 all the panelists, so let's wait a few more seconds to allow them to join back to join for today's round table. Okay, I think, yes, I think everyone is here. So thank you everyone for being back for to this last session of the school. I just counted the number of sessions we have and believe it or not this is session number 52. So I think that this was a long and exciting marathon and we are now in the very last kilometer of this marathon. So this session is a round table with many panelists that you had the opportunity to know in the last three weeks. So it's my pleasure to welcome again Stefano Lesina, Daniel Fischer, Jonathan Levine, Matteo Arcili, Mercedes Pasqual, Daniel Segre and Justin Icke. So thank you very much for giving the lectures and for being here to this round table. So the way I'd like to organize this round table is to try to have a sort of spontaneous and self-sustained discussion among panelists and also including you participants. So before we start, just a few engagement rules. So if you are a participant and if you are following from YouTube, you can post a question in the chat and I'll try to find the time to redirect them to the panelists. If you are on Zoom, as usual, now you know it very well, you can either type the question in the chat or use the raise and feature. Also, the panelists, if you want to say something just and I don't give you the word, just use the raise and tool or write me in the chat. So the title of this round table is Going Big Challenges and Opportunities in I-Dimensional Ecosystems and this title without hiding it in plain sight is an interpolation of the title of the chapters that some of the panelists have written in this book here, which is Unsolved Problems in Ecology and an interpolation also between the lectures of this school. So the two keywords, in my opinion, that naturally emerge from the lectures and the chapter of the book are coexistence. So the why and the how of species coexistence in large communities, in some sense the most fundamental question of ecology, because it's basically asking why ecology exists in the first place. And the other word is dimension, the fact that in large community there is a lot of variation on multiple axes, including many species, many conditions, many traits, many functions. So the fact that in the title we talk about Going Big and I-Dimensional strongly suggests that much of the intuition about coexistence and ecological dynamics comes instead from very low dimensional theories and models, for instance, to species competition. And in some sense in the title is also implied that this intuition should fail when we move to I-dimensional ecosystems, right? So I'd like to have a first round of answers from all the past panelists about the following questions. So do you think that our intuition that we shape with theories and experiment on low dimensional ecosystem should fail when we move to high dimensional ecosystem or whatever that means? And if you think that that should fail, what specifically what intuitions about the low dimensional ecosystem is wrong for I-dimensional one? So I will proceed with this round of answers in alphabetical orders like at school. So something with Stefano? Yes, so it is obvious even to a theoretician that no place in the world contains one, two or three species, right? And yet if you take like a book of theoretical ecology, 95 percent of the material is dedicated to the case of one, two or three species. So besides this obvious fact that there are very, very many species in the world like in the in Tropica Rainforest, we can find 10,000 species of trees. What strikes me as very interesting is whether we can use exactly the same tools that we use for small-scale ecosystem, imagine like experiments in a laboratory with one or two or three species to understand what happens when we have 10,000 species. My career basically was a bet on the fact that we cannot really extend the same like type of theories that we did for like small-dimensional system to large-dimensional systems. And we have clear cases where our intuition fails when we move that to more than a handful of species. For example, like the celebrated rule of intraspecific being larger than intraspecific in competition in two-dimensional systems in Lodca Volterra does not hold when N is greater than two, generally. Great. So, Daniel, are you sure? Well, I guess as implied by the title of my series, I think the answer is clearly yes. I mean, I think in many ways the most dramatic examples are not having many species that co-exist but having an enormous number of strains which co-exist and compete directly with each other and make almost any bacterial system that has been looked at one finds a huge number of strains that really co-existing in space and time. And trying to understand that in terms of thinking in terms of niches that somehow one starts from a picture where each type interacts more strongly with its own type than it does with others which is a lot of the beginnings of a lot of the work on high-dimensional ecosystems. I think that's sort of fundamentally fundamentally wrong, unless that is really an evolved characteristic of the system that somehow drives it towards that. So, I think at this point, I mean, certainly having worked on it a limited amount, my intuition is really poor as to the things that can happen in high dimensions. I just want to actually mention one example from recent work on evolution of microbes. It really sort of shows how different it can be. The traditional view is that you can get mostly neutral drift and occasionally get a selective sweep. But the other alternative is just there's always evolving, the population is always evolving, even without much diversity driven by ecological interaction. And the picture emerges as very different and there's something, the prediction for statistics of diversity and so on are very different. It took a long time to get to the point where we had enough theoretical understanding to start saying which predictions might be somewhat universal, not dependent on all the details, but we do have some understanding of that. And so I think it's going to take a while with the apology to know what ways one might try to make contact with data or which things one should find surprising, which things one shouldn't find surprising and so on. But I think, you know, Phil Anderson's more is different, absolutely applies here and it really needs developing different intuition and different methods. Great. So Jonathan? Sure. So I think the question is, as you say, sort of a leading one. But I think that it's worth sort of dissecting the question into two levels of organization. And one is to say, you know, while certainly nature around us is quite diverse, the question might