterning systems. You may have heard of curing patterns. And the third class of systems are there are patterns, there is self-organization, but there is no periodicity or regularity to these patterns. So there are these three types of spatial ways to think about ecosystem by stability. So I'm going to go one by one and see how we can do theory of these systems. How can we come up with these early warning indicators followed by, you know, testing them systems as well. Reaction diffusion system and we think of spatial system, reaction diffusion system and with no pattern. So what do I mean by that? Okay, by the way, before I go further, I want to emphasize that just one second, my internet seems to be fluctuating. We show also that connection is a little bit disturbed. So one second, I'll just, are you able to hear me clearly? Yeah, sometimes it, sometimes not. So perhaps it's better to remove the video. Okay, I will, I'll stop my video. I'll stop. I have to understand this for a second. Okay, now my connection, yeah, there's some, yeah, it does say it's a bit slow. Okay, I'll stop my video. I'll share the slide again. Okay. Okay. So some of the, many of the points I'm going to make today, they are actually nicely summarized in this paper that many of us who work in this area, kept together and wrote a review article. So this is a reference you can refer to to get a summary of the theoretical principles behind spatial patterns and how we can use to use spatial patterns to infer resilience. Okay. So how do we go about this? Okay, let's go back to the same model I showed you. I showed you this model where there was this simple logistic growth term followed by a non-linear grazing term. So I'm going to assume the same term as a local reaction term, meaning in space locally exactly same processes are happening. There's a local carrying capacity and a local grazing rate. Of course, the grazing rate can have some stochasticity in it, which is represented by this eta C term as a Gaussian white noise. And then we add a spatial coupling term via the idea that, you know, typically dispersal, which is a mechanism by which one of the key mechanisms by which spatial interactions happen is modeled by a simple diffusion term. So what diffusion term does basically intuitively is it spreads things out in space. So this is the model I'm going to use as you do know the mean field part of this. If there was no diffusion, if I did not have the diffusion, this system will show the same bifurcation diagram by stability. And for even when there is diffusion under a bunch of conditions, this continues to be whole, this continues to hold true. But of course, you know, there are some many subtle aspects once you add space. I'm assuming those are not in play here. So this is what we showed using a combination of numerical simulations and also analytical calculations. So I'm not going to show analytical calculations. These are actually stochastic nonlinear PDEs. There are methods borrowed from the statistical physics literature that we can use to compute the same things I'm going to show you today. But I'm going to focus only on the numerical simulations. So what we have that here is, over a period of time, we run this simulations. And then we sort of stress this ecosystem more and more over time by increasing this grazing parameter C. So by increasing this grazing parameter C slowly over time, we find that a vegetated system becomes a completely bare area. Okay. So and that happens over a period of let's say 52 years on the time scale that we chose in this model. So let's look at the top graph here. What this shows is the average biomass density. If you want to do a spatial mean of all the vegetation density, you find that it hacks, it goes, it sort of gradually decays. And then by year 48 or so, it suddenly undergoes sort of a rapid shift downwards and settle down to a very low biomass density region. So we plot spatial variance and spatial skewness for these spatial images. So what we basically do is for every, imagine every instant of time, we are computing spatial variance, which is basically variance of all the data available in a spatial image. Likewise, spatial skewness is the skewness of all the data available for a given image. So earlier it was computed over time. Now we are computing over space. So if you plot this, what you find interestingly is that even before this non-linear shift in the mean value happens, there is a dramatic increase sort of close to 10 fold increase in the value of spatial variance. Likewise, the skewness actually increases from a value of close to 0 all the way to 1 and even begins to turn downwards even before the mean value has shown any significant trends. One can do these calculations again and show that even spatial correlation, the third plot here below also shows similar patterns. So basically, the message here is that increase in spatial variance and spatial skewness, increase in spatial autocorrelations and also what I have not shown you here is that even in the spectral properties which sort of relate to both correlation and the variance, they also increase. All of these quantities increase much more rapidly than the spatial mean value alone would increase. So therefore, we can use these as indicators, early warning signals in spatial ecological systems which do not have spatial patterns. So that provides a theoretical background of how the same ideas of time series variance, skewness, autocorrelations can also be sort of nicely transformed into, can be applied to spatial systems. Now that is the theory, how do you test this in an empirical world? What do we need? Especially if you have an empirical system that you really want to apply to a large scale ecosystem, how do you do this? So we need three things to be able to do that. One is that I need an ecosystem that has undergone a transition. Secondly, I need to have spatial data over time at sufficient spatial and temporal resolution for the system. Finally, it turns out that there are very few or I am not aware of any such data available. At least five years ago when I was looking, there was no such clean data available. So what do we do? So here is an idea, how do we test this theory? Even when you don't have such an ecosystem that has undergone regime shift or abrupt transition over a period of time, we don't have such a data. What best can we do? I told you the theory, we have this state variable as a function of time. We need snapshots over time. And then we measure these metrics, for example. Imagine that instead of snapshots over time, I had snapshots over space. So the x-axis is not time anymore. It's now either space or the driver values. So this is actually an idea called space for time substitution. And it is widely used in the ecology field studies. For example, if you want to understand how shifting temperatures change species compositions. How do species ranges change? One idea that a lot of field ecologists use is, of course, you can't wait for 100 years for the climate change to happen. What you do is you all look along temperature gradients, altitudinal gradients, where you can find temperature gradients, and then use that space for time substitution to sort of infer or forecast what might happen in the future if the temperature were to change. So we use this same idea. If we have an ecosystem that goes from one state to other state as a function of space, can I compute these indicators? And do they show expected patterns? So indeed, it turns out that there are such ecosystems. So this is an example of the very famous Serengeti-Mara ecosystem in Kenya and Tanzania. And what you find in this ecosystem is the central area is sort of predominantly a grassland. However, the peripheral areas is actually a woodland ecosystem. So we asked the following question. If you now go from the central grassland areas towards the peripheral woodland areas, if you could think of this as space for time substitution, do you find signatures of these early warning signals as measured by spatial variance, dunes, auto correlation, and so on as you go from one end to the other end of the ecosystem? So we chose this very high resolution data at 30 meters. And then we classified each pixel of 30 meters as either wood or grass. And then remind you, the scale here is some, we are really talking about a few hundred kilometers by few hundred kilometers data. This is really a huge data set. So what we do is find the relationship between vegetation and the rainfall in this entire landscape. We find that if we in this landscape, the grass cover sort of shows a non-linear relationship with the mean annual rainfall. So it is sort of expected from many savanna forest ecosystems. Carla has spoken about this, Simon has mentioned this. So the data here again supports the same hypothesis. So we find that the grass cover shows this highly non-linear transition as a function of mean annual rainfall. So what we now do is, let me remind you the theoretical expectation if the mean value of the state variable shows a non-linear transition, then a spatial variance will increase even before the non-linearity in the mean begins. Skewness will again increase even before the mean will decrease, likewise correlation and the spectral properties. The black data here, black points here present a real model just to show that we are not getting any statistical artifacts. So inside exactly as predicted, we find similar patterns in our data. So even before the non-linearity in the mean has begun, variance has increased quite dramatically. Skewness, spatial autocorrelation and low frequency spectra. And likewise, we find this across many other hundreds I showed you there. So this provides an evidence that one can use these ideas derived from non-linear dynamical systems and models and apply it to messy real-world ecosystem. So that gives one example of how we can use spatial models of ecosystem by stability in reaction diffusion systems, no patterns. So let me now move on to regular patterning systems. Regular patterning systems are also called Turing Pattern Systems and here are some really beautiful examples. I'm about going to cover a whole lot of this. Again, I showed you some picture earlier. There are many, many parts of the natural world. We refined very nice regular periodic patterns and these are often modeled by a mechanism called Turing mechanism where there is a very short-range positive feedback and then there is a, you know, an immediate long-range negative feedback. So this combination of local positive, short-range positive feedback and a longer-range negative feedback causes these patterns to persist. And this paper in science argued that these patterns may actually provide some indication of a catastrophic shift. So look at this picture here. Look at this sort of, you know, diagram. So what this shows is there is a region of bi-stability here again, the region of bi-stability. As you move along this region of bi-stability, the spatial patterns are changing. So Rick Kirk and co-authors argued that these changes in these spatial patterns may offer some hints about the resilience of the co-system. However, there are other studies that sort of contest this to show that there are so many types of these patterns and the non-linearity and stochasticity can sort of influence and, you know, confound of interpretations. Nevertheless, but this is a very interesting idea that spatial pattern can actually offer some signatures of resilience. So now the third type of spatial patterns are slightly different. Look at these pictures. So if you look at these pictures, you know, these two have some regularity in the spacing between vegetation, likewise this. However, if you look at this, you know, this cluster is much bigger than this cluster, than this cluster and then this cluster. So what you basically see here is that there is a whole range of vegetation sizes, clusters sizes that are possible. And this basically gave led to a whole class of new models and new studies that found some very interesting results. For example, in this paper, Scanlan et al. including Simon Levin, they found that if you quantify these patch sizes, vegetation patch sizes, and if you look at the probability density functions, they show a power law. So power law basically is a very interesting pattern because power law often indicates that there is no well-defined mean and variance, which in other words, what this means that you can probably find really, really large values of clusters, which are impossible in simple turing like models. And of course, it's not only in vegetation that people have found such patterns. There are also examples of such power law clusters in mussels, saudras, cigars, and scrubs. Of course, let me add a cautionary tale here by saying that there are many, many studies that also very strongly argue that in a lot of these studies, the statistical evidence for existence of power law is really weak. It's something to keep in mind, a very important point. There has been quite a bit of research on understanding where do these power laws come from because when you have a power law nature of any quantity, and when the power law exponent belongs to certain ranges, especially if that exponent is between 1 and 2, the mean value is theoretically infinitely large. And so is the variance. What does that really mean? How do you explain such sort of seemingly unphysical patterns? So in physics, there has been a lot of work trying to understand power laws and physics. The basic idea in physics is that whenever there is a phase transition, look at the figure C here, whenever there is a phase transition from one state to other state, at the point of phase transition, what's also called critical point, you see certain universal features. As Simon was pointing out, this is a irrespective of the complexity of the system. Otherwise, at the phase transition, the number of degrees of freedom are often very low. And so a lot of very different types of systems happen to show very similar properties. And one such property is the existence of power laws. So there has been a lot of speculation in complex systems, whether whenever the power laws that we observe in complex systems such as vegetation systems, ecological systems and so on are the indicative of criticality. And this is a whole field in itself. And I'm not going to really touch upon it. I encourage you to sort of read critically on this very interesting topic. So I'm going to now focus more on the mechanisms. How is the some vegetation ecosystems show irregular patterns, meaning the cluster sizes are not a well-defined average value. On the other hand, there are some other ecosystems where the cluster sizes show very clear periodic patterns, such as steering patterns. So what's the mechanism that makes them so different? So it turns out that to, Haluk, can you still hear me? Yes. Ha, because my network set the net connection lost. I'm sorry. So the question I was trying to address here was, you know, how is that ecosystems of similar types show rather different spatial patterns. So one way to understand that is to look at the net interaction strength. So here a positive value means a positive feedback. Positive feedback means that the presence of, for example, a presence of a tree will facilitate the presence of another tree nearby. So there is a local positive feedback followed by no net feedback after a distance. So if you have only a local positive feedback, what you often find these are these irregular shaped patterns. On the other hand, if you had a local positive feedback, immediately followed by a short range negative feedback, this difference leads to highly regular patterns, which are also called during patterns. So therefore, as Simon was pointing out yesterday, when we try to understand spatial patterns, mechanisms become really crucially important. So what are the biological processes? And often these are integrated with many geophysical processes such as water that flows in the landscape. So therefore, eco hydrology plays a very important role in shaping these feedback as well. So moving on from these irregular, so let's go back to the original questions that I set out, which is can we look at these spatial patterns and then make some inferences about stability? So in this paper by Sonya Kaffee and co-authors, they made this following claim. They said that if you observe a power loss scale-free clustering, such an ecosystem is a stable ecosystem. On the other hand, if you observe that the cluster sizes are not proper law, but if they are exponential, then they are more likely to be less resilient. So basically, the argument was that you can use the cluster size properties to infer something about the resilience of ecosystems. So to make that point again, what you are seeing here is a example of low stress system. This is to high stress ecosystem. What you are seeing here is this power law is bending away. Bending away meaning this is not a power law anymore. So these parts are likely to represent more stable ecosystem whenever you see a power law, a heavy-tailed distribution. If you find an exponential distribution, this could be a case of a highly resilient ecosystem. So sort of summarize this idea of how one can use spatial patterns as signatures of tipping points. So I want to emphasize there are three types. First is that of no spatial pattern. When there are no spatial patterns, I discussed, I also showed empirical evidence. And then when you have these periodic patterns, and then you have scale-free patterns. So when you have this no-patterning system, you can use what we call generic early warning signals, such as variance, skewness and correlations. Those provide early warning signal. When you have periodic pattern, the very presence of the nature of the periodicity and usually the spotted patterns, they are often thought to be maybe an indicator that we are very close to critical transitions. On the other hand, when you have systems with irregular patterns, as you move from scale-free pattern to not so fact-tailed or thin-tailed distributions, then you infer that those systems are less resilient. That's a summary of various theoretical models. So far in my understanding, there is a reasonably good evidence that these sorts of indicators work well in real ecosystems. There is quite a bit of debate about these two. And there have not been too many empirical studies that look at these two. So now let me sort of provide a twist or a spin here, basically to sort of show that these results are a lot more tricky and complicated. So for example, in this paper that was led by my PhD student Sumitra Shankaran, what she showed was that this sort of claim that cluster-sized distributions or the patch-sized distributions that can provide early warning signal actually have nothing to do with this phenomenon of critical slowing down, which I have already sort of summarized. And in fact, the claim that loss of power law clustering is an indicator is not true. So basically in this loss of power law clustering is not a generic indicator of ecosystem resilience. So in fact, there is quite a bit of depending on the model that one uses and the mechanism that one incorporates, we can actually show sort of test the limitations of some of these metrics. So how do we go about doing this? Let me sort of try to describe how we build these simple models. So these are very different type of models. These are not reaction diffusion systems. So we call them, they are popularly known as cellular automata models. So in these cellular automata models, you have, so just one second. So you have, so you sort of assume that the space is divided into a whole large grid like in the central central figure here. And different cells either can be occupied by a, for example, a tree or it could be a muscle bed. So tree is only a representative organism here. And it could also be empty. So it could basically be one. We represent occupied cells as one and others as zero. And then you sort of implement certain stochastic update rules. For example, let's say if we choose this, this pane of a tree and an unoccupied area next to each other. So two possibilities happen. So one is that of death. So there is a probability of death here. And then there's a probability of birth here. For example, you can see that in this case, if this arrow is chosen in the simulation, this original tree has been, is now dead. On the other hand, if the birth was chosen, you know, there is now an addition of tree here. So there could be a birth event or a death event. Likewise, there could be additional complex interactions. So these are called facilitation or positive feedback interaction. For example, if we choose to update for a pair of trees, which are next to each other, two things can happen. One of them can die, like this happened here. So of the two here, one of them has died. On the other hand, the two together will facilitate birth of another tree nearby. And they happen with another set of probabilities. So now we can convert all these sort of intuitive rules of how birth and death happens in probabilistic terms and depending on the neighborhood. So and in these type of models, typically, there are many, many, many parameters. For example, in many of the papers I was showing you earlier, often there are 5 to 10 parameter values. And those large number of parameter values make it very hard to understand what parameter is causing what effect. So in contrast in this model, what we have done is we have chosen a very simple model inspired by statistical physics that has only two parameter values. One is P. P represents basically local birth rate, as I've demonstrated here, or even local death rate. We control the baseline, the production and death rate. Q controls the strength of facilitation, how a plant will influence the birth and death of plants nearby. So there are two parameters and therefore, because there are just two parameters in this simple model, one can sort of do an extensive set of simulations and find out what happens. So what we then have done with these type of models is to simulate them for a very large amount of time. So for example, I'm just showing you two representative simulations here. So on the left hand side, you're seeing a simulation for, I don't remember the exact parameter values, no, they're probably low P and low Q. On the other hand, if I am right here on the right side, we have kept the value of P, which is the baseline birth rate, same as the previous one. However, we have a much higher value of Q, which is high positive feedback. So now we can very easily control two parameter values and then see the effect. So you can already see very clearly in this simple simulation that all else being equal, increasing positive feedback increases clustering in these ecosystems. So therefore, one can study how the clustering properties change as a function of positive feedback values. So here is the sort of classic phase diagram. So what we do here in this case is consider two cases, Q is equal to zero represents a case when there is no, no, no, no, no, no facilitation. So in this case, you find that as you vary this driver value P, which is the baseline birth rate, the system undergoes a phase transition from a bare steady state, which means everyone is dead on the entire spatial landscape. And there's a continuous phase transition to a vegetated state or also called active phase in the physics literature. And the crucial point here is this phase transition is a continuous phase transition. On the other hand, look at the value with a large value of positive feedback. You find that the response of the ecosystem to reducing value of the driver value is highly nonlinear. Look at this. And for a very small range of P, the steady state density drops fairly nonlinearly sharply. And in fact, there is actually a gap, there's actually a jump for extremely tiny values of driver values. So this shows an example of how positive feedback in space affects the abrupt regime shifts. And so unlike the sort of, you know, phenomenological model I showed you in the previous talk, this is an example of a spatially explicit model where one can incorporate some realistic features and mimic features of bistability. So again, this would be the region of, so in this model, the region of bistability would be roughly this much. So it's not very clearly shown here. And using this model, what we do is the following, you know, we do simulations. And then, you know, from the simulations like this, we calculate at steady state, what are all the different clusters? What are the cluster sizes? And what are the statistics of cluster sizes? So I'm going to show you one result from that right now. So what we have done here is, you know, just assume that we have chosen a value of P, which is in the middle of this phase diagram, continuous phase transition, which is low positive feedback. So I have chosen a system far from the critical point zero here. And then you find that at this point, there is a power loss in the cluster sizes. So this much simpler model than the previous ones can also reproduce existence of power loss in the ecosystems. What we also find is that when the positive feedback is high, you can find this power loss even at the point of critical threshold here. So this is, you know, so this is the parameter value for this graph here corresponds to the exact parameter value with the system will abruptly collapse. And you find that you find a power law there. So what this basically means is some of the previous claims such as cluster size distribution can be used as how far or how resilient the ecosystem is really not robust. For example, I'm finding the same power law distribution, of course, the exponents are different only marginally, exponents are different. And yet this in this case, the system is really far from the threshold. However, in this case, the system is quite close to the threshold. So one can find the same cluster size distribution is irrespective of how far or how close you are to ecosystem. And what really matters is the positive feedback. So positive feedback is important. Mechanisms are important. So depending on the values of the, sorry, suddenly my slides went away. So depending on the value of positive feedback, we can find, sorry, my tablet is behaving a bit awkwardly. So it will be accurate. How do I raise this? There must be some option to raise. Yeah, I don't know if the, I guess it's not the annotation of zoom, otherwise you have to go to annotate it clear. It's called, okay, I'll come back. So the power law in the cluster sizes, therefore, is not a good measure. However, there are other types of power loss that do emerge at the point of phase transition. Unfortunately, the resolution of this figure is a bit unsatisfactory, but what you're really seeing here is a measure of correlations, spatial correlations. Basically, what this means is that, how perturbations in space are correlated across the entire landscape. What we find is that typically at the critical thresholds, correlations have, there are very, very long range correlations in ecosystems. And this manifests often as a power law in the correlation function or the power spectrum. Therefore, those could be used as indicators of proximity to critical points. So in fact, we now have a manuscript that is currently being written up where we find some empirical evidence, some supporting evidence, I wouldn't say very conclusive, but something consistent with this theory. Okay. So basically, if I have to summarize this, patient patterns are fascinating. Mechanisms matter. Therefore, however, the interpretation of the resilience from the patterns alone are subtle. One cannot naively use the patterns to make interpretations. So for example, if they're one by either by looking at the nature of patchiness or the cluster size distributions, we have shown in our papers that some of the previous simulation studies were probably finding a set of parameters where it seemed to have worked, but it's not really a general result. So with that sort of demonstration of various simulational results, let me sort of briefly allude to what kind of analytical techniques or can be used in these studies. So unfortunately, I'm not going to go into much detail. So for example, we can take the cellular automata model I have described, one can write down a mean field approximation. And the mean field approximation makes a very nice set of predictions about existence of critical points, whether the phase transition is continuous or discontinuous. It often underestimates the values of positive feedback one needs to find a discontinuous phase transition. One can also do something called a stochastic demographic approximation. Again, I'm not going to go into these details, I'm just going to mention to you. And if any of you are interested more in this, feel free to get in touch with me. I will be happy to share some of our own labs as well as more general manuscripts that sort of describes these methods. So basically, there are a whole variety of methods one can use. So classically, the idea of a mean field approximation is that we have a well-connected system and I'm looking at a deterministic limit where n, the number of sites are infinitely large, the number of individuals are infinitely large. However, we know that real ecosystems have finite numbers. How can we know the effect of those finite numbers? So to do that, something called a finite size expansion, it's a very powerful technique. And there are methods of methods called Fokker-Planck equation, Langevin equation, using which one can find the steady state distributions. So often in this approximation, you don't have a deterministic equation of this type. What you have is a stochastic differential equation of this type and the stochastic differential equation would then need to be solved using the methods of Fokker-Planck equation and Langevin equations. And in some cases, these stochastic differential equations can also capture the effect of the system sizes that you are considering. So I'm not going to go into any further details of this. So I'm coming to sort of end of my talk. So a lot of the work I presented from my lab today was done by these two PhD students. They have finished their PhDs now, really a very, very fabulous work done by them. And then also many, many collaborators, in particular Sonia Akefi and her students, Alex and Miguel. And of course, you know, there are many, many more collaborators and funding that has made this work possible. In particular, Amit, Ashwin and Stephanie, and they were all involved in some of the work I presented today. And so finally, before I take any question, as I had mentioned, so I'm going to talk about intrinsic noise and bystability in collective. So that's the sort of, you know, prelude to tomorrow's talk, how we can actually use similar ideas of noise and bystability and how noise has some very counterintuitive effects. When we study collectives, not of plants and trees, but instead of, you know, animals. So I'm now happy to take question. I think we have quite a bit of time. So I'm happy to go into details of anything that has sort of skipped over. So there are a few questions in the chat, which I read for you. I just remind that if anyone wants to ask a question, please use the- Oh, quite a bit of, I should have seen this midway through. Sorry. So it doesn't pop up on my window when somebody chats. Sorry. Okay, so go ahead with the questions, please. Yes, yes. So I was just saying that if anyone wants to ask a question about, can use the raise and tool. So I'm going to start reading the question. So the one question from Tuan is, so there is no universality for specially correlated systems found in ecology in general? So is there no universality for specially correlated stuff? Question. I can only give a lousy answer. See, clearly, you know, there are many common principles and common patterns. Right? You know, you look at Zebra code patterns or these, some of the patterns I showed you in the beginning, right? For example, sorry, I can- Yeah, look at these patterns, right? You know, some of these patterns are even the code patterns in Zebra. You know, we now know that the code patterns in many animals and these kind of vegetation can both be explained by mechanisms such as during instability, during patterns. So there is a lot of, there is generality and there is universality in the spatial pattern formation. But there are some, also, there are also some details that are important, you know, you know, certain additional parameters like strong positive feedback and the scale and the strength of positive feedback can confound these results. Therefore, I think one has to use a combination of these mathematical, general mathematical theories together with the mechanistic approach. I think one has to use a combination to sort of understand the limitations of universality here. I don't know if I answered your question. Well, there is no sign from, yes, thanks for the answer. So there is a question from Miguel Rodriguez, please. Yeah, I'm thinking a little bit of the lack of data sets that you mentioned to test these principles. And I was thinking if maybe land covers superpose, like land cover maps superpose with carbon sequestration maps could be used or that's just too coarse a resolution. Because for both of them, there are contemporary distribution and also historical distributions around it. So I think for the, so I spoke about three types of spatial patterns, right? One is the first one being where you coarse-crain so much that you don't know the spatial patterns anymore, right? The second one is there are very fine-scale spatial patterns, you know. So those images I showed you, those were patches over tens of meters of approximately those scales. So the same with third one as the regular patterns, they also need to be observed on those scales. The first one can be done using some of the data sets we mentioned, you know, so those, you know, Landsat kind of data sets, right? Which we are currently working on as well. We are using a whole bunch of satellite-based vegetation metrics to not only look at the patterns of various spatial metrics, but also can we construct model from data? Can we derive, you know, model from data as well? We are also looking at those questions. But if you want to look at these, you know, fine-scale spatial tuning like patterns, I could be totally wrong, but you know, I think that the data sets that clearly show evidence for the theory are lacking right now. Thank you. Great, we have time for more questions. I think there are more questions on the chat box. Actually, I can see that. Yeah, yeah, yeah. There were a few questions about the new model. Yeah. Yeah. What is the null model, one without bias stability? That's right. So the null model, if I don't know at what instant you asked me this question, so I think you are maybe referring to the null model I had in one of those slides. So for example, what one can do is imagine that the density, let's say there is a huge spatial landscape and you find that 40% of the area is covered by trees. So 60% is bare ground now. So now how do I know it's driven by positive feedback? That's one case. So what one can do is we can create a null model which maintains the same cover in the landscape, 40%, but it's randomized the distribution of the entire trees. So the clusters that will be formed in the randomized data set will be entirely, not because of the interactions in ecology, they're entirely because of the density itself. So that's one way to arrive at null models for some of these kind of questions. Yes, that's right. So it will not have bias stability. So it's just entirely, I made up the data. So there's a question on what causes the sharp negative feedback. I think it's the stirring system. So you find that there's a positive feedback for short range which becomes negative feedback for longer range. So what happens in these systems is that, so for example, if these are clusters of trees, so they draw water from neighboring regions. So the neighborhood of trees will have higher water retention. What that also means is that the slightly further away from this cluster will be devoid of water. So the water is sort of conserved. If you were to think of water as conserved on very short timescales. So the rainfall falls homogenous in a landscape. So there is a cluster of trees. They not only retain locally well, they also draw water from the local neighborhood. So because of which are slightly larger distances, there will be a lesser amount of water than the average. So that causes the negative feedback at this slightly longer distance. Oh, somebody has answered the question. That's great. So yes, it's the beauty of the chart. Another question by Zoray who is asking which, I mean, what does feedback bifurcation mean in ecological modeling? I don't think I understood the question. What I said was the positive feedback can cause new types of bifurcations. So when we have weak positive feedback, we typically have continuous phase transitions or continuous transition from one state to other states. On the other hand, when you have strong positive feedback, the transition can become abrupt. So that was what I was saying. I was not sure if I used the word feedback bifurcation though. Great. So we have, if there are no more questions, I don't see any hand raised. So great. So there will be the last lecture by Visho on Thursday. So today's from now. I think you will have opportunity to ask a further question. Now we are going to move to the, well, let me thank Visho again for the nice lecture. Now we're going to move to the breakout rooms and we're going to be back in 15 minutes for a seminar by Plaveman 50. Bye. See you everyone. Bye. Bye. Thanks. Okay. Welcome back. I think everybody is here because they don't see the breakout rooms open. So I guess they are have already been closed. So before we start with the next slot, let me remind you a few things about the program. So after the next talk, there is going to be a longer one hour break and then we are going to have other lectures. Then tomorrow there will be the colloquium by Professor Ned Wingring followed by a round table. And on Thursday we are going to have other lectures and round tables. So just to clarify something about the round table, so the round tables are going to be a discussion among five, six analysts who are like people from the pool of the lecturers who taught at the school. And there will be a discussion among them and there will be the possibility to ask questions and to participate, of course, with discussion. So that's what the round table is going to be about. And as you see from the program, we're going to have three and there is nothing you have to prepare for them, just popcorns and then watch the discussion and participate. So without further delay, it's my pleasure to introduce Flavia Marchitti, who is currently a postdoc at the University of Campinas in Brazil. And today she's going to talk about the phylogenetic patterns and how to understand them using microevolutionary models. So thank you very much, Flavia, for being with us and for giving this seminar. Thank you, Jacopo. Thank you for the invitation. And please check if the screen, share screen is working. Is it fine? So I'll be talking about the, just let me put you on the side here, sorry. So I'll be talking about these phylogenetic patterns using an evolutionary model. And I've been working with this topic in the past five years, but I'm very interested in many topics, explained and exposed here in this winter school. And I'll be clear about that in the next slides. So I'm very grateful to thank lots of collaborators and mentors that I had during my lifetime. The list is longer than you can see here, fortunately. And I'm also very happy to be, to have the finance of supporting grants in Brazil and to have the opportunity to go overseas to study. And this is not a great time for science in Brazil, and maybe not for many places around the world. So I'm very grateful to be financed by FAPA ESPN Cups here. And so during this winter school, we've listened a lot about coexistence between different species. How can we have different species sharing resources and still coexist in the same area or in the same and the same environment. And I'm very interested in this topic as well, but I'm also very interested in how these species form, how they appear the first time. And studying the species formation, how these species coexist. I've been working with geographic models of species, modes of speciation. And I've been working with neutral models to form a backbone to understand no neutral models, how we can learn from neutral models from the absence of competition, absence of any other forces, to understand how these things will change these species formation. And the species diversity form patterns, for instance, patterns that can be observed in phylogenetic trees. We see different species forming and they are related to each other in such way that can be described by these phylogenetic trees. And there are many forces shaping and process shaping these patterns that we observe. For instance, how species that could exist in the same area, how they diversify in different species. And what are the signatures that we can have for instance from species that don't share the same area. And with this and the main line of my research nowadays, it's to understand how this we can link the macroevolutionary patterns and the microevolutionary forces. And this fuels a gap that exists in the literature called the micro-macro gap. It's too hard for me to say that, but I think you got it. And when we talk about speciation, when we talk about diversification, usually we think about geographic configuration. We usually learn that species form when you have some barrier that separates individuals in two different areas. And these individuals accumulate differences. And once they are together again, they don't recognize each other as individuals of the same species. This is known as allopathic speciation and usually is invoked to explain how the species form. But there's another form and this is likely the process that happened with the Chippansese and Bonobo apes in Africa that were divided by the Congo river and especiated. But there's another form of speciation called Sympathric Speciation. So the Sympathric Speciation happens, or it doesn't happen, it depends if it exists, when individuals share the same area. And there's a debate in the literature if it is an important force for speciation to happen, if it really exists. But I think before this discussion, before this debate, we need to learn what are the, how it happens, if it happens, how it happens and what are the signature it leaves for us to understand that it happened. So that's why I've been working with models in Sympathric Speciation to understand how we can then deny this is the process that is shaping evolution in many species or in many phylogeneticities. And one of the most well known Sympathric Speciation models was proposed by Dickman in the bed in 1999, where they used it, a model where they included assertive mating, which is the individuals, they choose sexual partners based on how similar they are. They also included gene linkage between the mating character and ecological character, and also included competition, the model, to understand if individuals sharing the same space could then split in different species. And they showed that with these ingredients, they could observe these species formation, these bifurcations on the ecological character. However, earlier than that in 1999, Higgs and Derrida, also known as Derrida Higgs model, proposed that Sympathric Speciation could happen under a neutral model. And maybe some of you will think, oh, neutral model are useless. They don't show us anything. But I think we can learn a lot from neutral models to then understand the neutral models. And that's why I like this model a lot. So Derrida Higgs model proposes that we can define individuals by a very large genome, as large as infinite genome, that have each gene, this genome can have a positive one or minus one value in their positions. And they show, and I tell you how, this population of any individuals can then split in groups of different individuals that we will call species here. And they do this, require a simple thing that is a minimal similarity between individuals to reproduce. They do not prefer to reproduce with the most similar, but they must have a minimal similarity to reproduce. So what happens in this model is that we have two individuals that are A-ploid individuals. So they have only one string that finds the genome. The genome must be allylic, as I told you. And we can compute the similarity between two individuals for the reproduction. So here, individuals Alpha and Beta, they have similarities in some positions here and here, but they have some dissimilarity in other positions, for instance, in here. But if they have a minimum required similarity for the reproduction, they can then mate and form an offspring for the next generation. And this offspring will have the alleles from their parents with a probability of half it comes from parent Alpha and a probability of half it comes from the parent Beta. And eight of these alleles will have a chance of mutation, even by new. So here, for instance, the individual should be a positive one in this allele, but it should be a negative one in this allele, but it became a positive one because of the mutation. And with this, I should stop the video first. Sorry. With this, starting in a very, sorry, I don't know how to reproduce it again. But starting with a very high similarity, all individuals are very similar. Fasting the time with the sexual reproduction and with the mutation rate, we get individuals that have a lower similarity between each other than a given point that is defined by the minimal similarity that we define for the reproduction. So these individuals that have dissimilarity between each other is that where we see a species formation. So we get individuals that can not reproduce to each other. And so with this simpler model, the hidden higgs have shown that with the sexual reproduction, with a minimal similarity between the sexual partners, and with a very large genome as large as infinite, we can observe that we will have groups of individuals that are dissimilar to each other and cannot reproduce to each other. We can observe the speciation with no geographic structuring here, so in a sympathetic mode of speciation. And as you can see, the infinite genome is a very large cost paid here to have speciation under a sympathetic situation. So something that started with Marcus Aguiar in the past 10 years, he decided to study the hidden higgs model in a modified version. So we try to work with the model where it's more real, more close to real situation, where genomes are no more infinite. They are like finite genomes. So we have a genome that have like B lossy. And exactly as in the same model of the hidden higgs, we have two individuals that we will produce. They must have a minimal similarity for the reproduction. And there is a mutation rate that can change the offspring inherited allele. And with this, Marcus shows that it's possible to have not infinite genomes and still have sympathetic speciation. So he shows that as we have lower genome sizes for a fixed number of individuals, we must have a lower mutation rate as well to have speciation happening. And the other thing that is important is that for a given fixed mutation rate, as the genome size increases, the lower the number of individuals required to speciation to happen under a sympathetic mode. And this is something important. We show it's not required anymore to have an infinite genome for the sympathetic speciation to happen. So it's more close to real work. And also something that Marcus decided to study was to understand how we can enhance, how can we force speciation, putting some structure on the on the spatial, on the spatial area, where individuals live. What about if we decrease the sympathetic level somehow? And he has shown that if we put a radius around the neighborhood and in the neighborhood of a focal individual for the reproduction, forcing this individual to look for a partner for a sexual partner around this radius, and we can change this radio for a small radius, can we observe this two speciation happening? So here we are decreasing the sympathetic level, but we still have individuals in the same area. And he shows that when we have a mating radius, a smaller mating radius for looking for the sexual partner, we observe that the genome size required for observing speciation is lower. So we can model the sympathy somehow using small genomes and some structuring on the space for observing speciation. And more than that, he shows that in a given amount of time, if the radius is small, we observe more species and these species are more structured in the space than if we have a larger radius at the same time observing this one. So this was very interesting and very important to help us to develop the other research that we did in the past years. And one of them was trying to do that thing that I showed you before to look for some relationship between species and how this relationship between species could be related to the geographic mode of speciation. So we observed that species were farming through time in a special model. And we also observed that, that I told you before, when we have a spatial configuration, we can observe that as larger is the radius of individuals to look for partners, the less species are formed. And also, when we observe a smaller genome, it takes a longer time to species to farm and find an equilibration of the number of species formed. And this was very important. And we were interesting and relating these observations with the phylogenetic trees of the species that were formed in these spatial areas. And so we did, we developed methods to construct the phylogenetic trees under this speciation model and this individual-based model. So we developed a method where we could record all the speciation and extinction events during the evolutionary time. So we could say which species came from whom and if, for instance, extinction events were happening and how long it takes to one species to farm and then to form another one. What are the times of this, of this lens, of this branch lens? And developing this method, we can also annotate more information during the evolutionary model and have a more concise information by the most recent common ancestor. And we observed that these two methods, which are the two phylogenetic tree, he presented here by recording all the speciation events and annotating more concise information, the most recent common ancestor, we could use information from the phylogenetic trees to compare these two methods. So using, for instance, metrics to describe the branch lens, for instance, we have an acceleration metric or the gamma statistics that define us that the phylogenetic tree for us, that describes to us that the phylogenetic trees has longer brands or smaller brands is more accelerated or decelerated phylogenetic trees and also information about the imbalance of these phylogenetic trees. How low is the imbalance of these phylogenetic trees and how caterpillar is the format of these phylogenetic trees. So using these metrics to describe the phylogenetic trees, we could see that annotating all the events or also annotating more concise information by the most recent common ancestor was very similar. We could use the most concise one. And here I show you very happily that this annotating all the events, so having the two phylogenetic trees presents to us the same, using the most recent common ancestor, presents us the same traits about the gamma statistics that is about the branch lens and also about the balance of these phylogenetic trees. So these methods are very similar and they help us a lot to get information and do simulations more fast. So as I told you, I was interested to understand how these radios of the maching range could change the phylogenetic trees. So I would, I was interested in understanding how parapet and symmetric speciation were different in terms of the phylogenetic trees formed after the process. So just reminding you, we observed that we would have less species under larger mating radios and also would take a longer time for small genomes to form the number of species that we observed in the calibration time. And something very interesting happened when we did the simulations after that. We observed that there is a signal here, observed mainly in the radios, meaning the parapetric-sympatric level of the spatial use, where we observed that as more sympatric is the phylogenetic tree, the larger the radios, it means that more tipi are the phylogenetic trees. They have this format here. These smaller the radios, it means the more parapetric is the speciation in our model, the more steamy are the phylogenetic trees. And we also observed that the genome size, we can observe here the same radios and different genome size that increases from here to here, from orange to blue. We observed that it affects both the acceleration and the balance of phylogenetic trees. And we compared this to empirical phylogenetic trees, adaptive and non-adaptive phylogenetic trees. And we observed that we could have, we could observe some patterns in our data. And observing especially, these are the trees that we worked with. And we observed that the higher the genetic flow during the speciation time, the more balanced were the phylogenetic trees. While the less genetic flow happened during the speciation time of these empirical trees, the more unbalanced were the phylogenetic trees. And this was very related to the radios of the mating range that we had here. So it seems in our model, we can observe some signatures of the geographic mode of speciation. And maybe there are some signatures out there and the phylogenetic trees that we have and databases that we can relate to the geographic mode of speciation. So I was very interested in these results that we have about the synpah tree and the para-pah tree. But I was also interested to understand, okay, how can we tell about the barriers, about islands, about things if we have some barriers defining our space? Can we detect some something in our phylogenetic trees? So if we have a lopah tree, so going back more close to the real world, if we go to the alopah tree, can we observe some pattern in the phylogenetic trees? And by the results that I've just shown you, I was expecting that as we impose a lopah tree, as we decrease the radios, as we increase the structuring in this space, I was expecting that we would observe that phylogenetic trees will become more steamy. So I would expect that given a lopah tree speciation model, I would have more steamy phylogenetic trees. And then we performed our model in this structuring space and we observed that, contrary to our expectations, we observed more balanced phylogenetic trees. And I think here is where we can see it more clearly. So we observed that groups of species, sometimes called deans, were observable from the phylogenetic trees. And something very interesting could be detected when we put the balance of these phylogenetic trees according to the number of species. It's well known that the balance of phylogenetic trees, it varies with the number of species, even in a normalized metric. But still, when we did this, when we put the results of our simulations here, you observed that for a given number of species, those that were structured in mordines had a smaller balance or a balanced metric than those not structured in deans, just in one deans. And it was interesting to observe that for some Hawaiian species such as the Syvose Ward Alliance, the Tetragonapus spiders, and they stick to link lichen that are very, very splitted in different islands in Hawaii. We could relate that these species have been formatted in different deans. They did and it could be detected by the balancing of the phylogenetic trees. However, for some other species, for instance, for the fish, for the diving fishes, we didn't observe the balance, we couldn't relate the balance of the phylogenetic trees with the many islands where they formed. So maybe, and we explored it in the paper, maybe this information was erased from the phylogenetic trees. And contrary to our expectations, the alpha value that is related to the branch length of these phylogenetic trees didn't change a lot. It's true that the variation did, but we didn't we didn't see any change in the mean value of the alpha value. So it was a surprising result. And when running these models, we observed that we were not only creating new species, we are also losing some diversity somehow. And the diversity was being lost by different methods and the most well known and expected one was the extinction. So some species were formed and passed at some time they would disappear as the number of individuals decreased. And other process such as reversal and fusion that I would call broadly as hybridization process, we observed that some species somehow were being splitted and then joined again in another species. So we were forming species, but then we are losing them by hybridization. And together with the students, we decided to study how frequent these things