be rephrased as, is it fair to say that we can understand that diversity as some sort of simple combination of what are ultimately fundamentally pairwise interactions. So while the individual law, give or tear rules between two species, are not going to, you know, are not going to change in a many species system, the generalizations we have about what it takes to get coexistence intra-opportunity might collapse, but our overall framework is still okay. I think the more fundamental question is really, you know, when species are in these more diverse systems, do we really experience, but some are calling higher order interactions where you really have this simultaneous interaction of multiple species impacting a third and fourth and so on. And I think the jury is still out on that one. I think it's easy to answer the first question and say, yeah, you know, if you build it, you string together a bunch of pairwise interactions, you can't use the simple rules you develop from simple, you know, pairwise ecology to understand dynamics. But the big, but I think we'll get over that. I think we'll figure that out eventually. I don't find it sort of an insurmountable question. But what is really challenging is to say, is even the notion that we should be able to understand diverse communities as these sort of combinations of pairs is something we don't know. And, you know, and you could even, you know, another way of saying is obviously these models are meant sort of to abstract some underlying mechanistic interaction between species, whether it's through resources or consumers or allelopathic chemicals, whatever you like. And the question might be, what do you think about those mechanisms? Are those mechanisms one, which you think can be described in this pairwise fashion or ultimately require these more complex structures? And I think we don't know enough about nature and about how those methods are really driving dynamics of nature to even answer that question. But that might be the path with I would try to kind of veer towards getting some progress on the question at that at that hardware level, so that might say. Okay. So Matteo? Okay. So first of all, well, I think I should say from the personal experience, the situation where your intuition fail is a very fortunate one because it means that really there is something fundamental to be understood. And when there are two sides of this question, one is our intuition about models. I mean, when we study a very complex model and whether what we expect is what actually turns out. And the other thing is intuition about a real system. So I will not talk about real systems because I've always been dealing with models. But I have an experience with models where essentially my intuition was right half a percent of the time. You could flip a coin. And in the end, the answer, the true answer was either yes, your intuition is right, or no, I mean, and these type of models are precisely of the type that many people have been describing. Many people are now describing in this this community. And when my work was more related to models of financial markets and minority games, but these are essentially resource, disorder system, very heterogeneous systems with many different agents essentially living on many resources. Of course, the models now that have been studied by Danny and others are more complicated because there is also chaos. But these are the type of models that my experience show you really teach you something. They can really teach you a new paradigm, a new type of how you should think in high dimensions. And I think from what I saw in the school, I see remarkable advances. It's a very exciting time to be studying ecological systems and high dimensional models in ecology, because I see models and ecology and experiments really coming much closer together than in the past. Great. Mercedes? Yes, thank you. Yes, it has been quite an exciting course and also one that gives rise to many questions and ideas. So on the question you just asked, I would say yes and no. Yes, because I think many of the models we have had in the past do not help us with the very high dimensional systems, but they provide a basis to organize some ideas and some concepts. And I think we heard about that, for example, in the context of the stabilization and equalization forces. There are very good reviews by Saavedra, by Barabas, by Dandrea showing that it's highly nontrivial to extend those ideas and we don't know how to do it to high dimensions. But yet I think the organization of, for example, the different kinds of traits that we have to consider that that sort of low dimensional theory illustrated was very useful. On a different point, I think I like to think, of course, about assembly in this eco-evolutionary perspective. And there, I think the question of when we say high, I think there are some discontinuities and that what motivates our studies, I mean, Daniel just mentioned the very interesting, of course, microbial systems with the strain diversity. But if we move from the microbial world to the systems that really have motivated us to look at diversity, the rainforest, the coral reefs, we are looking at hyper diverse systems. And if you add the intra-specific variation, it's enormous. And the network of interactions is enormous. And I just like to think when I think about pathogens, and I call them in my lecture hyper diverse, I like to emphasize that biogeography has done the experiments of assembly. And if you take certain pathogens where there is very high transmission, they are completely different in diversity than when you have low transmission. And I'm talking about continental differences and discontinuity in the differences. And when I say that is I say that because I think I will make I think the most important or to me the most interesting point at this moment. I'm deeply convinced, and maybe I'm wrong, but I'm deeply convinced at the moment that we cannot build hyper diverse systems at one level of organization without the very high dimensionality and diversity at the lower level from which we build it. So I think like the diversity of the traits and the genetic variation that underlies the ecological interactions has to also be very large in places where we assemble a large number of strains or species. And this is not trivial because then it leads to the question of what maintains this high diversity of the building blocks. And I think it's fundamental because I showed you an example in malaria where we know that if we drive the system down in transmission, there is actually a threshold at which we lose the ability of maintaining the building blocks. And I think that when we go from very diverse to the more trivial low transmission systems, we are crossing a threshold of that