were. So these species could be defined somehow as the group of individuals that have some genetic flow between them. It is not necessarily a direct flow, but it must be somehow some flow between different individuals. For instance, this one and this one, they have a genetic flow through this third individual here. And so species could form and individuals were linked by genetic flow. And we observed that the hybridization could be defined that when we have a species formation such this blue one, but then reverse it somehow to the species that it came from. So this is the most typical hybridization process that is that we usually call fusion here. And the extinction is really the disappearance of a group of individuals that by fluctuation they just disappear. So we could have in our hemogenetic trees this three process, the extinction where individuals disappear just by fluctuation of the number of individuals and that species, the fusion where species is split into two and then fuses into one again. And the reversal that requires two speciation process, which is easier to see here, and then a fusion between the oldest one with the new one. It's not a fusion between the newest species, but a fusion hybridization between the most recent and the species that originated these two. So what we could see is that extinction happens all the time. And it's basically independent of the genome size. We see some difference here. We observe that smaller genomes have a lower extinction rate, but it's not so different as for instance fusion and reversal. So fusion and reversal, they happen in this hybridization modes at this hybridization process, happen all the time, but fusion happens more and reversal gets an equilibration. And we observe that the fusion is more common as a smaller genome. And we also observe that as expected, the population size during the extinction happens more frequently in the small population sizes. So just before the event happened, during if the event was an extinction, the population size is likely a small population size. While fusion and reversal, it happened in any population size that we had. And the extinction and fusion and reversal didn't change a lot on the brand length of the species that where that event happened. More frequently, extinction could happen in species that were very old or very new. And fusion and reversal seems to happen in more new species, more recent species. So I'd show here that the neutrality helps us to understand how the genetic fluctuation and population size fluctuation, also known as genetic drift or ecological drift, could lead us to structures of the genetic trees and how this extinction fusion and reversal could happen during this process. And it helped us to understand, to form the theory, understand more broadly how we could then develop non-neutral models and understand more, understand better non-neutral models. And in our group, we did this in two different ways. I will show you the results by Deborah, principally. I think it's just participating here and also a work that is being developed by my students nowadays. So we had the backbone to understand how genetic interactions, for instance, the methanuclear interactions could reflect on the phylogenetic trees. And we've been studying as well how the cooperation evolution is linked to the diversification or to the permission of new species. So I started with Deborah principally work. So they developed this very nice model where the individuals they have, not only the normal genome that is called the nuclear DNA, but they also have the mitochondrial DNA. And usually the mitochondrial DNA is inherited by the mother. And these DNAs, they must have some, some compatibility, the nuclear and the mitochondrial one, because the respiration, a very important process is, it's a link between the proteins and everything that is necessary for the respiration process made by the nuclear and the mitochondrial DNA. So they must have some compatibility between them. And using this, the difference, the compatibility between these two DNAs, Deborah did define that the individuals that have a better, a smaller distance between these genomes or more coupled DNAs, they would have a larger fitness that should be defined by a function. And again, individuals can be defined in this space. And something very interesting that they observed that is that as we increase the force of selection and the force of the selection is defined by the, how broad is this fitness here. So as we increase the force of the selection on the genome and the nuclear and mitochondrial genomes, we observe life species. So here the large, the smaller the value of a sigma here, the larger the selection force. And also species that were in the, oh, sorry, and the n i value here is when we had no interaction between the nuclear and the and the mitochondria. And also they observed that extinction were more frequent when we had selection, but not exactly in the higher selection in the most for the greater force of selection. They observed that intermediate values of selection provoked more extinctions in this model. And they also observed that the phylogenetic twins were affected by the force of selection between mitochondria and the nucleus. And so the comparing with when we have no interaction between these two genomes, when we have a selection force, the balance of the phylogenetic trees was the unbalanced metric of the phylogenetic trees was lower. And also the phylogenetic trees were more deeply. And this is very interesting. And I think this is how we can summarize one of her results. And when we we compare the coupled part of the DNA under a strong selection, and when we have no interaction between mitochondria and the nucleus, we observe that the mutation rate present on the on the genomes that were linked decrease the the mutation rate of the mitochondria and of the nuclear DNA. And also comparing inside the same individual, they observed that in the end the selection is decreasing the mutation rate is purifying somehow the DNA formed in this species. And something very interesting about the mitochondrial DNA is that they they can be used in biological environments and real environments for identifying species. And this is something that they have shown that the mitochondrial DNA is has a higher matching with the DNA of the nuclear part. And so someone could you could use the barcode the DNA the mitochondrial DNA for barcode. Yes, but it's not necessary. And this is something very impressive. It's not necessary that these these two genomes interact. Even when there is no interaction, there is a mating ratio between these two DNAs. And just to to finish with my my last work here, I've been working the last years to understand how cooperation evolves. And this is something impressive that happens in the most variety of species. You can observe, for instance, I mean, not to interact with each other. You can observe memos that cooperate with each other. And understanding how cooperation happens in nature, help us to understand how we can force cooperation in human populations. Maybe it's a dream, but it's something that we could say that we can learn for nature. So usually the cooperation evolution is studied using evolutionary game theory. So in evolutionary game theory, we say that we have individuals that cooperate. And some individuals that don't cooperate, they're called defectors. And in a given amount of time, depending on the interactions between these individuals, we will observe that one of these strategies will be stable. And usually we studied how we we studied systems where the defection is is the stable strategy. And one of the most well known games is called it. It's represented by this by this payoff matrix, where we have the two strategies cooperators and defectors. And we say that a defector receives a payoff of five when interacting with cooperator. And it receives a payoff of one when interacting with another defector. And the cooperator here receives a payoff of three when interacting with another cooperator. And the cooperator receives zero when interacting with the defector. And thinking that these columns here represent populations, we can see if the strategies in the rows can invade the populations defining the columns. And usually in this type of game, call it the prisoner's dilemma, what we observe is that independent of what happens, the defection is the stable strategy. Because the defector can invade a population of cooperators and a defector can invade and be stable in a population of defectors. So this is the final result usually and something that has been studied in, I don't know in the last 30, 40 years, I cannot calculate things now, but in many years, and is how to how we can have the cooperation evolve in situations where we were expecting the defection to be stable. And Novok and many collaborators have shown that the spatial structure can be an important force for establishing some cooperation where only defection was expected. And so using this simpler form of the prisoner's dilemma, where we have one here and the value that is very good here, Novok and collaborators have shown that even for values where we're expecting defection only, we could observe some cooperation if the interactions were defined in the space. If the interactions and the payoffs gained by individuals were defined by a neighborhood. And even for higher values of B here, where only again only defection was expected, because of the spatial structure, we could observe some some information of this group of cooperators. And so we decided studying these in our model in our individual based models. So if we've included in the end of the genome, these two traits, the cooperation and the defection, that defines the payoff that each individual gets in their neighborhood. So again, using the same payoff matrix used by Novok and collaborators, we observe that the spatial structure could form still form a species under this non neutral model. But under a game situation where individuals have some fitness because of interaction with others, the number of species the number of species farm is usually is usually smaller. And the cooperation frequency maybe is not clear here because I've started in the number one and not in the number zero. But when we start with the same number of cooperators or the same frequency of cooperators under a neutral game or the absence of game or under neutral model, we observe that the cooperation keeps the same frequency for the for the whole time. While for the game model, that is also special as Novok feed, we observe that there is a value of P, which defines values of P, where we were expecting defection, but we still could observe some cooperation. And these values are different of those observed by Novok. And I'll explore more that. We also observed that species could form. So we could, we could draw their phylogenetic trees. And this is something very impressive. We observed a very different balance during the species formation, and also more accelerated phylogenetic trees. So we could attack somehow as Deborah did in her work, that when we include some selection here, when we include some fitness here, there are things that are detectable in the phylogenetic trees. And so the phylogenetic trees here are reflecting how the spatial structure and cooperation evolution affect the phylogenetic tree. And something we are still interested in is understanding how the absence of the structure can affect the, not only the formation of species, but also the cooperation evolution. And so doing a greater neighborhood for the species to the mating range, and also for computing the payoffs of these individuals. I'm interested, and Louise is developing this work, my student. I'm interested in, we are interested in understanding how species form. And this is not any more a neutral model. So species cannot form, but we have many clues that they will form. And we are interested also if there are patterns in these species that are formed. Do we observe more defectors in some species? Do we observe more cooperators in other species? And how these leave signatures in the phylogenetic trees? Is it a conservative trait? Can we relate the cooperation or defection as an ancestral trait of a given group of species here? And so this is the kind of thing we are exploring now. And in the end, another sort of mind we'll be studying how the cooperation and the cooperation can affect the extinction and hybridization rates. And are they, is it more frequent that the cooperators will be extinct? Is it more frequent that hybridization happens in symbiotic speciation or in paraphatic speciation? So this is the kind of questions that I'm interested in now. So just to summarize, I think I have two minutes here. I've shown you that competition or natural selection is not necessary for symbiotic speciation. And this is a result of the Hedahids model. And sorry, I've shown you that even in finite genomes, when we have a given genome size, a given mutation rate, and a given number of individuals, we still can have symbiotic speciation. And especially structuring, when we define a mating ratio, ratios for the individuals, we can have more species. We can find signatures of the geographic mode of speciation in phylogenetic trees. And I've shown you that allopatry and parapatry affect mainly the balance of the phylogenetic trees. And almost in the end, I've shown you that extinction and hybridizations, they can be characterized in neutral models. And we can then explore non-neutral models. They can be interactions between the same, inside the same individual, or they can be through interactions between different individuals. But all this knowledge that we accumulated is said in neutral models has helped us to understand and to perform the non-neutral models. So I'm ready for any questions from you. Thank you so much. Great. Thanks a lot, Flavia, for the nice talk. So we have time for questions. So there are a few from the chat, which I'll start feeding from you. And then if anyone wants to ask anything, can raise the end on Zoom. So Elvira is asking, do you use empirical phylogenies without dating to compare with the simulation of these models? The empirical data without dating to compare with simulation. No, it's with dating. And then there is Margaret, who is asking, I noticed you made use of the random forest model on the phylogenetic trees. I wish to understand why you made the choice. Also, did you try other models? And what were your discoveries? Oh, maybe I don't know what is a random forest model. I don't know. I don't know if maybe she can ask and maybe. Yeah, Margaret, please. Yeah. Good afternoon. Thank you. Can you hear me? Yes. Okay. If you check, I don't know the slight number. When you are showing the inheritance from the phylogenetic trees is actually a random forest model that we used to model those trees. I don't know back to the slide. I can't really get the exact slide. Yeah, it does branching that you had. Is it in the beginning? Yeah, kind of in the beginning. I'm sorry. Yeah, before this slide, yes. Backward. Okay, yeah, here. Yes, exactly. And this one? Yes. And there's a place that is actually stated that we use a random forest model to actually get the models. So I actually understood why you chose the random forest. Oh, so this is how we represented this method that we call it. It's also known as the most recent common ancestor. And I don't know if it's exactly the same thing of the random forest model, but we get individuals of our simulation. And then we trace back from which species it came from. So for instance, this individual here, let's say the yellow one here, maybe it's easier. The yellow one here, when we trace back this group of individuals that are represented by this guy here. And when we trace back, it came from an exposition that happened just in the beginning. And the blue one here, we can see that the individuals of the blue one here came from yellow individuals. So when we joined information, so we have the information based on this individual here that the exposition happened two times before the present time. So we can say there is a distance between the blue and the yellow one that happened two times before now. And this is just like following back the species that identifies the species of an individual and which is the ancestor of the species of that individual. I don't know if it's the same of the random forest, they didn't know. But all the same, I want to know your choice of model. There are actually several models of the species, but really not generally the random forest can be like the most convenient and less accurate in terms of what to do, but also other models that will meet the criteria. So I just wanted to understand your choice of all these models. Thank you. So just one more thing, maybe it can help you to understand what was our choice. So this information, so using all the events, so recording all the events takes a lot of time and takes a lot of information that we need to recording all your computers. So doing this helped us a lot. But we also explored, for instance, genetic distances by different metrics. So yeah, because we have the information of the genomes of the individuals, we could do this genetic distance between individuals of different species. But we've noticed that when we compare to the real phylogenetic trees that is made during the evolutionary process, when we can record all the events, we observe that the phylogenetic trees made by the most recent common ancestor were more similar to the real phylogenetic trees. That's why we decided to use this method to construct our phylogenetic trees. Thank you so much. You're welcome. Thank you. Great. We have time for more questions. Since nobody's asking, I can ask my question. So in one of the first plots you showed about the model where you compare with the empirical networks, you had adaptive and non-adaptive networks. I mean, I'm not sure how it's possible. I also say networks, but it's trees. Sorry, sorry. Yes. There is gene flow, so they are also network in some sense. Yeah. So you have the adaptive and non-adaptive. So I'm not sure how these two are classified, but I would say the word adaptive suggests that there should be some at least difference in the structure, while it seems that you didn't see any difference between the two. So I was wondering. I can go back to that slide as well. But it's true. So when we decide to compare to adaptive and non-adaptive radiations, it's below here. It was because we were evaluating our phylogenetic trees. Let me show here. We were evaluating our phylogenetic trees under this when they reached the equilibration time. So we were interested in this radiation process. When it takes longer time, you see that they don't form new species. So the phylogenetic trees, you reach somehow some structure that is somehow fixed. And we decided to study how radiations could, how did, what are the signatures during the radiation? And then when we go to the literature, you only find or mainly find adaptive radiation. And maybe it's because we believe that the main process happened under adaptive radiation. So usually when they say adaptive radiation, they are informing us there is somehow some selection during the process. And the non-adaptive radiation. So this information of adaptive and non-adaptive radiation were also gotten from the, got from the literature. So as the authors inform us, oh, it's adaptive. It's non-adaptive. And if you see in our table, oh, maybe I should put in the presentation mode, we have more, usually more adaptive than non-adaptive networks. And it's true. We can see some structure here in the adaptive phylogenetic trees that are the triangle ones that is given by the natural selection, not by the spatial structure. But it was interesting to understand and to see that maybe the genetic flow that can be defined as low or high defines better how the structure of the phylogenetic more than if it's adaptive or non-adaptive. Maybe the genetic flow is the most important thing here. And we made this classification of the genetic flow based on the, how many islands or how was the structure doing the radiation process? Did I respond to your question? Yes, yes, no, no. I was, I mean, I think it was surprising that there was no difference between the adaptive and non-adaptive, right? Because they both match the neutral case. Yeah. And I think because we have this information that maybe this space, this spatial structure is very important. We have more, more, we are more prepared to evaluate the non-neutral models to understand what are the signatures on the non-neutral models that are not given by the space. Yes. Great. So is there any more, any other question? Okay. So if not, let me thank Flavia again for the very nice seminar. And we are now going to take a break for one hour and a half. So it's going to be a long break. You can even take a walk out of the screen and go out. And we are going to start again at 3.45 with the second lecture by Alvaro Sanchez. So thanks to everyone. See you in an hour and a half. Bye-bye. Bye-bye. Welcome back, everybody. So in a couple of minutes, we will start again. So I think many people typically connect the last minute. So we'll start in two or three minutes. Great. So we are about to start before I introduce the next lecture. Let me remind you to check frequently the program for the next two days. So in particular, tomorrow we are going to have a colloquium by Ned Wingring on modeling microbial diversity. And I strongly suggest to attend that activity. Again, a reminder, if you go on the website in the program, you will find a link to register to the separate Zoom meeting. So follow the link register and you can follow it. And you can also follow it from YouTube if you don't want to use Zoom. Then tomorrow there will be the first of three round tables on the pandemic, also with an interface with economics. We have a great set of panelists. And then on Thursday, we will have the last three lectures and the two round tables. So just to remind you what to expect from the round tables, this is going to be a sort of free informal discussion between the panelists. And there will be time for you to ask questions to express your opinion. So it aims at being informal conversation. With that said, I'd like to introduce again Alvaro Sanchez, who is giving the second of three lectures on the assembly and the evolution of microbial community. So thank you, Alvaro, for being with us. And when you're ready, you can share the screen and start the presentation. I think you're muted. Can you hear me okay now? Yes, perfect. Perfect. Okay, so let me see if I can move this here. Okay, so I'm going to continue what I started yesterday and tell you about this work we're doing in our lab to try to understand the rules that govern the assembly of complex microbial communities using enrichment cultures. And I just wanted to, before I get into today's material, I wanted to just give you a brief summary of yesterday's most setting points, just to emphasize what the basic results are and what it is that we're trying to explain. So a big question that I'm very, very fascinated with is this idea of how reproducible microbial community assembly is. And this is a question that can be explored in natural systems. And in fact, it has been explored in natural systems. I gave you an example of this one among many, but this one is particularly interesting, I believe. It's a work by Stigano's Loka and Michael Dobley and other collaborators where they were examining the assembly of microbial communities in these water tanks that form within the base of of the foliage of bromelia plants. And again, these are tropical plants. I think this particular study was done in Brazil, looking at water tanks in plants that are in close proximity to one another so that many of the physical components of the environment are shared among those habitats, temperature, humidity, et cetera, and also the same regional polar species. So when these folks looked at the microbiome of these different plants, they found that they did not contain, that they were very variable from plant to plant and most of the plants, most of the OTUs were absent from each other and only about one percent or less of all the OTUs were shared among all plants. So there was a lot of variation within at the species level in these microbiomes. Yet when they looked at the metagenome and they examined the abundance of different genes involved in non-metabolic pathways, they found that the fraction of the metagenome devoted for instance to fermentation, to respiration, to carbon fixation, natural respiration and so on and so forth, those were very, very consistent from plant to plant. They found very similar quantitative ratios of these metabolic functions in all these habitats despite the fact that they find substantial taxonomic variation across them too. And this, I also mentioned that this same finding has been made in a wide range of other habitats. It's been made in marine environments in the human microbiome, in algal communities and the list is long. However, it is difficult in natural habitats to disentangle what are the mechanisms that are underlying this phenomenon. There's many ecological forces that shape the assembly of micro communities. Some of them are governed by tans such as mutations, the arrival of species into a habitat or dispersal. There's other ecological processes that are more deterministic such as selection, which you would expect to be a force that will generate more homogeneity in community compositional cost habitats that are at least those that are very similar. And finally, you can also have the confluence of the two which we can call historical contingency. There's many different mechanisms that can lead to historical contingency. One of them is environmental modification, which is that when you have habitats that are very similar to one another, once they get colonized, the bacteria and metabolic activity of those bacteria will change the habitats in subtly different ways. And that will cause an inevitable level of historical contingency because when you have different habitats getting colonized by different bacteria, by random dispersal, those habitats that were originally very similar will become less and less similar as a function of time. So, what we have next is that the problem to understand this question of reproducibility is that in addition to many different ecological forces that shape the assembly of micro communities, we also have that the selective pressures that are present in most natural habitats are very difficult to know. We may infer them or we might try to guess what the selective pressure might be through data or through just knowledge of the environment, but there are many different if you think about it, we really don't know all of the physical and chemical and nutritional niches that might be occurring in a particular because they are so small. Many of these are molecular and really understanding in detail what are the forces that shape selection in different habitats is something that is very, very difficult to do in nature. So, the approach I'm following in my lab is we're trying to ask if it is possible to study the process of micro community assembly in a synthetic habitats where we can know the selective pressures, we can know the chemical composition and the nutrient composition of these habitats, we know exactly what niches are we supplying, and we can also know for a fact what is all of the spatial determinants of micro community assembly, we can fix them, we can know the temperature, the pH, we can control all of these factors, and we can also control ecological factors and ecological processes that continue to come across the assembly, we can control the rate of migration from the regional pool and control what is the composition of the regional pool, we can control to some extent the population size, the collectivity between habitats, and so on and so forth. So, the question we're asking is if we know all of the things that we do not know or are very difficult to know in natural habitats, can we then understand the more mechanistically the origins for these patterns of convergence at the functional level, but divergent taxonomic level that are found across a large number of natural habitats, so that's what my lab is trying to do, and in other words we're trying to more mechanistically understand the reproducibility of micro community assembly. I gave you also an idea of what are the experiments and the experimental pipeline we're following in my lab, we're using high throughput in between communities, we take for the purpose samples from the environment for example the soil