kind. And so I'm saying it's hyper diverse at different levels of organization. And this is not by chance. It's because the same force, the same selection is operating at different levels of organization. So I think that if that is true, we need to understand it because it's something very different for very hyper diverse systems that truly makes a distinction with the ones that just exist below this threshold. And anyhow, that is my pitch here. I think those systems are truly distinct. Yes, very clear. And Daniel, Segre? Okay. So I'll start by saying that, I mean, the kind of intuition I want to bring for something that guides the way I think about this, but also fails at higher dimensionality has to do with metabolism in my global communities. And in particular, sometimes you may find that if an organism is very good at using a carbon source, another is very good as using the nitrogen source, then you can think of the complementarities that arise in communities. But of course, the molecular complexity in real environments is much more complicated than this. And there are a number of molecules that contain the different elements and microbes that are very good at using this resource or that resource. And this economy of the molecules becomes really complicated. And I think one of the challenges that I see is that you know, on one hand, I think it's valuable and interesting to build detail models of each individual organisms and try to push that to the boundary of higher and higher complexity. But of course, at some point, this becomes too much because we don't have enough information, it's challenging in many ways. So the question I think is how do we find a good balance between the detailed models where we know how the metabolism of each individual organism works and the more, you know, distribution based models where we try to capture the general properties of how different microbes interact with each other. And I think that this is crucial because I believe that metabolism can be, first of all, as I said, very complex in rise to higher order interactions. But there is also the fact that when we want to study individual communities for all the different applications that microbiome research has, it could be this strain rather than that strain that makes you sick or this strain that can really produce the oxygen that can change the atmosphere of a planet. So the details matter for a lot of, you know, the reasons we care about communities that the details matter. So I think it's important to strike a good balance between the statistical properties of communities and detailed knowledge of metabolism. And the other thing that I want to say, even if I, you know, sometimes I like to hope that metabolism is really the driving force of a lot of these communities. And I think it is in many ways. But, you know, there are many other ways in which microbes interact that I think are so complicated and are barely taken into account into models from signals and form sensing, contact interactions, the interactions that depends on space and time. So I think this is all, you know, unexplored territory in terms of figuring out, you know, whether and how to take all of that into account. And I'll stop here. Okay, so it's now Justin. Yeah, no, I guess I would just say that, you know, a lot of the model approaches that we take are designed to ask very specific questions. And we have to simplify most of reality into these toys to be able to say something straightforward or to understand the models themselves, which can already sometimes be ununderstandable, as Mateo was saying. And I think that clouds, you know, that allows us to point in very specific directions and aim these tools to answer very specific questions. But it cuts out the reality of systems, you know, that the fact that there really isn't anything as, you know, we put these species into a node, or we say this node represents a species, but, you know, there's just individuals. And there's, you know, within the individuals, there's, you know, genomes, and they're all interacting in various ways over very complex environments that are ever changing. We might look at systems where we're considering only the biotic interactions between species, but, and those are complex enough, but then we think about the feedback that biotic organisms, you know, the biotic side of the equation has with the abiotic side of the equation, and that they're different within species, but also within individuals in terms of having an impact over both ecological and evolutionary time. So I think it's perhaps unsurprising that, you know, our models fall short. But as you add more dimensionality to some of the problems, it really expands the possibilities. And I often, you know, think back, you know, when we're thinking about organisms living in these diverse communities, some of the first diverse communities, we go back to the Cambrian explosion, what led to that explosion? What was it like before the explosion? And what was, what was the kind of instigator of the explosion? Was it the evolution of eyes, and suddenly opening this entirely new kind of sensory experience of the world that allows organisms to move through over, in terms of their evolutionary trajectories? I had a conversation with Charles Marshall at Berkeley, and he described this process as billowing lava, you know, underneath the ocean, like this changing niche space ever kind of expanding and evolving with the organisms that are using it. And, you know, I guess to me, that gives a sense of near infinite combinations of interactions that lead to this diversity. And, you know, again, I guess the last thing I'll say is that when we look at these model systems, we make these assumptions often of, you know, asymptotic time horizons and stability, but these systems are getting hit from every side all the time. They're in a constant state of flux and change, and they often disobey the various assumptions that we're making to be able to say something and anything about very specific questions that the models are appropriate for, but inappropriate for others. Thanks, Justin. There is a comment from Daniel Fischer. Yeah, I just wanted to comment on various aspects. Firstly, I mean, I certainly resonate very much both with what Mercedes said about the being, not strictly being a threshold for complexity, but somehow when things get complexity enough, maybe some sort of runaway to get it more complex, and if they're not, they're sort of stuck, and this maybe also relates to Justin and things early on. Just another comment about intuition from statistical physics and what it might tell one and what it doesn't. So I guess I would disagree with Jonathan. My instinct is that things like whether there are three species interactions or two species is something which is one of the details can change things, but it sort of won't make things somehow qualitatively different. But I think there are some things where the intuition from the physics is very bad, and that's particularly the sort of instabilities of systems to sort of runaway events, a pathogen that comes in, a new species that comes in does very well changing things dramatically. And then I think I mean Justin's comments about the crucial bits of being the whole system being very much dynamic rather than thinking of it as being sort of quasi-static. And then the other bit, and this is pretty relevant for coral reefs, but even more dramatically from the cyanobacteria, is one organism having a very big effect, or a small evolution we change in one organism, a seemingly small one, having enormous effects on everything. And so somehow, even if one wants to abstract out quite a lot of the details, there's still going to be some sort of dominant things and dominant interactions and so on. And I think again, I mean, I think some of those ones are some of the things that are hard-coming physics to get a grip of. I mean some of the details really matter, but I think the hope is that a lot of them don't if one knows what questions are, right? And if one set defines sort of the kinds of questions of being ones where you can apply them to many systems without having to redevelop everything, I think in those kind of questions I think one has reason for optimism that not everything will depend on all of the details. Jonathan, you want to comment on that? I mean, I think my comment is more a question of an empirical one than one that maybe is about sort of what is possible theoretically. I agree with Daniel that I think that it might not fundamentally change the rules. These might have to have some different expectations. But I guess what I really meant to communicate was just that we try and understand nature, the question might be how much do we need to actually incorporate these interactions that only emerge in diverse systems? And I just can be answered on that as I know. Whether incorporating them fundamentally changes the way we think about species diversity in complex systems, I wouldn't want to propose at this point, partly because we don't even know what those rules are. And I can tell you that for example, like I have a PhD student that's currently working on questions about what even are our expectations for how a three-way interaction or a higher interaction might modulate the dynamics of coexistence, and you get some really funny things. Now, whether there are any funnier than they would be if you had streamed together a bunch of pairwise interactions, I don't know if that's fair to say. But it certainly is something that violates what we have from the simple two-speed ecology that we focus on. So I think I basically agree with Daniel that I'm not sure there's actually a real sort of game change here. The question might be just how much do we have to incorporate these dynamics with interactions if we want to understand the dynamics of newer systems? Yeah. I think it could be now to turn it around and agree with what you said earlier, is it could be that there are some of these more complex interactions that are crucial that somehow sort of drive the environment that everyone else is feeling and everyone else is riding on top of. And so I think in that sense, it's some of the things which in certain ways it could end up being pretty crucial for a particular system. It could also be towards this driving towards sort of getting enough complexity that everything else can somehow complexify on top of that, diversify on top of that. Yes, Mercedes wanted to say something. Yes. This is called the issue of the dominant processes that we may hope to understand with models. It's very related also, I think with the issue of obviously what can we hope to understand with models in these very, very complex systems? And in my view, probably what I would call progress is if we can not really hope to understand these interactions in any bottom-up fashion that will be credible, because I think it's an impossible goal. I think ultimately if we can, for example, reject neutral theory and understand that we may be in a situation of niche construction that is the complete opposite, then I would ask, then how do we look at data to know this? How do we look at data to know how far we are from a threshold where we will not lose demography, but we will lose diversity? Those are questions that I think we can approach without understanding the mechanisms. We need to understand which microscopic properties give away the dominant forces. And what does that tell us? I think anything else is hopeless. I think we will never understand the interactions that have been built to maintain a rainforest. I truly think we will never understand them. But I think we will understand the consequences. We will understand the phenomenology. And I say this because I really like a paper by Mark Lipschitz, Pamela Martinez and others, where they see that they can predict the strains that respond to vaccination with considering the frequencies and certain forces that indicate that of the order of 3,000 or 4,000, non-core genes are involved in this. So what interactions are they creating? They are not even essential genes. They are not even the genes that define the strains. So they must be involved in a myriad of interactions. If we look at 3,000 non-essential genes and they give us some predictive ability just on the basis of frequencies, I think anyhow, I just think that we have to return to this question that, of course, neutral theory, the main thing of neutral theory was to show that the microscopic patterns we were stuck trying to study didn't tell us anything. They were not informative. So the question is which patterns are informative? And I think models will be very useful for this. So thank you, Mercedes. There is a comment from Matteo. Yeah. So if I may, I think this is a very important point because trying to understand the, say, stylized facts in terms of systematic deviation from neutral theories, I think because, I mean, my way of thinking of neutral theory is like a maximum entropy model. So a model that where essentially you cannot hope to learn anything about the microscopic interactions from the macroscopic behavior. So I really think this approach to address, I mean, as Danny was saying, I mean, how do you find what is the right question? I think this is a general approach that could be useful. Yes. One question, I guess, is whether neutral theory is the sort of a useful baseline for understanding the, understanding these dimensional systems. And if anyone wants to comment on these or on either other parts of what has been