samples, we stick that in a bottle with a water saline solution, we filter this to eliminate all the larger particles that were left only with the bacteria, and then we sample from that large bottle of bacteria into a small miniature test tube, and we find synthetic medium, and here we are supplying the nutrients to the bacteria that we have a lot of control over in today's talk, those nutrients and the first part is going to be glucose, later on we're going to tell you what the results we get when we use other resources as well. And what we do is that after we inoculate the random sampling from the regional pool, we let the bacteria grow for a period of typically 48 hours and after that period of growth we apply a bottleneck, we take a small sample from here and add it to a new little test tube, where we replenish the nutrients, we let that grow again, and we keep iterating this process, and I showed you, well at the end of every 48-hour period we are doing 16-h sequencing to quantify the composition of different species in our communities. And I showed you also the results of a typical experiment. This is the relative abundance of different genera in one of these enrichment communities as a function of time, as a function of the transfer that we're looking into. This is with relatively shallow sampling, where if you think about it we're just kind of sampling 10,000 random individuals from its community and identifying them, that's essentially what we're doing. And the different colors here, its color represents a different genus and the width of this color represents the relative abundance of that genus in the community. As you can see in this plot, after about maybe eight to nine transfers, community composition stabilizes and becomes quite constant through time. So what we are asking here is how reproducible community assembly is and then the main question is, if we do the same experiment multiple times, do we find identical outcomes? That is the ultimate question we're asking. So to answer it, what we have done is that we have inoculated multiple replicate communities from the same regional species pool and we can take, say, eight different test tubes, we fill them all with the same medium, put them in the same incubator, and we inoculate them from the same species pool. And what we find is that when after we propagate those eight communities in identical environments for about 80 generations or so, 12 transfers, and we examine the composition of these communities, we have found two things. One is that we see very strong convergence at the family level. All of these wells contain essentially very similar ratios of two main dominant families, but very much more variable community assembly when you look at it at taxonomic level of genus or lower. So this is reminiscent to what we have observed before in the studies that was mentioned before. There's a lot of variation at the species level, but a lot less variation and much more convergence at the level of family. Well, what they were saying actually is that families is function, right? So our idea is that perhaps the two are connected, right? That this family level convergence that we're observing is reflecting a convergence at the functional level too. And just to give you an idea of what this looks like when we repeated our experiment with 12 different regional pool species, what we find is that this is across 12 different inocula, eight replicates for each, and I'm plotting the family level composition of the communities for all of those experiments. Now, you can find is that there's a very strong reproducibility, most of them have dominated by the same two dominant families. In blue it's in terabacteria, in red it's in monadacea, you have all their more rare families that appear in some of the communities. And even the quantitative ratios of these two are quite similar. I just wanted to give you another example of this kind of phenomenon of family level convergence, and this is work by my colleagues at the Connecticut Agricultural Station, Tim Blair, and Trang Zeng. And when you find this in the study, what they did is they looked at community assembly in the stigma of the flowers of the apple tree, and they looked at the communities that assembled on about a hundred different flowers. And one of the things they found is that, again, they find fairly consistent community assembly in these habitats at the family level of taxonomy with intervectories, again in blue and in monadacea in red, which are found across all of these flower communities, yet they find a lot of variation at this species level. If you look at the different OTUs with the submonadacea and the OTUs with the intervectories, you find that even though at the family level these communities are very similar from one another, they contain different specific members of its family. So this result, again, is consistent with this pattern, but in this case, again, they're finding this pattern not at the level of function, but at the level of family, which is what we did. And I'm just uploading these two things side by side so you can get an idea of the results. Of course, they're not identical, but these environments are very different. We're talking about a flower and a sugar-based synthetic medium. It's interesting because we think that the environment that these microbes are experiencing the flower is, at least the nutritional environment is not that different from what we find in our experiments. Anyway, well, this is always painting a picture that presents a number of questions. So the first one is, why do so many species coexist on a single limiting resource? And this was the subject of yesterday's lecture. Second is, what we need to understand is, why is community assembly so convergent at the family level? Again, in our experiments, family level convergence in others, they're from functional level convergence. So we need to try to understand that better mechanistically. And in tomorrow's lecture, I will be talking about why community assembly is so variable at the species or genus level. And again, this was yesterday's, and that's going to be today. So today's, what I wanted to go through is the work we've tried to do, I tried to understand why we're finding these results. Why do we see a community assembly so convergent at the family level? And matching this with the results that I've been hammering to you yesterday and today, our first guess is that this is actually reflecting some form of functional convergence. And to test that idea, what we did is very simple. We took 13 or 14 of this chemical number, the exact number of the communities that I had shown you before that we had assembled in glucose as the only carbon source. So we took those communities. And we did dilutions and we spread them over agarose petri dishes. And we spread them at very low densities of cells so that we could when cells would grow on these petri dishes, they would form little colonies and cells from different species form colonies that are different from one another. So we could take those colonies, then we sequenced their ribosomal DNA to understand who they were, what was their identity and compare those with the 16S ribosomal RNA sequence that we had previously obtained from community level 16 sequencing. And the two matched very nicely. So we were able to isolate a large number of the members of 13 different communities for a total of around 100 different pseudomonadnesia and intervectivitis strains. So we were able to take the members of those communities and separate them and grow them in isolation from the community where they were isolated. And what we did then is that the first thing we wanted to do is we wanted to ask whether the pseudomonadnesia and intervectivitis, which has these two families, would differ at the family level in the growth rate in glucose. I remind you that glucose is the only carbon source we're supplying. And that intervectivitis is about two to three times more abundant than pseudomonadnesia in our communities. So we wondered if that was because intervectivitis is actually better at growing in glucose than pseudomonadnesia is. And so what we did is that we took each one of those isolates and we grew them on media containing that is exactly the same medium where our community had been assembled. It is minimal media for those of you who know or are knowledgeable about this, this M9 medium with glucose as the only carbon source. And we determined the growth rate by just looking at the growth curve over a period of about 48 hours. We determined the maximum growth rate of the intervectivitis strains and the pseudomonadnesia strains individually and we're plotting them here. And in blue I'm showing the growth rate of the intervectivitis in purple I'm showing the growth rates of the pseudomonadnesia. And as you can see, the intervectivitis grows better and reaches higher growth rates than the pseudomonadnesia as a family. So what we find is that at the family level there's conservation in the growth rate of in the supply resource right which may explain why so intervectivitis is observed at higher abundance than pseudomonadnesia. The next thing we did though is I told you yesterday that an important component of coexistence in our communities is metabolic crossfeeding that the intervectivitis when they grow in glucose they are known to secrete various metabolic byproducts including acetate, succinate, lactate, as well as others. And these three are we use mass spectrometry to determine what are the most abundant byproducts and these three are the ones that came out as being the dominant ones. And one of the things that is interesting is that we find that the pseudomonadnesia here I'm showing is the amount of acetate produced over a period of 48 hours as a function of time for our collection of isolates and in blue I'm plotting those results for the intervectivitis and in purple for the pseudomonadnesia. And you can see that as the intervectivitis grows on glucose the amount of acetate they produce particularly after 16 hours and this is the relevant time scale and I'll tell you why in a minute is very conserved right all of this bacteria produce very similar amounts of acetate in our in these habits. Now the reason why 16 hours is the most important time scale is because this is the time that it takes for glucose to be exhausted and so what happens between this and that is that the single strains that are growing in isolation ended up then metabolizing some of their secretions and in many cases we find for instance for citrobacter which is the these guys that you see over here that acetate secretion continues for a little bit longer and that's probably a byproduct of organic acetate metabolism because the glucose has been exhausted by that time. But so the relevant time scale which is what happens with the glucose when they consume it is that all of these all of these intervectivitis produce very similar amounts of acetate which is the dominant metabolic byproduct. They also produce similar though the less so amounts of succinate and lactate and what you can see is that there's a conservation on of quantitative niche construction for all of these species of intervectivisia over with respect to my comparison with this one. And what's more is that we find that the when you when you it is when you plot the amount of acid that is being produced as a function of the maximum growth rate that these bacteria can can attain you find that there's a fairly strong correlation between the two and this is something that has been documented before for other intervectivisia such as E. coli and and salmonella which is but that the faster they grow the more acetate they release right and that is because more and more of their metabolism is shifted to fermentation rather than respiration even though it's really called overflow metabolism. But more of that of their metabolism kind of stops acetyl-CoA and then leads to pyrithermination and secretion of acetate and less and less of the of the glucose flow is directed to TCA cycle and to full respiration. So what that means is that the faster bacteria needs to grow the more overflow will have to to do and that leads to a strengthening secretion of acetate and other organic acids the faster these bacteria grow and that is also observed this is this its point represents a different strain these are for many different genera of intervectivisia including brautella, citrobacter, interbacter, pylpsiola, seracea and others and and you can see that this this kind of trade-off between yield and growth rate is applicable to broadly to all of these strains of intervectivisia regardless of of of the specific species or genus they are. By contrast, pseudomonas doesn't engage with that as is known way that overflow acetate production where flow metabolism is not documented to have to occur in pseudomonas which is primarily a respiratory bacteria. Okay so it is believed that this this trade-off emerges from physiological constraints in plot and malocation but that's a subject that is beyond the scope of this talk. But the point I wanted to make with this slide is to illustrate that this this amazing picture from the two slides I've shown you before. First is that the glucose is selecting for fast growers and strong growers and glucose and the faster and we find that intervectivisia grow faster than pseudomonas and we find that the faster the cells grow the more acetate they produce. So strong selection for fast glucose growers leads to to bacterial secreted organic acids and which do so that the amount of secretion are relatively similar. The variation you see here in the way access is not that high but it's around 10 plus minus five and but also we find that that leads to the secretion of organic acids in a manner that is correlated with the amount of growth you have. And the next thing we did is we repeated those first measurements of growth rate for all the other dominant fermentation by products that are released by the by the intervectivisia acetate succinate and lactate. And what we find is that in this case the intervectivisia grows on average less well on those byproducts than the pseudomonas does. And so we find that both for acetate succinate and lactate the pseudomonas grows faster on average than the intervectivisia. So we also find that in addition to there being a phylogenetically conserved growth of the bacteria in the supplied resource where intervectivisia grows better than the pseudomonadisia in glucose there's a convergence in each construction and there's also a convergence at the level of growth in the byproducts of glucose metabolism where in this case the pseudomonadisia grows better than intervectivisia. And I just wanted to show you this this is for the evidence for this thing I'm trying to tell you let me see if I can move this here. What we find here is I'm showing for a specific community the concentration of glucose as a function of time and the ratio between pseudomonas and intervectoria and this r and f ratio will I will explain a minute but this is the ratio of pseudomonas to intervectoria right. So you find we see that glucose is depleted and after 21 hours there's none actually it's a little bit earlier than that but you know in this plot there's what we quantify. And acetate goes up as glucose is being depleted peaks that around 21 hours and then drops to zero after 48 hours for this one community. And at the same time we find that the ratio between pseudomonas and intervectoria declines in this first phase when glucose is being depleted and this is consistent with the idea that the intervectories are consuming the glucose right. And after the in the last 20 you know 23 hours or so I mean 27 hours or so you find that as the acetate is being depleted the ratio of pseudomonas to intervectoria in this community goes up right. That is consistent again with the idea that the pseudomonas are eating this organic acids primarily. I mean again this doesn't mean that none of the glucose is being eaten by the pseudomonas or none of the organic acids are eaten by the intervectoria. We have every reason to believe that actually both of those things are happening but the primary consumers for the glucose is the intervectoria and the primary consumers for the organic acids are the pseudomonas. We've done other experiments that confirm this point. We have truncated the growth time at 24 hours and when you do that the pseudomonas goes away and the community becomes entirely dominated by the intervectorisia and with organic acids that accumulate and no one eats them. So you know we have substantial evidence that that's what's happening in our communities. Let me see if I can put this back in here. All right so let me give you a summary of what we think is happening in our at the functional level. We have these communities that assemble into very similar ratios of these two dominant families intervectoria in blue and pseudomonas in red and what's happening is that the intervectoria are being selected for by the glucose because they grow faster and as one thing we observe is that the faster they grow the more organic acids they produce. So as this bacteria and intervectoria are growing on the on the glucose they are releasing organic acids like acetate, succin and lactate and as they accumulate the environment in the second half of the incubation time of this 48 hour period the environment is no longer a group of environment. This is primarily an organic acid environment and in those environments the pseudomonadiesia has an advantage and that's what we're seeing it here. So the intervectoria are occupying a functional niche which is that of respiratory fermentative bacteria that specialize in the glucose whereas the pseudomonadiesia are occupying a functional niche which is that of respiratory bacteria that specialize in organic acids and we call this respiratory functional group R and and respiratory fermentative group F and the coexistence between these two groups is stabilized by a metabolic pulse feeling that primarily goes from one direction to the other although that's only the first order effect there's also and we have evidence for that too all other by products that have been released by both right so it's not that we're saying that the only thing that happens is that the glucose goes entirely to one and not the other we know that that is not true we're just describing a first order effect and and what is the primary consumer of each of the two niches. All right so all of this what shows to you is that this family level conversion will be observed and does represent functional convergence right and and it is so through the evolutionary conservation of the relevant functions for growth and fitness in our environments but now the next question we wanted to ask is whether it is possible to take this ratio between R respirators and F fermenters that we're seeing here and explain that quantitatively from the known physiological and biochemical processes that are occurring at the cellular level. So again we we get a ratio between pseudomonas and interactoria there is around 0.27 and that is the ratio between respirers to fermenters in our ecosystems and to see if it's possible to recapitulate that finding what we have been doing is genome scale metabolic models that are based on flux balance analysis and I'm not going to go into the details of how fba works but suffice it to say this is a genome scale metabolic model where you could take a metabolic network as you can take for instance a metabolic network of bacterium like E. coli or you could make as we did for this particular project we built a super metabolic network that contains all of the known metabolic reactions in prokaryotes and put them together into a big matrix and what you do then is we you give that network an input which is a set of nutrients and with flux balance analysis what you do is you calculate the vector of metabolic fluxes that would optimize growth this is optimized a a given biomass function that you give the model in that environment that you're supplying and what fba will do is we'll find what is the the vector fluxes that will maximize growth and and that vector fluxes will give you an output which is the amount of biomass produced per per unit molecule consumed you you could put it away and also an output which is the byproducts that are released in the process of growing optimally on that substrate so what we did then is we we looked at a we took two models one of an enterobacteria and E. coli and another one of a I think this is wrong this is actually P. butyta it's a another of of a sodium monaceous in this case P. butyta and what we did is is very simple we took and calculated what it would be per group of molecules well how much biomass of E. coli would be produced and how much acid it would be secreted and now we took that the acid that had been secreted and fed it to this model of P. butyta and calculated how much biomass would P. butyta produce and this was by taking basically this off-the-shelf models and and evaluating their their growth and what we find with E. coli and P. butyta is that the predicted ratio of of P. butyta to E. coli biomass per glucose molecule that enters this this this trophic chain that we created was actually around 0.3 again this is only true if all of the glucose goes to to E. coli and and not and all of the acid acid it goes to P. butyta right but even with these very simple assumptions we we get a ratio between P. butyta and E. coli that is very similar to what we found before which is around as being the the average ratio of respite to ferment which is 0.27 and we repeat the same exercise for a large number of previously well-created models metabolic models for both interbacteria and pseudomonadasia and for for each of those models we calculated the did exactly the same exercise that I showed you before and we calculated the ratio of biomass of pseudomonas biomass to to to interbacteria biomass and the the here we're plotting every possible pair of those 100 models and you find that actually that value of 0.3 that we just found before is not an outlier it sits very very close to the average ratio that we find between pseudomonas and interbacteria biomass and by comparison we show you here the ratio pseudomonas to interbacteria in all of our experiments and the two are fairly close right this is really not a prediction per se what we're trying to argue here is that one can explain these ratios from very simple arguments and assuming that you're making the the simplifying assumption that all of the glucose goes to the interbacteria and and all of the by-products go to the pseudomonadasia and when you do that as that simple exercise what you get is something that seems very similar to what we find in our experiments right okay so now the the last thing I wanted to show you is results that we've collected a while ago and and it's the this paper is not being written at the moment and what we did in the same experiments but an large collection of other sugars and here the question was okay we found that this ratio of around 0.3 of pseudomonas to interbacteria or respires to fermenters and we found it for glucose right but how different would it be if we had done used other sugars what if we had used I don't know galactose which is another hexose or ribose which is another sugar in this case apentose or or any other sugar alcohols like like inositol, manitol and blissful right so we did that experiment we repeated this this enrichment experiment that I've been discussing before using two different inocula these were two different potted plants in in in Josh's house and from that from that soil what we did is we established communities on environments that contain either one of these sugars in isolations again not all of this mixed but one at a time right and here on the on the on the x-axis I'm plotting the identity of the of the sugar we're adding in on the y-axis I'm going to plot the ratio between respires and fermentative bacteria this dashed line marks the average of the glucose communities that we have seen in the and you have been showing you before and this this gray zone here is 95 percent dispersal around that mean for the data right so when we we plot this data on this plot what you find is that for all the sugars the we find a very similar metabolic structure right that the ratio of respires to fermenters are extremely close to the value that we found for glucose well there are some outliers but by and large the results are very consistent and just as a control we wanted to see if okay what if we don't use a sugar right what if we use a a metabolite the nutrient that cannot be easily fermented and would be more likely to be respired and to that end we used a collection of different organic acids many of fermentation by products but others are just you know components of a tca cycle we also used some organic alcohols and a bunch of other other nutrients and and repeat the same experiment from the same to inocular but now we assemble them on each one of this collection of of nutrients and we find is that the ratio of respires to fermenters when you do not use sugars is very different from what you get when you do use sugars and this experiment is quite interesting for instance I think I particularly like this data like this here is pyrovit which is an organic acid that sits in between glycolysis and the tca cycle right and it's kind of intriguing that that you get something that is kind of a transition in between the the kind of ratio between respires and fermenters that you see in the sugars and this cloud that you see here when you use organic acids okay so I guess this plot would make the case that when you have similar nutrients you are expecting to see similar similar community compositions but can we more quantitatively define what nutrient similarity is I mean we're saying the sugars are similar and organic acids are similar to one another but I'm basically weighing my hands so far right can can we make a more precise definition of how similar to two different nutrients are so we again resorted to flux balance analysis and what we're doing here is very straightforward we're taking a again our metabolic model and we're feeding it different nutrients right so for instance we're feeding one nutrient and we're calculating the vector of metabolic fluxes and we can implode this vector in that space of metabolic fluxes you know we could take and through the same metabolic network I mean we can in this case what we're doing is we're constructing a universal metabolic network on things all of our chemical reactions that are metabolic reactions that are known we're asking what would be the optimal way to metabolize its nutrient right so this is the vector of metabolic fluxes for nutrient A this is a vector of metabolic fluxes that would be optimal for another nutrient B and the distance between the two can quantify how different those two are right so if two nutrients are very similar then they're going to be metabolized optimally in very similar manners right and if they're very different they're going to metabolize in very different manners right for instance glucose and galactose are metabolized very similarly and they're going to give you a very small distance between the two whereas glucose and I don't know losing are going to be metabolized more differently and they're going to give you a larger vector here a vector with a larger distance right so the next thing we did is we took this library of carbon sources that we had that we had studied experimentally and then we calculated the metabolic distance between all of them and the first thing that and then we did the simple hierarchical clustering and one of the things that was very reassuring is that the the results we got from this exercise made a sense we find in this dendrogram that all the sugars are plastered together all the carboxylic acids and organic alcohols are also plastered together we also find that within the these these two groups their structure here you find in this neighborhood around here most of the hexoses and all this glucose containing the saccharides and here you find the most of the sugar alcohols and the pentoses and here's the same thing right in in this cyan group over here you find all the tc cycle intermediates these are organic alcohols and so on right so there even there is within this the structure that makes sense so that that one would expect perhaps that those nutrients would be more similar to one another or less right so so then what we asked is to what extent this similarity between carbon sources can predict quantitatively similarity in community assembly in those nutrients and we find is that that it does actually do a very good