said? I think it's only useful in the sense that one of the questions is why do things end up looking that way. But they almost certainly won't look that way once one starts looking at the dynamics. But there are rather too many things that can give rise to distributions that look roughly neutral like. And you're roughly speaking, it's like assuming that all the physics is like an ideal gas, which is clearly isn't right. But it's somehow useful to make the observations and start looking at how things, what aspects go wrong. But I use the word neutral theory in a broad sense. So if you are interested in asking, I have a bunch of data on this very complex system, how should I look at it to ask not whether a process occurs, many processes occur, whether a process is dominant or important, even just important, then I need a neutral model that is the appropriate neutral model for that question, for that process. But you mean you need a null model? Yeah, yeah, yeah. I'm using it. No, I don't know. Thank you. Thank you for a different subject. I don't know. I agree. No, absolutely. But I think we can make progress that way because we don't even know. Look, the clusters, the clusters that are predicted from stabilizing interactions, they disappear in equevolutionary models at very high dimensions. So my point is, if we ask what should we even be looking at in data to say that that process is important, we don't know, but I think the models are useful there. Yes, with the appropriate null model. So Stefano, what would you say? Yes, I agree with Daniel on the distinction between neutral model and null model. And I think that the underexplored null model that is not neutral would be a model with random interactions as opposed to no interactions. And my belief is that by and large, they would produce the same results as a purely neutral model, but removing the need for these strong assumptions. Jonathan? Yeah, so I think Mercedes raises some very good points and the coverage is going in a certain very pragmatic direction, I would say. But I think the challenge and especially a challenge for theoreticians as an empiricist primarily is to say, well, you know, it may be that the only source of progress with these hyperdiverse systems involves some sort of null model statistical fitness kind of approach. But the problem is that many people really want to know why that tropical forest is diverse for some practical reason for managing that forest and so on. And the question might be how do we deal with that tension between what is potentially the most rational, quantitative way forward in a system with many dynamical processes that are communicating coexistence at some abstract level. And the thought that someone wants to know, are the monkeys dispersing the seeds across the component to the diversity that I observe in that forest? And you can't really answer that with a distribution or a null model. So I think there's real tension within ecology, but what we're actually aiming for within this understanding of diversity of these hyperdiverse systems. And the question is, you know, what is maybe the right approach? Or is there a meeting of the of the minds on that kind of framework is what I might Yeah, but I think there is I'm with you. But if you mentioned the monkeys distributed in the seeds, also, you are thinking about some of the the effects of the negative enemies that you can find in the major sort of stabilizing forces. Now, there is a more critical question. You may come to the conclusion and the most practical conclusion that if we want that that given the niche construction that is involved in maintaining that forest, the best we can do is not preserve the monkey is do what you Wilson is saying preserve, you know, parts of the the landscape for the for for nature. I think once you get to the point where you say this complex interactions underlie hyperdiversity, the only way to maintain it is to give it space and and leave it working at that because these thresholds of hyper complexity, you are going to lose them if you don't give if you don't give those systems enough. I'm going to call it abstractly space enough to essentially maintain this, this, this diversity and this level of complexity. And I think the interactions are so rich and have been built over such long time with pieces that that are built from eons of evolution, not the species, the pieces that constitute them, that if we that if we cross the thresholds to keep that diversity, we lose it all. I think the only practical solution, one of the components of a practical solution is not to ask is this particular thing important is like how do we save the the the system as a whole enough of the system as a whole and I think that the 5050 idea of your Wilson, whether it needs to be 5050, but I think there is something very real there and very urgent. Mostafa, yes. Yeah, I agree with Mercedes on the practical aspect, but I think that this is really like raising the white flag to some extent right like so so we're going back to a sense of like conservation in which we go back like to ancient texts and they say this forest is sacred no one can enter or only like the warriors can hunt in this forest or only like this period of the year if we can hunt in this forest, which is like saying because we don't really understand what is important but it's not important we just have to conserve the whole no I completely disagree I'm saying that when we get to understand it will be too late because we will understand that the only way to preserve it is to is to leave it to and I'm not saying pristine and don't touch it but I'm saying you are going to if you lose what maintains hyper complexity and I'm saying I think we have enough in theory in the theories that exist to begin to see that this is the reason it's not a white flag it's exactly the opposite is the realization of the very rich niche construction that goes on in these systems and and what how you can lose it right I agree on the practical aspects I disagree on interpretation but I agree with you that that's the best but it's not a white flag and it's not going back to the past it's like what is the theory tell us today so on this issue about the the pieces of the interaction and the building blocks I'd like to hear from Daniel Segre and regarding the building blocks of many interactions with instance in bacteria and from just in about the fact that then these building blocks of the interaction sometimes have like sort of underlying regularities and and that I made through skating so Daniel one thing I can say is right metabolism is what it is right it is a well-defined system it's the outcome of you know four billion years of evolution and and I think there are two sides of this one is that because of its underlying