job so here i'm showing you the composition of at the family level for all the sugar and sugar alcohols here now in blue you find in interactive isia and in green the sulmona isia this orange guy here is alkyligenesia and when you compare that with organic acids and the alcohols you find that it's it's quite different in most cases interactivity is gone and this is dominated by risk-related bacteria like sulmona isia alkyligenesia and others but even within the sugar structure in this first group that are made by glucose like sugars we find very only very rarely that you find alkyligenesia whereas in in this other group of pentoses and sugar alcohols you find that alkyligenesia is much more common and in fact it's interesting that here in galactose when it isn't actually this this is probably just a misclassification because of the the nature of the hierarchical plastic algorithm because the galactose is the hexose the same is true for the organic acids and the alcohols if you look at the the tca cycle intermediates you find that all of them contain interactive isia here in blue and even within those there's even structure so this group here is formed by fumarate, malate and succinate that they enter side by side in tca cycle and all these three carbon sources recruit rhizobiasia and they are the only ones that do right it's an endemic species for this group of carbon sources um likewise there's endemic species in this group here uh sphingomeral asia is not found anywhere else and also this uh convergent community composition uh within uh this other group as well so another question is whether the distance between nutrients can explain distance between composition of the family level and what we decided to do is just plot once once against the other right we can at the family level you can also have the communities assembled in nutrient A and the communities assembled in nutrient B and you can calculate the the family level composition for both and once you have both you can calculate the distance between them right and when we did that we were plotting here the Euclidean distance in metabolic fluxes against the Euclidean distance in community composition and uh what we find is that uh there is a fairly decent correlation between the two and this is just a very crude measurement I mean we're trying now trying to extract uh do smarter ways to extract information that's simply plotting the entire distance uh of the entire metabolic space maybe there are some components that are more telling of how different uh two two nutrients are that's simply the entire distance of metabolic fluxes and to see if if there's more signal that can be extracted this way but this is where we are at the moment we've been also using machine learning algorithms to to see if it is possible to predict what's going to be the communities assembled in a new carbon source from a new um uh from a new Euclidium so just very basic doing cross-validation at this moment uh and what we find is that um the the the the for the families that are most represented like Enterobacteria and Pseumonia there's a very decent um the very simple machine learning model is capable of um of uh of predicting the um family level composition and the same is true for uh for function which is even better right so if you now group the the taxonomic uh composition by whether they are fermentative or or respected bacteria and and again you train a model with one inoculum and uh with a set of carbon sources and then you investigate what would be the the expected um the expected community composition from another inoculum in uh in in one of the carbon sources that you left out of the training set what we find is that it is possible to measure fermenter to we get results that are make make sense right and and and that the model is predicted to some degree um and I mean this is all very plainly work but I just wanted to give you a sense of where we're going with all of this all right so what I wanted to tell you today is what we think are the reasons behind um the fact that community assembly is so complacent family level and um what we have guessed that this could reflect a functional convergence because people have seen um metagenomic convergence uh when being by metabolic function right so we had our original guess was that family level was uh representing uh the evolutionary conservation of metabolic traits uh that are functionally important in our in our ecosystems and that's why we're seeing the signal at the family level but um because our environments are so simple one is capable of resolving these questions mechanistically and that's what we've been trying to do and we are finding that uh when you have sugars and not only glucose but any other sugar you find that there's a very predictable ratio of bacteria that are respiratory fermentative that are um that are found and especially in the sugars and there's another group that are respiratory that specialize in in consuming the by products released by the former so um one of the things that that is interesting about this result is that when we tend to think of metabolic traits uh in particular the consumption of of of carbon source um of of of of of nutrients that are based on carbon the previous work has found right that this is um a highly variable trait this it's a tree that is not supposed to be conserved at the family level right so if if you look at um uh for instance uh by contrast there's other metabolic traits like the usage of specific electron acceptors that are much more deeply conserved um evolutionarily and uh I just wanted to give you one example right this is this is um an experiment that was done with the bacterium E. coli that um was grown in um I'm sorry I'm missing the reference here for some reason um that it was grown in um in a collection of different different nutrients and it was assessed whether E. coli could grow or not right and this this authors took a I think it was 150 different strains of E. coli and close to 100 different nutrients and they're just measuring whether growth or not growth in each one of those I'm just zooming in because this this plot is it's a bit of a mess but here you have for instance a subset of these of these strains and you have serine raffinose and sucrose which are three different uh nutrients and as you can see some of those strains can grow uh on serine but others cannot and these can the others cannot right the same thing is true for raffinose sucrose and and most of these other carbon sources on this group here only seven of the carbon sources tested uh were able to be used by all of the E. coli okay so what this suggests is that metabolic traits are typically thought of as being uh shallow right and and that it's easy to for for bacteria to gain or lose the ability to metabolize a specific substrate and so that that's kind of seems to be contradicting what we found right there's family level consideration of all these all these metabolic traits but I just wanted to to bring up again that the what we've been studying is not the the ability of a microbe to use a substrate or not to use it but rather how good that microbe is at using it right we're measuring quantitatively how much uh a bacterium how well a bacterium can grow in a given substrate and what byproducts are being released and how well those other bacteria can grow on those byproducts it's not just that you can use glucose in fact we find that uh glucose can be used by both therobacteria and submonadiesia it is how well you can grow on those that determine whether you can only found in that environment or not because again um as you may all so very intuitively think that's because a species exhibits a trait um doesn't necessarily mean that that trait is going to be relevant for the ecological role that species plays in nature right and and that is true for bacteria as well and I think this is making a case for us measuring quantitatively um the not just the the the basically to to measure the realized niche right and to quantify um how competitive microbes are on on different carbon sources if we want to really understand whether a microbe will be found or not in a given habit and that's it again this work was done by amazing people in the lab and I think we may still have time for some questions so um should great thanks a lot Alvaro uh so we have time for questions yes there is one from Silvia um yes hi I wanted to ask a very general question on the patterns that you showed us in the previous lecture and at the beginning the fact that the functional composition and the family composition are constant so I was wondering can we compare these patterns with a null model that would tell us that we would expect more variability in the absence of a mechanism that brings this constant constants right um right yeah the question is what would be the null model right I mean like um yeah I mean like you you may imagine multiple different null models for community assembly right you could have neutral models for committee assembly you could um you could assume that uh all nutrients that basically that all all of these species are equally good at eating all the nutrients that you that we're providing them um so I guess yes I mean it is completely possible to compare the expectation to um the two null models right um if you just sampled randomly the I guess the simplest one is that if you say that you sample randomly species from the original pool and and put them together right and in our um and the question you may ask is then do you see the patterns that we observe and the answer that is no you don't right like there is no uh family level conservation of any kind um and in fact depending on what nutrient you add you're going to find different um different species um on each right so that that really tells you that that there's a very strong selection by shaping the assembly of these communities um and that's if you compare these two very neutral models um and then of course if you if you're trying to compare these patterns to other null models I guess like always with null models right the null model will needs to reflect uh a null assumption or a null hypothesis right so um so you would need to define what that null hypothesis is and and then in absolutely you could you could create a null model that that predicts what that expectation would be and and and you could quantitatively compare findings with with that yeah or the patterns we observe with with that null model uh but for the one the very simple ones which you may imagine is just simple random uh randomly drawing ESB from the original pool um and asking whether the the same is true the the answer is it right uh we we have checked and that is for sure not the case but as for other null models again it would it would depend on what the the the null hypothesis that you're trying to to disprove is okay thank you great there is then a question from uh Kiseok uh hi thank you for the great talk and my question is when you're constructing the when you're doing the simulation with the fba model and the experiments with this metabolic model for like Sudomonas and Antrobatic Partisie do you use like 100 strains for each of these uh family or like how do you represent the family right so we we took just models that were well benchmarked that people had um they've done a lot of work with before and so I could I could send you the list of the models we used if you're curious um they some of them they're basically published models by other people that um and then we had to just adjust them a little bit to the specific environment that we had uh but this was not our models right we were taking models from from other groups and there were not a hundred I think that I can't really remember the actual number for each of the two um uh there I think the the trial it was around 70 something models I believe um but they weren't uh equally represented so I think there were more interactivity on Sudomonas in fact um and the Sudomonas were not sampling the entire phylogeny of the Sudomonas Asia uh so the there's some degree of um of you know of not homogenous sampling of the of the two families in terms of the models right we we focused on on those metabolic models that they were well benchmarked experimentally before right and if you want the the list I can I'm happy to to send it over if you're interested I think so for the experiments you did you did use your um like different kinds of strains for each family right right and and also they they're not again we were not trying to sample the entire um you know phylogeny of the Sudomonas Interactive Asia um we were already biased by those bacteria that came up in our in our um in our communities right so we took bacteria that from communities that had assembled in glucose and both Sudomonas Interactive Asia um and uh we've also we also did similar experiments with random soil isolates um that were not in our communities and we included them into the into the set the and we don't I'm sorry we don't another set of experiments um the the results are not that different right so it doesn't seem that I mean there's some there's some patterns but but it's not very obvious that the randomly selected bacteria from soil um are very different in their patterns of secretions or even maybe have a slightly lower growth rate um than than the ones that in our that were having selected on average but but the patterns of secretions were similar and we didn't really appreciate any in the significant difference but it's not it's we have not really tried to do a very exhaustive search for Interactive Asia to see how conserved they are throughout the entire the entire taxonomy group okay thank you very much great there is a question from Martina hi thank you this was all very interesting and I have actually two questions if I can one is uh how do you I was looking at your plots before and how do you do you justify the fact that pseudomonas don't really have different growth rates in acetate um when you show the different plots let me see if I can get your question right uh uh yeah sorry yeah yeah for here it seems that you have definitely two strains that grow much better but they're not really different from one another or am I getting it wrong it's a different strain right so each of these are different uh the strains have different 16 s right so uh we we're we're not even um every single one of these has a different every 16 a sequence right and we did stronger sequences for for the entire region so it's a high quality sequence so they are they are different all of these strains yes no no but my question is uh it's not the big difference between entero bacteria and pseudomonas and that's why I was wondering uh how then you justify these changes in acetate even though the growth rate doesn't appear to be completely different and while no it is no it is no but it's different right I mean I think even even if you remove those two strains the the um it's statistically significant right um and this is just the maximum growth rate we also find that if you look at the average growth rate which is not just the maximum you have but basically the counting the lag phase and uh and how long does it take for them to reach half of the of the maximum growth they have pseudomonas also grows better than than than uh the enteroactory asia um and the same the same thing is true for lactate I mean um even though we're focusing a lot of acetate the concentration of lactate actually is not that let me show you here um it's not that much lower right from what we see in acetate and and there's more carbon per so lactic is lactic is is more valuable than acetate metabolic right so uh we think it's actually um something you cannot neglect and we're not trying to understand exactly how it's not just the acid itself is a combination of acetate lactic and succinate and other organic acids that together recruit the pseudomonas so it's not just it's not just one and it also is not just the growth rate right it's the I mean the growth rate is defined I mean as you know the growth rate changes right over the entire growth period and you have on the one hand the maximum growth rate which is important uh but but of course that is only sustained for a brief period of time by the entire population right and the how rapidly you you get out of lag phase and and the average growth rate over that period is also an important parameter but you know just to clarify um that this this is a statistical significance is not just because of these two guys right it's uh it's it's the entire distribution um and this is only reflecting the maximum growth rate but the same patterns would be um seen if we have uh I was showing you the average growth rate over the entire um over the the first uh I think until we we chunk it until the the first this t one half right until it reaches half of the maximum od okay and if I can link these to another thing so I was wondering if these two strains that have higher maximum growth rate are then those that are more abundant in your experiments and related to this I was wondering if when you find these convergence whether it's driven by the most abundant strains or do you think that this has nothing to do with abundance no I mean like the because it's a good question so I really don't think we have correlated the growth rates and something that we we've been meaning to do for a while the the growth rates uh of this bacteria in isolation with their abundance in the at the committee level um this is an idea that we've been floating for a while but I haven't quite done it yet um although we have all the data it shouldn't be very difficult to do um the other thing that you brought up that I think is quite interesting is if you look at this data right and we see there's converges there's still a substantial variation right uh among the um communities right there's still um variation in the race between so we want to send into activity and I absolutely agree that oh and in fact we have some evidence that points to that right that which is the identity of the dominant bacterium um matter impacts the actual hour of race you see I'm going to show some data tomorrow that we'll submit that point that when we have alternative stable states from the same inoculum we have um we have looked at the specific um ratio of respite to fermenter on each one of the two and depending on on which is the identity of a respirator if it's an azulemora these are not calidemacia they don't quite reach the same abundance there's variation between the two and I think because these communities are very small right so we're still talking about you know five to 20 species but most of them are very rare so um there's still going to be variation on which is exactly the the solomonas they find on each community right um if these communities were larger I think all of these things would average out and you would probably have like more convergence that would be my guess but we don't know right um but because you only have three species right which happens which one happens to be the dominant member of its taxonomic group um of course you know adaptation to the specific dominant carbon source is not the only the only selective force we have right and and and any other differences as well as variations on adaptation to our carbon source that we we also find should matter for this area of ratio so that's what we're focusing on averages rather than than the fluctuations because this is an area we haven't yet explored but I think here's like a very fair point that but I think it's very likely that if you examine in more detail and try to understand the fluctuations around this this average value and and that that could be correlated with traits um all the specific tax that are found in those communities right and maybe there there are correlations between them we just haven't looked yet okay thank you very much great I don't see any other questions in the chat or in the um participants link list so if there are no other questions well thanks Alvaro again for the lecture of today just to remind that the next lecture by Alvaro is going to be in two days on Thursday um and so thanks again and now we are gonna split in the breakout rooms for 10 minutes and we're going to be back at 5 p.m uh it's time for the seminar by Alejandro Rodriguez so thank you very much to everyone welcome back to the main meeting room um so everyone should be back from the breakout rooms in a few seconds uh in the meanwhile if you are following from uh youtube I remind you that you can ask a question by posting them in the chat um while if you're following from zoom you already know that you can either post the question in the chat and I read it for you or use the raise and tool in uh zoom and if you just connected I remind you to check the program and that tomorrow at 4 p.m there will be a colloquium by net wing green and you need a separate link to connect with that but you'll find all the details and the registration link on the program of the school so with that it's my pleasure to introduce the next speaker Alejandra Rodriguez Verdugo Alejandra is a professor at the department of ecology and evolutionary biology at the university of California Y and she works at the at the interface between ecology and evolutionary dynamics doing experiment trying to combine the two and today is talking about the evolution of microbial interactions in fluctuating environments so thank you very much Alejandra for being with us and uh be free to share um yeah can you see my screen thumbs up excellent well excellent so thank you so much for the invitation I'm super excited to be here and to talk about my work that I started in a tth week when I was a postdoc um with Martin Ackerman and then I'm continuing this work right now in the department of ecology and evolutionary biology at UC Irvine in California in the US and today I would like to talk about evolution of microbial interaction in fluctuating environment but first why do we care about microbes so microbes are the oldest organisms on earth and they have been able to colonize any possible environment on the planet from the driest places such the Atacama desert in Chile to the icy lakes of Antarctica so microbes have been able to thrive and adapt to the harshest condition and not only they have amazing adaptability but we know they are very important for life on earth so many of these microbes underlay the biochemical cycling on elements on earth and then therefore essential for ecosystem functioning and we know that many of these functions are not performed by microbes in isolation but they are performed by many microbial species that mean uh is really microbial communities that underlay these functions and now we know also that these microbes are really relevant because for example they can influence climate change by mediating um the carbon atmosphere land exchange and therefore they can actually feed back into the climate so it's very important that we understand how these microbial communities respond to change also we know that these microbial communities live in close association with animals and plants and they find they find their well-being and keep us healthy but sometimes also uh cause disease and here in this image I'm showing a beautiful microbial community that lives in our gut in the human gut and this gut microbiota we know is very important for keeping us healthy and um there's recent studies that have shown that disrupting these communities with changes of diet or antibiotics can actually lead to chronic disease such as chronic disease or Alzheimer or anxiety and even more um recent studies can also show that they actually control cognition and behavior so it's very important and we understand then how disturbing these microbial communities can actually influence or help and then finally microbes can help us so they are used in industry and for example they are used for energy production and they are the next generation of biofuel which are clean and renewable and also now in industry they are engineering whole microbial communities for example to improve the health and the fitness of the host that carries them for example plants so given the importance for the environment for health and uh for industry more and more people are trying to understand how these microbial communities work and although these things are very simple question and very straightforward question we still don't have a good answer for this and the reason is because microbial communities as you already know are complex systems so if we look at it they are composed by populations of one single species which are interacting with population of a different species and then this interaction can actually lead to emergent properties that give certain functionality at the group level and finally we have to consider that many of these microbial communities live in structured environment and fluctuating environment so then the environment also is not static and changes so one way to approach then this complexity is what we can do is to just isolate some of these species and instead of dealing with the whole complexity of thousands of species from nature we can just assemble these few species in what we call synthetic communities and then we can bring them to the lab and study them in the lab so this is the approach that I'm following now in my research group and then in my research group at UCI we study two questions overall we are interested in understanding how do species interaction influence evolutionary dynamics and on the other hand we're interested in understanding how changes in individuals can influence evolutionary dynamics and in general we follow a bottom-up approach which probably Alvaro Sanchez talked a lot about this so basically we use these synthetic communities simplified system and what we do is we try to build quantitative prediction with mathematical modeling that we can then test with experiments and then these experiments can inform can feed back to inform or quantitative prediction and mathematical models and for today I would like to talk about one project we look at how the species interaction influence evolutionary dynamics and this is in the context of the ecology and evolution of per wise positive per wise interaction so this work again was done at ETH Zurich in collaboration with Martin Ackerman so what are positive per wise interaction so positive per wise interaction are any interaction between two species where either one of the species get a benefit from the interaction or both of the species get a benefit from the interaction and we know that these ones are very important for ecosystem functioning so for example we know this kind of association occurring in nature and for example we can think about these neutralistic association between methane oxidizing archaea and sulphide producing bacteria and these ones are very important for deep subsurface ecology and they are really the base of these ecosystems but for example a more familiar example you might be more familiar so coral reefs for example is this association between an animal and an algae and we know that this actually positive neutralistic association is really the base for these shallow marine ecosystems so therefore given they're important for the environment more and people are trying to understand how stable are these positive interaction but then one thing one has to consider is that they actually the environment is not static and for example we can have that there's changes in resources and these changes in resources in the environment can alter species interaction so very simplistic what can imagine the interaction between two species a squirrel and a bird that live in an environment with a lot of resources and different kind of resources so we have that they have a neutral interaction but then if the condition changes and now we have that actually they are in an environment with limited resources now we have that this positive these neutral interaction change to a negative interaction and now they are in competition so then we should try to address this question of how stable are positive furwise interaction considering that the environment also varies so to address this question I use the synthetic community composed by these two bacterial species which is acenotobacter and pseudomonas and these two bacteria are very interesting because they have amazing metabolic capabilities also they were isolated from nature from a polluted aquifer in Denmark so they coexist in nature and what we did was to just isolate them and bring them to the lab and then the metabolic capabilities that they have is that they can degrade aromatic compounds which are very hard to degrade by many other microbial species or any other species so they definitely are of interest for bioremediation and we have that for example we can tune the interaction depending on the resources so for example if we grow these two bacteria in an environment where we supply them with pencil alcohol as a carbon source and carbon of energy source we have that only these bacteria acenotobacter can use these benzyl alcohol but then if we grow them in the present of these other bacteria what happens is that acenotobacter can actually oxidize this benzyl alcohol and then it accumulates an intermediate product which is benzoate which passively leaks out in the external environment and then in the external environment pseudomonas can utilize this benzoate so we have in ecological terms a conventional interaction where pseudomonas get benefited by the presence of acenotobacter and acenotobacter is neutral to the presence of pseudomonas so we have this cross feeding interaction but then now if we change them in a minimal media where we grow them with citrate as the limiting nutrients we have that these two species compete for this citrate so now we have a negative interaction so as you can see it's very nice model system because we can then tune interaction depending just on the carbon source so with this model yeah so first how do we measure interactions in the lab so the way we do it is we use a batch culture system so that means we just grow these bacteria enough in a shaking cube with these nutrients and then we wait until they grow 24 hours so at the beginning they have a lag phase then they have exponential faith and then they saturate the nutrients in the media and then after this whole cycle after 24 hours we transfer one percent of the population into a fresh medium and we continue these cycles for many days so at the end the kind of results I'm going to be showing is this kind of graph where in the x-axis I have the time in days and in the y-axis I have the cell density which we estimate as colony forming units in agar plates and then in this particular example for example you can see that the blue type is able to sustain this serial dilution regime so we say that it has a stable population over time well for example in this particular case the red type even though it's able to grow it's not able to sustain this serial dilution regime and it gets extinct after four days so the first thing we wanted to see is to do these experiments first in what we do is monoculture so that means we grow them in isolation to see how these bacteria behave and we can see that as an active bacteria is very good at using this benzyl alcohol it achieves high cell densities while silver monas is not very good at utilizing this benzyl alcohol but then when we do these experiments in co-culture so now growing them together we have now a different situation where we have that to the monas achieve two orders of magnitude higher cell densities in the presence of asynetobacter than just alone and then what happened in oh yeah so also we can visualize actually this kind of interactions using microfluidics and coupling with a microscope so what I'm going to play now just to visualize this direct cross feeding interaction is I'm representing asynetobacter as this round cells and then see the monas is in green like a road shape so you can see that actually we play this time last movie we have first the grow of asynetobacter and this growth is followed by this kind of green green fluorescence and that's the grow of pseudomonas so we really see these sequential growth where we visualize this cross feeding interaction so now what in the other condition so in the condition of citrate when we do our experiments in monocultures growing them in isolation we have that both species can grow well in monoculture and achieve high densities but now when we put them in co-cultures we do see that actually pseudomonas is a very good competitor and is such good competitor and it utilizes this citrate so well that it actually outcompete asynetobacter only after five days of growing them together so we can see this very asymmetric competition situation so what we wanted to test in this experiment is then how are these I mean can we predict this ecology and evolution of this pairwise interaction so what we did was to ask two questions so how stable are these positive pairwise interaction in block trading environment so not just keeping the environment constant and in particular we ask what happened if we interrupt this positive interaction with periods of competition or negative interaction and our second question we address is how stable are positive pairwise interaction over evolutionary time scales both in constant and in block trading environment so for our first question the first thing we did was to build a mathematical model and this was done in collaboration with Clemore-Villain which is right now at the University of Zurich and what we did was to build this mathematical model that we parameterized with single species growth measurement so for this part what we did was to just do grow curves assay of these monocultures and then from there we also estimated for example the excretion rate of these benzoids by HPLC and at the end we end up defining the parameters that are important for model which are the maximum growth rate in exponential phase the maximum optic rate which is just the rate of us how they saturate the optic rate for high resource concentration then we have that another parameter that was very important for model was the health saturation constant which is the resource concentration supporting health maximum optic rate then the duration of the lag phase which is how long the bacteria remain in this non-growing state and finally the excretion conversion rate which is a proxy of how much benzoid is treated in the environment and then what we did was to just use a set of differential equation in which we model the resources explicitly and then in here I'm showing those equations so basically we just modeled the bacterial growth which is dependent on how much of the resources they are using and then in the second set of differential equation we have the changes in resources over time which is related to the growth of the bacteria and then with this model well I mean I can spend a little bit more time so basically as I mentioned before this basically these dynamics are really related to the maximum growth rate of the bacteria and also is related to the health saturation constant and also to how they are taking these resources over time and then finally to the excretion rate of the benzoids so the first thing we wanted to do with this model is to just validate the previous results that I show so basically when we actually use this model we do see that we can recapitulate the behaviors in monoculture in co-cultures in benzil alcohol and also in side trade which is the other competition so we do see that with this model we can recapitulate and capture these ecological dynamics quite well so now the question was what dynamics do we observe in fluctuating environment so for example in this case we define one day fluctuation environment means that one day we simulate that they grow in citrate and then we transfer them in benzil alcohol the next day and again to citrate and that's what we simulate our fluctuating environment so when we do this we do see that when we have it in one day fluctuation environment the two species can coexist over time and one species is more favor in one condition than the other but then when we for example start increasing the length that they stay in each of the carbon sources so for example two-day fluctuating environment means that today they spend in citrates and two days in benzil alcohol we do see that we still have species coexistence but hopefully you can start seeing that the more they stay in one condition the amplitude between the two species start getting larger and larger and then when we heat the four and five days fluctuating environment we do have that actually pseudomonas bring as in tobacco to extinction and this in the model also what we observe is that pseudomonas eventually also end up going to extinction and the reason is because it outcompeted the co-former that it needed to coexist in this environment so in these four and five days fluctuating environment we see a complete extinction of the community so now we wanted to actually see if we can see these results with experiments so what we did was to just grow the bacteria in co-culture starting with a ratio one to one and we did these in triplicate for six days and with experiments we actually see again these dynamics that we actually predicted with the mathematical model so we have that in one two and three three days fluctuating environment we have coexistence of these two species with the amplitude between the two getting larger and then for the four and five days fluctuation we have extinction of asthenetobacter so we do not see extinction of pseudomonas we just see that pseudomonas is actually to persist at very low densities when when we have them in benzyl alcohol and eventually with citrate they just recover so now that we defined this part so the conclusion is that past fluctuation maintains species coexistence but for example in an environment that fluctuates slowly what we can see is that we observe coexistence breakdown so all of these that I've been talking about are ecological dynamics so this is over six days which is around 70 generation for this bacteria so we assume that evolution is not playing a big role for these ecological dynamics so the next question we ask is what happened if we repeat this experiment but now in evolutionary time scales and then we were particularly interested about this condition of the cross feeding interaction so we wonder how stable is this cross feeding interaction if we do it over evolutionary time scales so for example 200 generations and the other condition we were very interested is the one-day fluctuating environment so in this condition we saw coexistence of these two species so we wonder if we can actually have coexistence over evolutionary time scales so in order to perform this we did a large-scale evolution experiment in these three conditions so keeping just benzyl alcohol as a sole carbon source just keeping citrates and then in our daily fluctuating environment and with these experiments in monocultures and also in co-cultures and then finally we did for each of the conditions four replicates and the whole experiment run for a month which is 200 generations so the first question so is cross feeding interaction stable over evolutionary time scales so here I'm plotting the result of just one of the replicates which is consortium number two so you can see that now in the in the x-axis I have the the time now over 30 days and in the y-axis I have again the cell density and then what you can see is that they are actually there's species coexistence over evolutionary time scales and then there's definitely some kind of fluctuations in the cell densities over time so it's not that constant but overall for the four replicate or four consortium we see species coexistence until the end of the experiment so we concluded that indeed these cross feeding is stable over evolutionary time scales but now if we actually look at the second condition which is the one day fluctuating conditions now we do see a different case so for example here again I'm plotting just the result of one of the consortium consortium number two and then here is very interesting because we see that at the beginning of the experiment the two species coexist and and maintain certain stable population dynamics but then around day 14 something happened to one of the species in this case to a synetobacter that they start decreasing in cell density until actually it gets extinct and even more interesting at least for an evolutionary biologist is that actually this outcome of extinction of one of the species was only one of two evolutionary outcomes so we do see that this extinction occurred in two of the replicates but in the other two replicates we do see coexistence of these two species until the end of the experiment so then this is very exciting because this is definitely a different evolutionary outcome so the the one thing we can do with evolution experiment which is very nice is that we can freeze these bacteria at different time points during the experiment and that's exactly what we did so we kept a frozen record of this populations at every seven days so every week we will freeze these whole tubes with the bacteria so what we can do then is to go back in the experiment let's say at day 14 before the extinction of one of the species and then revive this bacteria and see for example if we do a replay evolution experiment to see if we again see the extinction of a synetobacter or not and when we did these replay experiments this time we did it with higher replication so we repeat this experiment for each of the consortium we did six replicates so what we do see is that for the two cases where we previously observed extinction of a synetobacter we again observe extinction of these species when we replay the experiment and in the other two cases what we previously saw coexistence we again recapitulate this coexistence when we do this replay experiment so the conclusion is that extinction was a highly deterministic event so it's not random at all so we can definitely replay these dynamics so then the next thing we wanted to know is what is causing this extinction of one of the species and for answering this question what we did too was to isolate some single clones at different time points so at the end of the experiment at day 14 an ideal zero so which is the ancestor so we isolated one single clone for each of the replicates of the population and then we did grow curves experiments and also we sequenced the full genomes to try to see if there were any genetic changes that could explain these deterministic dynamics and first i'm going to show the results that we have when we actually do the full genome sequencing the end of the experiment so when we take this clone at the end of the experiment we did the grow curves so again we just estimated the maximum grow rate and the yield and when we do this experiment i mean here i'm just summarizing the results of all the experiments but hopefully you can see that there's a lot of green and the green indicate that there's actually a significant higher growth of the evolved types compared to under ancestral types and these indicate that actually over the course of the evolution experiments the evolved type are definitely growing better than the ancestors so this is already a sign that these strains actually have adapted to these conditions and then when we actually look at the genomes from this single clone so what we did was to sequence the genome of the evolved type and the sequence the genomes of the ancestral types and then we just compare the two genomes and then we call the noble mutations so anything that was not present in the ancestor and then that we observe in the evolved clones and overall we can say that we observe that there's we observe around one to two fixed mutations per clone and when we look at where are these mutations located in the genome we see that these actually mutations are not randomly distributed in the genome but tended to hit certain genes so for example in asynetobacter we observe 15 mutations in these or acetyltransferase gene and then for example in pseudomonas we do see that they accumulate mutation in these three genes which is a sensor protein a flagelar component and transcriptional cyclic DGMP so basically we do observe a high level of parallelism which already indicate that these mutations are most likely adaptive and then also when we look how they are distributed not necessarily in the genome but among conditions we do see that these ones tend to not be specific to one particular condition but they were observed in many of the conditions so for example in the case of asynetobacter we do see these mutations in the condition of the constants benzyl alcohol in monoculture and co-culture but also in the citrate and in the fluctuating environment and it's similar in the case of pseudomonas so overall the conclusion is that species show signs of adaptive evolution after a 200 generation but these changes are not specific so it seems to be general adaptation to the culture conditions so now we go back to now that we characterize these evolved types so then we go back to this idea of trying to see what happened at day 14 which is just before the extinction of one of the species and when we go back to that time and we do the full genome sequences i'm summarizing in this table what we observe so pseudomonas even after 92 generations of evolution already have two to one fixed mutation in the genome and again this kind of mutation we observe them in monoculture suggesting that general adaptation to the culture condition but i think what's really interesting is that in the case of asynetobacter we do see that in the two cases where it went extinct we do not see mutation at this time point of 92 generation where in this consortium number three and number four we do see that this asynetobacter has two or one mutation so our current hypothesis that we are trying to test is that mutations in asynetobacter rescued somehow from this extinction and in particular our hypothesis is the following so we think that pseudomonas accumulate mutations so it's rapidly evolved and these mutations actually confer higher growth to these pseudomonas and these exert an indirect effect on asynetobacter which either has to it goes extinct or it has to keep up with this higher growth of pseudomonas higher competition and then it can actually it has adaptive mutation then it can coexist with pseudomonas and this hypothesis is again sustained by this observation that pseudomonas actually has higher growth after 92 generation so we think it's really the mutation that is causing this higher growth and also the second line of evidence to support our hypothesis is that we went back to our mathematical model and what we did was to input these growth that we observe after this evolution and when we do input this growth into the model so for example in the case of the ancestor competing versus the evolved types of pseudomonas with this higher growth we do see that pseudomonas can actually but just growing better at compete asynetobacter only after 20 days but actually 20 days is quite different for 14 days so we believe that it's not only indirect effects but they might be actually direct competition they might be some antagonism or some yeah some kind of type six secretion system that pseudomonas might be antagonizing asynetobacter in addition to using more resources so to conclude this part we see that positive per wise interaction are stable in a constant environment that's the cross-feeding environment and we do see that there's two outcomes outcomes in a fluctuating environment so we either see coexistence or extinction of one of the species and I don't have to actually give this take-home message to this audience because you're very well aware of this but our conclusion is that the environmental context matters so it really matters who is your neighbor and who is evolving next to you in terms of species and then in that sense we should move forward into not only studying experimental evolution with single species but try to do these evolution experiments in a community context considering interaction with different species and this concludes my talk I left ample time for questions and I just want to thank the people involved in this project in Switzerland so my postdoc advisor Martin Ackerman, Clemence Villain and Jean Claude who helped so much with the sequence also the whole lab in Switzerland and the funding which mostly came from EMBO and from the adaptation to a changing environment from ETH Zurich and thank you very much for your attention. Thank you very much for the nice talk so we have time for questions so if you have any please use the raisin tool or type it in the chat and while we are waiting I can ask one question since we have a lot of time so have you tried to do a co-culture experiment where you put the pseudomonas evolved in or the acinetobacter evolved in co-culture that coexisted with the pseudomonas that actually outcompeted the acinetobacter so sort of two where probably technically it's difficult but to isolate the evolved strains in different experiments and pair them together across different experiments. Yeah no absolutely that's that great one so we did like a preliminary experiment with only one replicate and unfortunately then the pandemic hit and we couldn't continue this experiment because this is definitely the way we and we can test this hypothesis so evolving these clones so what I can say is from our preliminary experiments which I have here so this is evolving like competing these clones at generation 92 and actually from these pairwise competitions of the evolved clones we do not see this extinction of acinetobacter as you can see consortium one and two which is the one that acinetobacter is supposed to go extinct actually we do not see this but this was with one replicate and we definitely have to repeat these experiments and also the conditions were not fully optimized to replicate the conditions from the experiments but definitely we need to be trying to play with these evolved clones versus ancestors and these kind of replicate transplants kind of ideas to try to test this hypothesis so far it seems like it's really at the population level and not at the clone level that we do see these behaviors so we don't know exactly what's going on if we didn't isolate the proper clone or if it's something that is really characteristic to our whole population with whole like genetic diversity in some sense. There is one question from Flavia. Oh yes can you hear me? Oh yes. Okay cool very nice talk congratulations. I'm interested to understand if you can measure somehow if these bacterias that you work with if they differ somehow in their mutation rate or how they evolve. Yeah no that's a very great question so we definitely tested the mutation rate so they have very similar mutation rates these two species so we thought for some reason that pseudomonas may evolve faster because that's kind of a common belief in the literature but they are actually very similar in terms of mutation rate and in many other ways they tend to be similar species so they have the same substitution rate for example. Okay yeah I was curious because of that maybe I don't know if there is any other bacteria that you can select and make an experiment with these different rates of mutation or I don't know just yeah no that's that would be super exciting to start tuning like this mutation rate and to start seeing like how like by like yeah tuning the mutation rate in either like very fast evolving versus slow evolving like how in all dynamics and that's definitely possible and that's definitely something I would like to do in the future. Okay I'll look for it sounds good. Great we have time for more questions if any. Hi I have a question sorry I'm a video thank you very much for your very interesting talk I had one question I wanted to ask about the plot when you've done longer time like when you didn't look anymore like when you wanted to look at the evolution so you took longer time I think up to 28 days maybe I didn't get it from the talk like did you keep the subculturing time like every day or yes it was okay yes yes so we didn't adjust anything based on how they started evolving so we didn't adjust that so we just for now for simplicity we just kept that content to 24-hour cycles regardless of the if they are first evolving faster and like they are growing faster and saturating faster like we we ignore that part for simplicity for for now. Yeah and in the case like because at some point in this kind of experiment when you see the the the abundance decreasing of course because they are going towards extinction did you like is it possible to adjust the the amount that you subculture because of course if you subculture you're going to take a smaller amount of cells and that can kind of a bit bias like the the direction towards extinction yeah yeah actually that's a very interesting point because we we did the experiment starting a different ratio so starting either at very high density because we wanted to make sure it was not just the stochasticity in the terms of just ecological stochasticity so actually we repeated this experiment not in a ratio one to one but starting with a lot of acetobacter and even starting with a lot of acetobacter compared to pseudomonas we still see the same increase to extinction so it seems definitely not this this other kind of stochasticity. Perfect yeah and if I can ask like this is a further curiosity because I really enjoy this topic like are you thinking or is it interest at all like to test co-fluituations like more than one parameter fluctuating because in this case you apply fluctuation in the nutrient supply but like would it be of any interest to to model and then apply fluctuation let's say the temperature or another like increasingly idea to reagency of the environment? Oh absolutely so one of the experiments that yeah we're very excited is like to somehow try to add a biotic stress to this so for example yeah temperature is a great it's a great like kind of suggestion and something we thought about it and then try to tune a little bit more again what would happen if we favor more one than the other in this particular case for example what would happen if we favor the the one that is not doing so great like as an interactor so yeah definitely in a way I feel like this is just the start of setting up the system and playing with it and now is the fun part because we can actually start testing a lot of ecological and evolutionary theories and tuning stuff and actually this system is nice because we can definitely tune interaction evolutionary rates and many things we can also add more species if this yes yes thank you very much yeah thank you great there is another question from Aditya hello thank you for the talk so I was wondering so I guess you showed here that when you have evolution in the case of a externally imposed fluctuating environment it destabilizes the co-existent but so we saw some we saw some talks earlier having to do with bacterial phage interactions in this case the fluctuations are internally driven by the by the dynamics of the different strength and in that case I think we saw something like that evolution can change the dynamics qualitatively by by changing the direction of the of the cycles between bacteria and phage in in in phase space but I guess like I'm not sure if I have a specific question but I would just be interested in like whether you can comment on the difference between externally driven and internally driven fluctuations and whether these are having whether you think these might have qualitatively different effects on coexistence or not yeah no that that's a great great point so actually I mean reviewing literature I feel like this interesting fluctuating dynamics is mostly given by this interaction that either predation or or like you know like where you have like more like a plus minus interaction or you can have a plus plus interaction but in this particular case when you have just competition or commensalism it's kind of interesting not to observe these internal fluctuations it seemed like it's really like this is more it's more likely to happen with certain kind of interactions than with other kind of interactions so in this particular case um yeah we do not see anything of that sort yeah but do you think that so do you think that exogenous versus endogenous interactions or like would they qualitatively uh have different effects on on coexistence is I guess yeah I don't know like it's hard to I haven't think about it to be honest with you but I think that's a really great thing to think about it's definitely like it gives me like some something to think about I don't know how to enter but it's a great point it's really a great point thank you okay great uh if there is any more question please uh type it in the chat or raise I don't see anyone okay so thanks a lot and again for this very nice talk um thank you very much for answering all the questions and now we are going to be split again in the breakout rooms and we are starting in about half an hour with the second lecture by Justin Ike so thanks Alejandra again and thanks everyone for staying with us well thank you so much for the invitation thank you okay welcome back everyone to this last