structure it it shapes the way microbes sense their environment and respond to their environment in a very specific way and I think that maybe and I really truly don't know I'm curious of you know whether ultimately we'll find that if you could build alternative metabolisms the the rules of the the way communities work would be similar but I but I say I think that there it is important and there may be aspects of this that strongly depend on the specific structure of metabolism the way it works and the other aspect of this is that which I think also is somewhere in between the extreme statistical nature of complexity and the extreme detail one which is that there are classes of bacteria and microbes that have specific types of metabolism so maybe we will not need to understand the metabolic capabilities of each individual organism but maybe having a categorization of guilds or or types of metabolic activities might be helpful and it's also true that people keep discovering new metabolic pathways new capabilities that were not known before you know things that seem quite amazing like new pathways for utilization of organic acids and people engineer new pathways there are newly engineered pathways for carbon fixation so looking also forward that at this you know rising field of synthetic ecology where we can try and build new communities based on what we know I think striking a good balance between detail and and the and the statistical nature of communities might would be important I don't know if this addresses your question and before I leave the word to Justin to sort of give another perspective on metabolic metabolism or metabolic theory I'd like to ask all the participants if they want to ask questions to please type them or raise their so Justin yeah I you know one of the things that really is striking to me and I think deserves a lot of attention is is how this idea of redundancy and systems and how organisms can adapt to fulfill similar functions as others as as they disappear or are replaced etc um an example of this is fruit dispersers in South America um fruit a lot of larger fruit was dispersed by larger mammals for example like the gompatheers and the avocado uh example and then when those organisms disappeared uh the dispersal of those fruits was replaced by it by humans and and then later by domesticated animals um and so we have like these these interactive interaction niches that change over time and are dynamic over time even within the you know the time scale of a of a species without including evolution these ecological plasticity that isn't really realized until the community itself changes I think uh I think understanding how these large uh diverse systems operate um in the face of disturbance um really is to some extent a product of what extent there can be redundancy um that may only be realized you know post disturbance um and so I think you know we our understanding of the dimensionality of interactions is often very simple um you know we we describe interactions in in one or two dimensions um and in reality the interactions themselves can be very diverse in their effects and change over time uh in response to how the system changes great yes this point about redundancy I think it's uh like sort of connected in some sense an alternative at least I see it like that but perhaps I'm wrong with what Mercedes is is saying about the i-dimensional function space and i-dimensional trade space right so if there is redundancy it means that somehow the trade space the function space is low dimensional and there are multiple way to realize a given function so I don't know if anyone wants to comment on these dichotomy whether it is a dichotomy or I think there's a there's a general question here also which is the how much complexity at the sort of phenotypic level and the interactions are needed to get a very diverse very diverse community and that one is not I think is not at all clear I think it's you know for example can it be that a rather small number of chemicals associated with a metabolism are really already sufficient um to get you a um of high diversity or simple features of pathogen host interaction is that already is that already enough so I think that's not clear I think the issue about somehow the redundancy it seems to be one part where there's an absolutely crucial but which is connected to all this is in the the evolutionary level the fact that there are very many different ways that an organism can do somewhat better in a given environment right and then for any ways it's going to change its sort of organismic um phenotype there are very many changes that it can do the possible genetic changes and then sort of at the nano phenotype level that can give rise to that or give rise to something close to close to that and that may end up sort of having consequences that there are always going to be different ways of replacing certain of the functions of that sort of redundancy but I think that's another one of those sort of you know big number of things that we don't understand at all that it tends to get way undemphasized and certainly game theory unfortunately does this is that there are extremely large number of possible strategies in a in a loose sense right and that that's a really important um um important part of the the evolution and presumably of the the ecology yes anyone wants to comment on this or another part I guess what may be one comment is that I think there is really you know this idea that functions rather than taxa ultimately dominate the uh community dynamics I think to me is really fascinating and uh and it is in the end about redundancy because genomes may have this mosaics of functions and how exactly these functions are coupled in different genomes is an outcome of horizontal gene transfer long-term evolution and so on so understanding whether there are um aspects of this that that have been optimized throughout evolution I think is very interesting and uh yeah I'll stop here I think I mean this is largely unexplored and still I think there is an experimental question there which I suggest to my colleague Michael first who works on on uh gut microbes that has these consortia of 60 gut microbes in the in the lab which he claims fill up all the niches now my other colleague Alfred's foreman says there's no such thing as bacterial niches and we can't think of it that way but I as Michael I think can you do an experiment where you take one of the bacharotes and put a lot of the other functions into it so you move a lot of the the operons that are supposed to be crucial of the niches filled by the other ones and is it possible that one organism can at least you know roughly fulfill um fulfill many do many of those functions all at once and then there's the immediate question is if you then let the system evolve does it immediately diversify in your the into a whole bunch of organisms that do them better each do them each do them better so I think there are some things that one could really try to actually do experimentally on that in you know moderately complex um um uh complex communities I think one of the other important things to consider is just the the importance of the constraints in the system um you know consider uh the rubisco protein and how little it's changed over so much time um you think really you can't think there isn't something better that that could evolve but it's almost this evolutionary kind of dead end obviously it's a very successful uh protein and doing what it does but organisms have found incredibly complex ways around to get around the constraints uh set by by carbon fixation um designing entire physiologies to re reconstruct early atmospheres to be more efficient uh within their tissues and you know I think a lot of diversity I think stems from uh the limitations in the system just having strong constraints and then uh many pathways around those constraints uh that different types of organisms have to follow and that might not have been the case if if there was always a better uh if there wasn't a constraint everything was following the same pathway towards uh higher and higher fitness peak and then each evolutionary accident is the which direction is taken constraints and opens up possibilities for all the future directions so anyone else wants to add something on this for someone from the participants if they want to ask a question since we have 10 minutes toward the end and nobody wants to ask anything so I I mean what one uh sort of direction that has been uh sort of a little bit explored in this discussion but perhaps can be unpacked a little bit more is a question that actually emerged during one of the lectures which uh is exactly related to uh to evolution and evolution of diverse communities so what are the conditions uh under which evolution produced these highly diverse communities so we we said these trade-offs and constraints so I don't know if anyone wants to comment on that and add something I'll say something I think this is actually a case where Mercedes is an original point that there are some useful abstracts from the two species case to any species that could be useful because if there is going to be some diversification it's going to be one splitting into two in a simplistic sense of the word I know it's more complicated and presumably those two do interact more intensely than they then each then they do with anybody else in that system and I think it's very interesting in the sense that we've very been very good at trying to think about this problem in terms of some sort of stabilization regulation of the coexistence that emerges from those two species that that that form but we've really not paid much attention to what comes out of some very simple two-speeds coexistence work which is that there's probably some competitive balance as well and and something about the need to think about that competitive balance axis at the same time as we think about the um the stabilizing niche differentiation if you want to call it that um axis is probably worthwhile and hasn't been done and you probably wouldn't have thought of that had you not gone through a theoretical ecology experience at some point in your and your career if that makes sense so interestingly you know it would have been so good if obviously on one axis of the problem and not really thinking about the other um and I think that's that's that really has a real gap in what we are approaching on this problem right now theoretically and empirically yeah I think I I mean I agree and I think the one of the reasons I sort of want to focus on on strains or two species with lots of interacting strains it's sort of the beginning of the of the diversification and one hopes that the one doesn't need all the ways in which many complex species interact with each other if one understands more some of the basic ones in which you know two species do and then what can happen um um what can happen within them and in some ways it's learning to walk before one tries to to run and I think you know my sense is we're still at a stage for to for understanding diversity and so on of really crawling right I mean we we we're trying to get up on our feet and sort of go some stumble steps um forward and I think there's where you know there's this luck and experience of various other things of sort of choosing systems and models and so on which might um go one uh make one go forward I think one of the really nice things from this school is it's become clear the sort of you know diversity of ways of uh of approaching these kind of problems even from people with relatively similar backgrounds at least superficially right and and of course a lot of things from different um um uh from different backgrounds these exchanges if one if everyone agreed on what was important it would be totally boring and we would almost certainly will be wrong well I think Daniel touched on an interesting question because we we either heard about species or we heard about strains because that's convenient and we are kind of avoiding the the sort of uh macroevolutionary question in a sense of how how do you connect the two and and of course that is very interesting because even in the word of strains uh what also evolves is the reproductive already the reproductive isolation in systems with incredible recombination for example there are groupings of genes for example that recombine more with each other and uh and some that are more conserved and so on so these building of the barriers even within for example pathogen strains that we assert and recombine it's not like a free for all and this uh we see this uh even at that level the buildup of of these barriers which I think is a very important part of this of this evolutionary process and I think it's another area we don't fully understand and it's you know how do we go also of course it's the old question going from the micro evolution to the micro evolution but and this uh that I think is a fascinating question because I don't think it's so this continues uh I mean you you also see it within strains sorry yes uh Justin you want to say something about these uh sort of macro macro evolutionary aspect and deep time uh changes um yeah well I I I guess um I guess I would just argue that um um that a lot of the energetic constraints a lot of the kind of simplistic perspectives that we put into how we capture um how interactions shape systems um they're they're at least we might be able to argue that they're better um when evaluating macro evolutionary systems uh because