session of today we have now the second lecture by Justin Ike so please Justin you can share your screen and and start when you're ready great thank you let me okay uh so I'll assume that you can see my screen um thank you uh it's it's a pleasure to be to be back um today I would like to focus on uh the role of humans and ecosystems and how we can understand that from from reconstructing past systems um and so I'm going to spend part of the talk today focusing in general um really well more more specifically to the Pleistocene um with respect to the Pleistocene extinctions and then focus in on a particular system that I've worked on in Egypt so that's uh that's kind of the the roadmap for today okay so the effects of humans on ecosystems we've around we've been around for a while um the human species for 150 200 250 000 years depending on where you make that break point um and of course our relatives um we've have been around much longer uh I like to think of the process uh of our involvement in systems as a continuum because it has been and our role in ecosystems has likely changed over the last uh you know five million years or so um that we we began to diversify uh into different species and then of course uh throughout um our history as as Homo sapiens I'm really going to even though I'm showing uh our ancestors or uh close cousins um I'm really going to be focusing on on humans and specifically so let's start uh more recently uh than than what is shown on the last slide and think about the Pleistocene extinctions this is um a a period of time where we've come to understand the role of humans had uh much better in the last number of years um but this is a period of time where we had a large influence on on the global diversity especially of mammals and I'm going to focus a lot on mammals today specifically larger-bodied mammals um greater than four kilograms so uh this graphic let me walk you through it a little bit it shows a lot of information and it might be a little outdated it's from 2006 and there's been a lot of work this is a really quickly developing field um but what we're showing of course are different continents and the numbers and pictographs of of species relate to the number of extinctions that these different continents experienced as humans colonized them the black bar represents when humans kind of showed up on the scene of course in Africa we've been on the scene for a very long time before we were Homo sapiens and as we colonized the planet we see a series of extinctions that we collectively call the Pleistocene extinctions some of these are very well timed with human arrival and some of them are less well understood so in Europe for example there's fewer extinctions and our arrival is likely much earlier than the extinction than then we have evidence for the extinctions being the circles represent evidence for extinctions yellow is provisional evidence green is robust evidence and we have really robust evidence around 14,000 years before present humans showed up a lot earlier before that so it's not as clear in Europe what's going on in Australia it's very very um well I guess I could say clear um I would or or maybe to be a little more careful um correlated uh where humans arrive right as we find evidence uh for mass extinctions in Australia and that's around you know 72 to 44,000 years before present uh in north america it's also very correlated to use a more diplomatic uh term um where there's a large number of extinctions um that we have evidence for right around the time that that humans arrive on the scene in south america there's also a large number of extinctions but it's less well understood so humans appear to to our understanding humans appear to have played a large role in the Pleistocene extinctions across the planet uh so what can we learn um when we we we get down to business and we want to reconstruct how these ecosystems function before and after uh human arrival and so that's really the goal today um to to reconstruct patterns of interaction to understand the role of humans uh on community dynamics over this period of time uh what I'm showing on the right is is an american lion skull lions are an interesting example of what occurred at the Pleistocene boundary um lions were one of maybe the most widespread large mammalian carnivore on land um they were successful in many many different continents uh they were all over north america the north north american lion was actually had larger body size than than the modern african lion which is interesting to to imagine um and and now of course their range is restricted to sub-saharan africa and a small population in india and I want to focus a little bit more on how we go about reconstructing interactions um in in this particular way because I'm a little more involved in this style of research and really the idea here is to take advantage of modern contemporary systems um to understand the rules of interaction so so we'll use the serengeti rules to kind of quote the documentary film and and book on on ecosystem processes um and use body size uh from contemporary systems as a window into what likely occurred in past communities how past communities were arranged um I'm showing one of my two favorite graphics here figures from uh from a paper uh published um it's covered up by the window here and in the 2000s by uh Anthony Sinclair and Justin Brashers and Simon Maduma on patterns of predation and a diverse predator prey system so this is in the serengeti and what you're looking at is on the y-axis is mammalian predators arranged by their body size so the smaller bodies are on the top and the larger body is on the bottom of course the lions at 150 kilograms are at the largest uh terrestrial carnivores in in um in sub-saharan africa um you know if we throw in like crocodiles they might not be but we'll we'll just focus on the on the grasslands in the savannah um and what we see is uh on the x-axis is the is the prey weight range in kilogram so this is their food um and of course as we go from the smaller carnivores to the larger carnivores they're eating larger food they're eating bigger food right they're eating or herbivores that are larger and that makes sense but the other key thing to see here is the is the range um and that's what's highlighted by that black bar so as we get to larger carnivores they're eating larger ranges in addition to the larger body size uh the mean uh and it would be nice to see distributions on these bars but um i guess you want to plan your publication strategy you don't want to throw it all into one go because i think the data are out there uh so so so lions have this huge range of food that they eat um you can see one of the interesting things here is wild dogs they have this like shifted range relative to their body size they're so they're uh eating above their weight um and and that's because they're such efficient pack hunters so that's a a pack hunting signal um so but it's a nested relationship so the diets of smaller predators are subsets of the diets of larger predators now this means that if you're small and if you're a small herbivore and you live in the savannah uh you're you're you're going to be eaten um and that's shown on the bottom graph uh you're you're somewhat doomed that's your that's your future has to be food um and only if you're larger do you escape predation so in the bottom graph which is really striking is uh the percent of mortality due to predation on the y-axis and on the x-axis is the log prey log herbivore weight i have to move around my little zoom bar that's in my way um and what we see is this very sharp sigmoidal uh kind of switch here uh where below 310 kilograms you're you're you're doomed uh and above 310 kilograms you've effectively escaped predation for the most part and the dividing line appears to be zebra and buffalo so the z stands for zebra wildebeest um they're they're eaten uh buffalo in upwards you escape predation so buffalo giraffe rhinos hippos elephants uh very small percentage of their population is actively killed uh we're not counting scavenging here okay so bottom line body size really matters in these terrestrial systems and these mammalian systems and we can really think of sub-saharan africa um as as being a remnant of the Pleistocene it's kind of one of the last surviving Pleistocene systems uh for us to to draw inference from and correlate our understanding of these systems to the past especially a relatively recent past like the Pleistocene uh organisms were it's not like we're going back to the dinosaur world and trying to reconstruct uh which dinosaurs ate whom um you know this is a little closer in time so so we can more confidently make uh relation relationships between what we see today and what we saw back back then oh yeah okay so this is how we're currently doing this and it's based on a method published by Rudolph Rohr I think in 2010 an American naturalist uh where he establishes a uh logic function um where uh the log of the ratio of the probability that there is an interaction between a predator and prey divided by the probability that there is not an interaction between predator and prey is a function of the mass ratio between predators and prey so here m sub i is the mass of a predator and m sub j is mass of a potential prey um and you can see that there's three different terms here um one of which is squared and one is linear and one is constant and this allows and by fitting alpha beta and gamma which are unknown parameters that need to be fit to a particular system by fitting these parameters we can establish a Gaussian like distribution and log space that defines the probability of a link existing between a predator and a prey as a function of the predator and prey's body mass in this case so for example by fitting and and this is you know uh fitting these uh three parameters uh could be done by by a you know any any kind of um you know simulated annealing or neldermid um uh you know algorithm uh so by fitting these parameters for example in the serengeti in the known serengeti system uh we can accurately predict uh 74 of link presence as well as link absence um and what i'm showing on the bottom here is not the serengeti uh it's the one that i had on hand when i was making my talk uh because i'm working on some ocean systems right now but this is the benguela system this is from the famous paper by peter yodze's and it shows predators and prey or species arrayed by their body size um and the known trophic interactions being the darker colors the darker squares in this adjacency matrix and the predicted probability of an interaction overlaying on top in the color so by feeding in a known adjacency matrix we can fit these unknown parameters alpha beta gamma and um derive a a equation that tells us uh the most likely you know the the probability of an interaction given body size ratios um so by looking at the serengeti which i'm showing on the bottom and and for some strange reason uh i've put large herbivores on the left and small herbivores on the right um my apologies i tried to switch it around but it wouldn't let me um uh it's a detail uh and uh what we see is um by looking at the uh probability of an interaction or an established interaction modern systems uh we can equate that to the likely interaction uh structure for past systems assuming body size rules um stand okay and and there's not really uh a whole lot of evidence to suggest that uh past systems wouldn't be following the same alimentary principles as modern systems especially if we're we're within the same uh kind of families of organisms but that's an assumption okay so let me see if i can pull up my chat window just in case okay all right so not only do we get uh mean probabilities um well this is just kind of showing a different cross section right so so here on the on the bottom left now i'm looking at uh we have the probability of an interaction on the y-axis and this is the mass ratio um on the on the uh on the x-axis and so we you can see this this isn't logged the x the x-axis isn't logged so it doesn't look Gaussian but but it is um if you log it and uh this just shows that um for a given predator and prey let's say if we keep the predator uh mass constant and we're moving the prey mass there's uh a prey mass where the prey is too small for the predator uh so you're it's energetically inefficient for a lion to run around trying to catch mice um but then it's also energetically inefficient and uh risks death uh to go after the largest animals as well so there's these boundaries on either side and this is what this is capturing where those boundaries change as a function of what the organism size is the consumer size is okay so not to belabor oh yeah and then obviously not to belabor the point that i belabor it uh but then when we expand this uh looking at prey mass by predator mass we can picture this in two dimensions and you can see how um the probability of a link is is changing and captures that nested uh relationship that we see uh in the serengeti so this is one of the important things that this is capturing now the the original rural model also allows for latent traits so traits not associated with body size so you know thinking about marine systems what you know uh sperm whales or not sperm whales that's a bad example um but humpback whales are not going to obey this this relationship uh because they're they're going after really small things and they happen to be really really big um and and so there are other latent traits that are not body size related that you could account for uh using this this type of approach as well that i'm not going to go into okay so the questions that we want to address here is how do changes in structure translate to dynamics so if we take modern serengeti systems as kind of the baseline and use it to reconstruct Pleistocene systems uh to get the structure of interactions and really these are probabilities of interaction so when i say reconstruct a Pleistocene system i'm really talking about a large number of potential systems that fit those probabilities um are there differences from one Pleistocene system to another uh so this is really awesome work um uh led by machias pares um and in 2015 and proceedings of the royal society be i really like this paper um where they they they implement this method they reconstruct structure and um using body mass ratios and then just look at the structure of the system they look at modularity by nestedness um to see if there are differences between continents uh Pleistocene systems from north america south america and africa and what they find is that there are large differences um from one system to another um but it doesn't always divide out by by continent uh so for example in south american system there's a large range of modularity predicted by this approach um and a relatively constrained amount of nestedness that's predicted by this approach as well in all places uh in north america uh there's more modularity than um and some of the Pleistocene systems than is seen in some of the Pleistocene systems from south america and then africa kind of falls in the middle here it's it's in mid-range and that's that's represented by this i'm pointing at my screen like you can see that but i should use my pointer i guess um so african systems fall fall here somewhere but um machias uh in his group went uh one step further and they asked well since we can estimate the structure of these Pleistocene systems can we assume some very simple dynamics and put those dynamics on that structure so they used a lot of altera framework uh with allometric vital rates okay so i'm just showing the very basic framework that they used uh our subi and so this is you know the change in uh abundance um for species i over time and our subi is is positive it's if it's an herbivore negative if it's a carnivore uh to capture that difference in in growth and mortality and um in in addition to the consumption of different prey species and um r is assumed to be uh an allometrics so it's scaled allometrically uh to mass to the negative one quarter and um this term b sub ij is is extrapolated from these probabilities of a link existing between species okay and um you know the system uh it's a you know high-dimensional od system uh is stable if if the uh leading eigenvalue is less than zero and what they experimented with is simulating the system the Pleistocene system as is and with the presence of an added apex predator so they did it without humans and then they included humans and they assumed humans had a similar um hunting behavior or hunting focus as other apex predators in the system so as for example uh a large lion or uh saber tooth cat um and there is a lot of evidence to suggest that humans were consuming at the top of the food web in the Pleistocene um and by looking at the system without humans and with the added effect of humans they could assess the destabilizing effect of humans okay so this is what they found so on the so on the top i'm just showing the structure as before on the bottom uh the y-axis is the destabling destabilizing effect of humans and we have the different systems across continents according to the colors uh coded to the key on the left and what we see is that in North America and South America humans had a much larger destabilizing effect on the system whereas in Africa they had a much smaller destabilizing effect okay and this is suggestive that because well the idea here is that humans evolved in Africa uh and they involved they co-evolved with African systems um and it's possible that African systems as we know them are to some extent a product of those interactions so the um the organisms that are present in African systems and the interactions that they uh have within themselves are a consequence of interacting with humans in particular over the last 200 000 years or so um and this may explain to some extent why there are have been so few documented Pleistocene extinctions in Africa relative to North America or South America where humans were brand new on the scene so those communities had no um preparation uh for for the arrival of humans uh and that could explain the destabilizing effects that we observe um when applying this type of theory to those communities um just a very brief mention so we're applying some of these same approaches to understand the the change in the Northwest Atlantic uh over time we're specifically focusing on the Nova Scotian shelf here um and that's that's circled uh in the map uh and and thinking about how that system might have changed over the course of the Holocene uh of course that system began as a subarctic uh kind of icy environment um and is now not uh in addition human fishing has been a huge uh stressor on that system for hundreds of years um and we wanted to understand how that system may have changed as species were lost uh and we're using the same types of approaches here I'm just showing the same Benguela Food Web adjacency matrix that we're using as one of the food webs that we're characterizing the probability of of links occurring between species um one of the challenges we've been having is many of the species in the systems that we're trying to parameterize the contemporary systems that we're using as a baseline for this it's very hard to find mass estimates if you're trying to do to do a complete system you know like what's a mass of a jellyfish um so so we we we think so far it looks like these estimates work for length as well so we could use and that makes sense because it's it's a ratio anyway so it's really uh whatever the the organism is queuing off of to make its foraging decisions is what's important for this type of um uh procedure um and just to give you a sense uh this is what the North Atlantic Northwest Atlantic looks like today we have um some very charismatic species like the Greenland shark which is one of the oldest organisms possible animals in the world um we have porbical sharks uh blue sharks uh haddock shrimp all these interesting organisms um and this is what it looked like uh historically in the 1700 it was very different I circled the organisms that are no longer large players in the system or extinct locally we have Atlantic system coastal sharks white sharks killer whales walrus cod all of whose populations have either collapsed or gone away in the system that we're looking at and so there's large structural difference between these systems and we expect that there's going to be large dynamic differences as well what's interesting is you know all of the fishing and managerial decisions that we make in modern in the modern um system here the Northwest Atlantic are basically working under the assumption that this is this is the system as it should exist uh whereas very recently it was very different so the managing management decisions are contingent on our historical understanding of the system um and we think the historical understanding of the system isn't very good uh so we're trying to add to that okay I'm moving on now to Egypt um this is a beautiful palette um at the Ashmolean Museum uh of uh that's dated to the pre-dynastic era in Egypt and what it shows is among some mythical organisms uh there's many many modern species that are no longer in Egypt uh so it's a portrait of the past where the past is very different than the present and Egypt in the pre-dynastic area era was a very different place and our goal here is to reconstruct the patterns of extinction to understand what Egypt looked like before and use that to inform how Egypt operates today and this is common uh we have bared witnesses oops sorry as I hit the table we have bared witness to these changes as humans and we've documented these changes in many different places um this is uh this is a cave in Spain in a pictograph of a bison of course there's uh cave paintings all over Europe and many other parts of the world documenting organisms that no longer live where they live um sometimes organisms that are extinct and um that's in the relatively short history of our being on the planet uh the world has changed quite a bit and we've we've likely played a role in it not always and and sometimes there's natural climate change reasons as well but we've certainly played a role this is another beautiful picture the lion panel in cave in France I believe I've not had the opportunity to see it in person although many of you might have but it's just incredible the not only just the the images that are the artistry in the images but they almost depict motion and it's actually been thought that multiple pictures like this of of lions next to each other were kind of a cartoon uh used to to illustrate motion oh yeah I wanted to delete this okay so I'm just going to skip go a little faster here okay so the goal here is to use paleontological and historical information to reconstruct the pattern of extinctions in a single community over millennial timescales and specifically we want to ask what have been the cumulative dynamic effects of climate urbanization and industrialization on mammalian communities and can this inform our understanding of how communities operate today now I want to be really explicit in saying that I'm not trying to say what caused the changes that will be that I'll be presenting the causation is a different problem really we're looking here at the consequence reconstructing what those changes are and looking at the consequences of them so let me just introduce you very briefly to the area we're looking at the Nile Valley in Egypt this is how it looks today and I just love this description of the area desert vegetation can be classified into three basic subdivisions based on how much water those areas receive perennial ephemeral and accidental it's a very dry area and water really drives everything and if we look in in Egypt today these are some of the species we might be lucky enough to see we have the blackback jackal canosaurus or the golden jackal sorry hyena hyena striped hyena caracals these really cute small cats foxes and if we were to go back in time we would have seen other organisms as well we would have seen leopards we would have seen cheetah these organisms are no longer there the last individuals were killed relatively recently although their populations collapsed a long time ago the last leopard was observed in 1913 the last cheetah was killed in 1974 near Almagra if we look at herbivore species we see of course a little more diversity we see the wild ass we see ibex gazelle many multiple species of gazelle many of which are red listed and then we look at those that are no longer there the heart of beast was last observed in 1935 the egyptian boar the last specimen in egypt was a british specimen number 2450 1912 attics 1957 and oryx oops at the bottom disappeared in the last half first half of the 19th century however if we look farther back humans keen observers of the natural world that we are have been recording our observations for a long period of time so our goal here is to not only integrate paleontological information of species occurrences but integrate artistic representations of species occurrences as they have been depicted in egyptian artwork over over time and because egyptian antiquity is so well documented and dated dating artwork and the presence of organisms is in artwork is relatively straightforward and so the idea is to use these representations many of which are in ecological settings so you know pictured here is is the enjoyment of hunting and we see well herbivores being hunted by dogs but herbivores in their natural environment being hunted by egyptians and what we're going to capitalize on it are these see ecological depiction depictions of organisms rather than religious iconography here's again a beautiful pictograph of from the tomb of amin amhat in dynasty 12 picturing many different species of herbivores being hunted with a net which was a common way of you know surrounded area with a net and then and then hunt them at ease heart of east dorkus gazelle leopards oryx fox cheetah ron antelope so just incredible diversity most of which are not currently in egypt today again here's here's a couple different pictures just to show you the diversity of in natural history in some of these depictions we have bird hunting on the upper left and and the nets that are they traps that they they used in the upper right and then the fish diversity on the bottom is also really kind of astounding i don't know fish very well but i would bet a lot of these fish could be identified pretty well from these pictures now one of the other important things about egyptian artistry is that they were very focused on documenting they documented a lot of details and they clearly distinguished organisms that were domesticated and imports from other places that might have been captured and paid in tribute to a pharaoh or whatever was going on and this is the symbol on the bottom that symbolized a domesticated organism it's pronounced ran and it means fat fattened and and they use this to distinguish between wild and domesticated stock so just a really quick and really brief history lesson on on the egyptian past and what we're what i really want to focus on which is the climate change so 15 000 years before present we have the oldest known artwork out in the desert and i'm showing that picture on the on the sides of these rock cliffs now 5000 years before present was the end of the african humid period so before that period in time egypt was like east africa it was wet it was a savannah woodland and it had all of the organisms that we associate with savannah woodlands which i'll show in a moment uh but at around 5000 years before present the monsoon shifted and the rain stopped falling on the area and it became uh it began its desertification process of course that had nothing to do with humans um five or sorry 4580 years before present we have the establishment of the old kingdom uh 4140 years before present we have the establishment of the intermediate period along with a large erudification event which i'm showing with the orange dots by the way and this erudification event was an important one it's noted it's discussed in tablets and pictograms and it's been linked to uh this erudification event has been linked to large political upheaval and quick successions of rulers and it's thought that that quick succession of rulers was brought about by large famines from the erudification 3270 years ago was the establishment of the new kingdom and then 3000 years before present was another large erudification event that's documented in the records as well as um uh sediment cores now we can confirm a lot of these these erudification events and then more recent history with the greco-roman um description of egypt and and of course more recent industrialization okay that was a very quick history of egypt just to show you some early early holocene uh rock art from the egypt area uh we have uh elephants described elephants depicted up here so we don't usually associate elephants with egypt they were there giraffes were in egypt um the damadir was likely a recent migrant from mesopotamia and just a whole suite of organisms that we don't think about living in egypt today because they don't and if you go through and categorize all of the different um species that are present both in archaeological deposit or paleontological deposits as well as those represented in ecological settings um this is the list that you have you have uh cob wildebeest hardebeest oryx camels um deer damadir giraffes hippos uh you know just everything we associate with the serengeti was in egypt in terms of the carnivores we had um striped hyenas spotted hyenas cheetahs leopards uh two distinct species or subspecies of lion a short main lion and a long main lion and i'll get to that in a minute and that was distinguished apart from being male and female um and there's well i get to it i'm getting ahead of myself but if we go through time and document when these organisms disappear uh from the um these these ecological depictions uh and from plight from from deposits uh we can build a pattern of extinctions and we can put error on that too to account for uh organisms being um you know depicted after they've gone right and so what i'm showing here is uh the the first appearance and for some organisms but primarily the last appearance of these different species which is the black circle uh and then the red the color that's overlaying on top is the probability of extinction so where we have a last appearance we we have we have a a gradually declining sorry gradually increasing probability of extinction following their last appearance okay and so it's a very particular pattern and so that is what we used to infer changes in food web uh structure over time now i mentioned that there's two subspecies of lion a large-bodied long maned lion i gotta keep an eye on the time because i get trapped in uh egypt stories here a large-bodied long maned lion and a smaller-bodied short maned lion and these were represented as two distinct uh subspecies within within the artwork and descriptions and this actually correlates with with a known lion population that was last uh seen in the in the atlas mountains um so we think this might this might represent the barberry lion um which was a larger-bodied longer maned lion uh that existed in north africa until relatively recently there's still stories of of relict populations surviving in the atlas mountains um but it really disappeared at the end of the second dynasty in terms of its representation in the artwork and then of course the short maned lion um lasted much longer so it didn't disappear from egypt until the end of the until around 3000 uh 35 years before present actually correlating with it within a ratification event okay so one way that we can depict structure over time before we even begin to reconstruct interactions is to just simply look at the predator to prey ratio so what we see over time and i would also draw attention to the fact that these timebends are not equally sized okay um they they really correspond to the information that becomes present due to different dynastic cycles beginning or ending uh and antiquity um but if we look at the predator-prey ratio over time we see that it's increasing until about 3000 uh years before present as um herbivores uh disappear so herbivore species uh are disappearing first increasing the predator-prey ratio after which it decreases at around 3000 years before present uh and then increases again of course as the system becomes uh as it loses species it becomes much more volatile the predator-prey ratio becomes more volatile because smaller changes make larger differences in the ratio but i'd like to draw your attention to three uh larger shifts that we see in the predator-prey ratio at least historically um and that's outlined by these stippled lines and those correspond to the three large erudification events um so it would seem in a very correlative way that um erudification events uh appear to have impacted how this uh the structure of the community may have been changing over time and again i'm not really drawing uh causation to this uh there's many different causes that we could imagine could feed into this and this might be you know room for theory in the future um it could be driven by bottom up forcing it could just be driven by you know changes to the environment um as as as directed by changes to the climate which i'm showing on the right or it could or humans could play a large role um we could play a role by competing uh for uh space really you know in this area as it becomes more and more desertified uh water is the key and in and finding habitat where you have access to water is is really the limiting resource in these systems so as humans begin to expand their agricultural base uh they're taking up space where water is available and that's pushing out wild animals and then this could certainly have led uh to um many of the extinctions that we observe uh in the record or humans could have actively been hunting these organisms uh and and had a large impact especially as we have the establishment of a relatively sedentary uh human civilization for one of the first times um they that that where they're also subsisting on crops uh for food they could have a abnormally large impact on on populations of wild organisms okay now i'm not going to go through this because i already did um but we use body mass information because all of these species are are extant uh so we know the sizes of these organisms and from their body sizes we can reconstruct the probability of a link existing between them and then build series of food webs uh that we think best represent um these systems dynamics okay so this is kind of the fun part um and and i know you guys have had awesome talks about dynamics so far um this is our this is we wanted to not only reconstruct food webs but say something about the stability of those systems and we wanted to see how a stability or or measures of stability might have changed over time uh to do this we used an approach called generalized modeling and i've got a couple key citations on the bottom uh this was really pioneered by uh tilo gross in 2006 and later in uh 2009 with a um and then we have a description really focused on ecological systems uh in theoretical ecology in 2011 um and i've been meaning yeah i'll try to make a reference list for all of these things that i'm citing and not doing a very good job of reporting which journal they're in but i'll make a reference list for all of the different things uh that i'm talking about for those of you who are interested uh that i can make available um okay generalized modeling so uh you know this is really useful where we know the architecture of the dynamics of the system but we don't know the functional relationships that um that are embedded within that architecture so for example let's consider an ecological system where we have the change in biomass over time so b is biomass and we have some function of growth so we have a source right so there's biomass is growing by the function s and it's draining where there's a function of mortality as this function d um but we don't know the specific nature of these functional forms uh this actually might better represent our knowledge of the system um but and this is particularly true for past systems where we really don't expect to know the exact architecture of the system or at least we don't want to assume that we know the problem is of course we can't simulate a system like this and we can't solve for its fixed point or steady state so what can we do with it we can do quite a bit actually um we first uh the method very simply and generally and quickly uh is is to establish b star as a very as a variable representing all internal equilibria of the system so these are all non negative non zero equilibria that represent uh you know states where where all of the organisms persist uh in in our system okay but it's unknown because we don't know the functions we can then define a new set of parameter parameters representing the normalized variables of the generalized system so here we're defining little b as the biomass divided by the biomass at steady state which is unknown a little s of little b is the is the the growth function of the biomass divided by the growth function of biomass at the steady state and little d of little b is the mortality function divided by the mortality of the biomass at steady state uh the important thing about all of these uh new parameters these normalized parameters is that steady state they're all equal to one and that helps us a lot this allows us this normalization procedure of the of the generalized system allows us to extrapolate biologically meaningful and this is the key biologically meaningful and relatable um uh coefficients terms variables etc so here we see that when we set the system equal so when we set the normalized system uh equal to zero right so so assess the system at steady state uh little s of b and little d of b i'm getting covered up here uh so this term and this term become one and we have this simple relationship of s star over b star which is just a constant is equal to d star over b star another constant and we'll just define this as the turnover rate at steady state so this um this gamma here is directly biologically meaningful it is the biomass turnover rate at steady state and it's equal to the normalized function of growth minus the normalized function of mortality okay so we've generalized we've taken this general system and we've normalized it okay now we want and then we've redefined uh some of the constants in the system to be biologically meaningful but now we want to assess the system stability and what's our what's our interpretation of what can be our interpretation of this so we're going to perturb it and we're going to look at the uh conduct linear stability analysis as we would to any other ode system that we might investigate so we're going to look at the change in uh d little b over dt as a function of little b uh with sorry with respect to little b and this equals the single eigenvalue of the system and uh we simply take uh the uh the the derivatives with respect to little b across uh the different elements of the system so um we end up with this uh derivative for example for the growth function for the normalized growth function with respect to the normalized biomass is equal to uh the derivative of the log of the unnormalized growth function divided by the derivative of the log of the unnormalized biomass evaluated at the steady state and this actually has a direct biological interpretation it is the percent change in growth divided by the percent change in the argument and and the unnormalized biomass it's a functional elasticity um so functional elasticities in this system are the logarithmic derivatives of the unnormalized functions relative to the unnormalized argument and this provides a non-linear measure for the sensitivity of the function to variations in biomass so we have in this very simple 1d system we have the single eigenvalue of the system equal to the biomass turnover rate times the elasticity of growth minus the elasticity of mortality and we can directly relate this to the conditions under which this uh single eigenvalue is going to be greater than zero or lesser than zero uh as a function of the values of the elasticities of growth the elasticities of mortality and the biomass turnover rate which uh doesn't matter so much as in terms of determining the the positive negative uh value of the eigenvalue okay so one of the important messages here is that or why are we doing this uh is that elasticities characterize whole families of functional forms so consider power law functions we have a function where the word's constant a function with a with a linear power a function with a square term and if we take the elasticities of these functions we see that the constant term is simply zero the linear term is one and the squared term is is two so power law functions have direct single values associated with their elasticities with their functional elasticities and this allows us to set realistic bounds to the elasticities in the Jacobian if we're talking about a multi-dimensional ODE system that that go into the Jacobian so you'll have a Jacobian matrix that you derive to look at the linear stability of the system that's a function of all of these elasticities from the generalized model but the elasticities themselves have realist have very small bounds associated with them to be biologically meaningful and that really sets a lot of constraints into the system so you can more efficiently search across uh you know combinations of parameters that are biologically realistic and get a better sense of what the stability of biologically realistic systems is given the architecture fed into the generalized model more complex functions have elasticities that are functions of the unknown steady state but also range between small ranges of values so for example in elasticity that's more complex that might be a function of the unknown steady state may only realistically be able to vary between zero and one or between one and two and this really sets lots of constraints that enable enables us to more effectively search biologically reasonable space so just to kind of depict this as a cartoon if we're doing a random matrix type of approach we have a large parameter space to search across to get a sense of the stability of the system however the generalized modeling approach allows us to subdivide this large parameter space to biologically meaningful unit so we can more efficiently search across the system and ignore parameter combinations that are biologically unrealistic okay so now that we've done this we have oh yeah so we have uh i'm pointing at my screen again we have a large uh system of many interacting species and we have uh so change in the abundance of species i over time is equal to the growth of i if it's an herbivore uh plus the growth of i if it's a carnivore and consuming many other herbivores minus the mortality of species i if it's a carnivore or minus the predative loss uh if it's an herbivore we normalize that system to a steady state so this is just kind of the the higher dimensional version of what i've already shown you but all the principles are the same and then we can drive the jacobian matrix so we can drive derive the uh on diagonal and off diagonal elements of the jacobian matrix which are now all functions of the functional elasticities each of which has uh relatively constrained ranges and so now we can search across many different potential jacobians uh by randomly drawing from within those ranges to determine a percent of those systems that are stable relative to a percent that are unstable and this allows us to translate the structure that we've reconstructed from the body mass ratios to the likely dynamics of the system and do so for all of the different snapshots that we have of egypt in the past as it changes over time so we are um really going to look at three different measures here we're going to look at food web stability which is just the percentage of uh drawn food webs that are stable out of the large number that we simulate um i think i think we simulate around 10 to the 7th um and so this gives us a sense again of just the general stability of the entire system um is the system stable right and that's just what percentage of those uh systems those drawn systems those jacobians that we draw from the functional elasticities uh have a have a leading eigenvalue that's less than zero um secondly we wanted to assess the species specific roles and sensitivities to change okay so um let's see yeah so we did two things which i'll describe in the next slide so one is related to the stability of the system and that is once we have the stability of the system then we can start pulling out species and determining whether or not that stability increases or decreases with the absence of a given species so for example if 90 of our food webs that we draw are stable and then i pull out lions and now 95 are well then that means that lions are a destabilizing force in that system okay if we have a system that's 90 stable and i pull out gazelles and suddenly there's 10 percent that are stable then that would mean that gazelles are an incredibly stabilizing force in that system so that's something that we're going to look at we're going to look at the change in the percent of stable food webs relative to different species being present or absent in the system the third thing that we're going to look at i don't even know if i have a three on here i should do i no i don't okay the third thing uh that we're going to look at is the sensitivity of species to a perturbation to a different type of perturbation so we're going to use this idea of a press perturbation where we push the system to a different equilibrium to a different steady state and examine how each of those species that are in the system respond to that push and this is given by the equation in the bottom right and it's a function of both the eigenvectors and the eigenvalues in the system where we sum across the modes to get the the stability or sorry the sensitivity of each individual species in the system sorry i'm going through this really quickly we explain it more slowly in the paper i guess as slow as you'd like to read it so what are our results what were the dynamic consequences of community change over time so on the on the y-axis is the proportion of stable food webs with 100 at the top and on the x-axis we have our time bins and so we look at each system and simulate many different iterations of its structure as well as as the potential dynamics that can go on to that structure and what we see very straightforwardly is over time the system becomes less stable and this is true whether we apply tons of uncertainty into the disappearance of species so you know upwards of you know plus or minus 200 years plus or minus 500 years to the different disappearance of species uh from the the you know both the artwork and the paleontological information archaeological information it doesn't change the overall picture of of what occurs as species go extinct so the egyptian system at the end of the pleistocene we can interpret as being much more stable as it is today as it has fallen apart and unraveled over the course of the holocene perhaps a little more interestingly we we can evaluate the stabilizing effects of different species in the system so again on the x-axis i have the time bins and here we're trying to determine whether there are key species that contribute to the stability of the system in which case if they're lost they are contributing destabilizing forces into the food web now on that y-axis we have the change in the percentage of stable food webs with or without a given species and each lie and each trajectory represents a comparison of the presence or absence of different species and i've illustrated some of the species it turns out all of the herbivores are stabilizing so and meaning that their trajectories are going to be above zero because they have a net positive contribution to the stability of the food web whereas carnivores tend to be destabilizing and what we find is that the most stabilizing species are the smaller bodied herbivores and as we've lost the redundancy of smaller bodied herbivores over time their stabilizing effect of the on on the system has increased which means the consequence of losing them has become larger as well we can see farther back in time losing any species has very small effect on the stability of the system whereas today because there's so few organisms left in the system losing any species for the most part has a much larger effect but it's the smaller bodied herbivores that have the largest effect because they're shared by so many carnivores because the carnivore species rely on those herbivores losing them is losing losing the core of the system and the last result that i'd like to share with you it has to do with the sensitivity does sensitivity predict persistence i mentioned yesterday that one of the keys about paleo ecology is that we know the future when we look into the past we know the future when we look into the past so we can evaluate whether species that we think might be likely to be important have large effects on the system or perhaps we can consider whether species that appear to be more sensitive based on some theoretical argument actually go extinct so here we're calculating the sensitivity of species to a perturbation in other words we're pushing the system to a new equilibrium and seeing you know how how how different species react how sensitive are they to that disturbance and we could postulate then that species that are more sensitive to a disturbance may be more likely to go extinct in other words species that are more more sensitive to a disturbance may persist for a smaller amount of time in the system and because we know the persistence of species how long they're in the system after the end of the Pleistocene that's what we have on the y-axis we have how long the species are in the system after the Pleistocene it's logged and then we have the log sensitivity on the x-axis and what we find is a is a negative relationship so species that are more sensitive have shorter persistence times in the system whereas species that are less sensitive have longer persistence times in the system and there's this kind of roof here the ceiling because that's the maximum amount of time since the end of the since since we sorry since we begin making the record so at the end of the Pleistocene until now this is kind of the maximum these species are still present in the system and these species have been lost so what have we found we found in Egypt as the system has unraveled in the presence of all of the changes that have gone on in Egypt both climate human induced everything added together we found that with the unraveling of the food web has come decline in stability and that there are key species that have played in a larger role than others in determining whether that stability is eroded or not and finally the sensitivity of these species which is again a consequence of their structural relationship within the food web as well as the elasticities that we attribute to them through this generalized modeling perspective that that the more sensitive species are the less likely the less length of time they are expected to remain in the system so persistence in this case is predictable okay so moving on into the future right we think these community level frameworks are vital for understanding how our ecosystems are expected change in the face of these traumatic events that they witness over long periods of time and of course you know we've looked into the into the past at mass extinctions in the past and we've seen large changes in food web structure and function on either side of extinctions and today it's important to note not to end on too sour of a note anyway but that that we're in the six mass extinction all evidence points to the fact that we are in the six mass extinction and so building upon paleontological insight I think in my perspective is vital absolutely vital for having a sense of what to expect in the future um yeah so if there's any time I'm happy to take questions and then we'll on Thursday I'll I'll really switch gears and and take a much more a close view of how energetic constraints can give us insight into systems that are that are no longer around that are extinct so thanks so much thank you so much Justin for the very nice lecture so you're sure there is a bit of time for questions so if anybody has any question you can either raise your hand or write it in the chat as usual I guess everybody's a bit tired after hours of lectures anyway Justin will give another lecture on a Thursday if I'm not wrong so if you get any questions later you can always ask them on on Thursday great sounds great well thank you everybody I appreciate it actually there was oh sorry there were raised hand I didn't see them sorry so there's a question from Flavia hey Justin how are you good hi Flavia how are you very nice to all congratulations thank you for that I'm curious with one result you presented you show that the small herbivores are more or less the keystone species and this is a little bit contradictory I don't know how to say that but it's like the opposite of the expected and theory usually we think that large mammals or large predators are those that are the keystone species is it is your result a consequence of the dynamics or a consequence of the biomass approach that you use what is that yeah you know I think I think and I wouldn't necessarily say they're keystone species because that's assuming you know some kind of stabilization relative to their known abundances but yeah they're they're key to stability but they're but I would say they're only key to stability in the systems that we were looking at recently so it's only after the systems are unraveled that they really become that important but if you look at a fully fledged system so if you go back to the end of the Pleistocene which is very serengeti like they you know there really aren't any species that make a large they have a large impact on stability when they fall out and so I guess I would argue that that is an artifact of the unraveled state of the system and that perhaps only very disturbed systems will observe that importance for the smaller bodied herbivore but you know even in these large systems and I think that's because of redundancy you know if you look at that that mortality graph in that Sinclair paper showing that sigmoidal relationship to the probability of predative mortality the smaller animals are getting hammered but there's a lot of them and so if one goes extinct you know I can't find a a topi I'll go after Thompson's gazelle but if there are no if there's only Thompson's gazelle then then I think that would be a very different situation okay let's see thank you okay there is another question from Matteo hi yes just a curiosity just to what extent you can think the sixth mass extinction is similar to to the others because essentially it looks like there's a factor which is the prevalence of humans which is might be different from from from the other extinctions yeah that's a really good question and I'll be waiting and I guess to answer that I'll wait into things I don't know a ton about because a lot of people are working on this right just just determining whether or not we're actually in a mass extinction which has a lot to do with figuring out extinction rates and projecting into the future and to into a very unknown future I guess if anything I would think that the rate of the extinctions that we're experiencing today is probably a lot faster than the rate of extinctions experienced in the past which are kind of unknowable you know the Permian Triad Permotriassic mass extinction likely occurred over hundreds of millions of years or sorry not hundreds of millions of years you know millions of years or hundreds of thousands of years and because it was this kind of gradual change to the climate brought on by these massive volcanic events the KT extinction might have been a lot faster the asteroid impact but you know we don't really know how the extinction rates changed for different taxa afterwards but it but you know we've had a huge impact on a relatively short time scale and and I would say if anything's different it's it's faster we're more efficient than than volcanoes so in terms of you know contributing to extinctions so that would be my guess but I know a lot of people are working on on trying to understand how the current mass extinction if it is a mass extinction it does seem like it is um compares to prior extinction events thanks okay I still see the raised hand of Flavia I don't know if she has another question or if she didn't unraise her hand okay it was not a question so I don't see any other raised hand so if nobody has any other question or if I am not not seeing them like before I think we can say thank you again to Justin and hear you again on Thursday on Thursday have a nice evening thank you well you guys have had a long day but my day's just beginning so that's why I have a good day to you then and to all the other people on the other side of the world that's right thank you so much bye bye