you're really looking at these big general trends and you've zoomed far far away from have the noise of ecological systems and I kind of coming from a deep time perspective I always am concerned about how much we're focusing on contemporary uh ecosystems um much much more than we tend to to look at kind of these average quantities of systems that the fossil record um averages out for us um and so in some sense kind of the the fossil record um and and the deep time perspective it's it's it's already isolating out some of the biggest signals um and to what extent are we trying to apply these very simplified models to noisier systems that are much more difficult to try to understand it's kind of like trying to predict uh where a molecule of gas is with um you know uh very the average gas law you know it's it's it's impossible um but but we do find I think um if you if we try to integrate more of uh deep time perspective and take advantage of systems that have uh been around for a long time and the average signals that the the signals that they leave behind which are which have to be averaged um we might be able to uh leverage kind of ecological theory um in different ways thanks a lot Justin anyone wants to add uh I think this is a macroecological perspective of a very different kind but um one of the things that I like to think of is the you know you can view microbial metabolism as a planetary phenomenon of course and and now from a very different perspective that sounds like science fiction but people look at the atmospheres of extra solar planets right in search for kinds of life and and the limit there is a lot of interesting research on you know non-equilibrium of chemical systems on these extras of our planets and I think that it's really interesting to think how um you know the overall chemistry at that such large scale with just an influx of energy from from light and given the the molecules that are present uh how does that link to the you know scale of microbial metabolism as we were used to think of and the microbial ecology side of this and and I think there is also room for what I think is a really interesting way of thinking about this in terms of just you know besides the details of the chemistry in terms of you know the flow of electrons um that that are kicked up by solar energy and and gradually find their way down to lower energy levels and I and I think there is a lot of potential for linking this large-scale theories of non-equilibrium biospheres to to the lower level microbial metabolism models I know there's a little bit out there but I think it's something interesting yeah great so we have all less than one minute so anyone wants to give some final thoughts or any question from the participants I use that one one comment I think is one of the things which often doesn't get into papers is really sort of struggle for all the group questions if you and certainly doesn't get into got proposed or discovered or at least they get rejected if they do have those things and somehow the writing sort of more things down about not just okay this is the question this is just my sort of struggling to try to make good questions out of these out of these very things and when things normalize about I've been meaning for a long time to get a series of talks I'm going called BioY something called BioX it's the answer they're called BioY with a letter Y but where it would really meaning the WHY and really trying to get people to talk about questions that they didn't even quite know what the question was yet and I think this this you know this discussion has been really good that way but it's it'd be really nice to people the community generally took effort to write such things write things down maybe collectively that would be fun Mercedes you want to say something or no I was listening for a while well there is actually one question from a participant Monday yeah yeah thank you so much the panelists for giving us the round turbo talk please I want to get a real tickle message regarding this intuition and modeling I is it that when you want to model you need to first of all have your intuition on what exactly you want to get or is it the other way around please I need I need a key tickle message so that I can get something and get it clearly from here thank you anyone wants to respond thanks so very much for the question I can only speak for myself but I when I start designing a modeling approach I usually think I know what I want to get and that often isn't what I get and it changes my understanding of what I was actually wanting in the first place so for me anyway it's a it's a method of kind of clarifying what I know and what I don't know and it usually doesn't what I think what I want to know when I begin doesn't match up exactly where I end up but that's just me yeah anyone wants to add something or ask a question great so if not I want to thank Stefano Daniel Jonathan Matteo Mercedes Daniel Segre and Justin for this very nice discussion I think we could go on with this discussion for other 50 hours and in fact we with Mercedes and Matteo we have decided to have a follow-up of this of this school which will be a workshop to be held again online in a month from now so we can sort of take a break from zoom and screens and I think all the participants will receive information about that and there will be a lot of space in that workshop to discuss about diversity and the limits to diversity assembly so with that I well again thanks to all the panelists I also want to thank all the participants there are now 60 people connected to this zoom and looking at the names I saw that most of the people actually attended like all the 52 sessions so that was pretty impressive and they really appreciated that I mean also the interaction with you was great and I'd like to thank beyond the lectures of this session all the people that lectures and gave talk during this school their contribution was great and I think there was a lot of material that has been put forward that could be available for many people that wants to enter in this field or understand what are the challenges and the opportunities for research I'd like also to thank the people in the in the sort of in the background that you probably have not seen I'd like to thank Monica Victoria and Adriana the Secretaries of this school and in particular I'd like to thank Massimo Mafione who gave the IT support and really stayed here for 52 sessions so and at the end I'd like to thank Matteo Simon Levin and Antoine for organizing this with me so this is the end thank you very much and now stay away from zoom for a while and I hope to see you either virtually or hopefully physically here in Priesti soon so thank you very much thank you thank you yeah thank you very much