 Conversations outside the talks are better than the talks, and I fear this talk will probably continue that trend, but Because I'm the only thing keeping you between a day of fun and And and lunch and everything else And I don't know if the group photo is something people are looking forward to maybe there It's more fun than my seminar for sure. I agree, but I thought that you know What I do is I'm a theorist And I'm a very much a very much theorist and I think I view myself as a provocateur So this is just gonna be a talk to provoke a lot of people. It's gonna make a lot of bombastic claims. You should take him You should argue with me. So having said that please interrupt me Interruptions are built into these things make arguments, but what I'm gonna try to convince you is that now that we're thinking about microbes We can start thinking and thinking about complex communities. We have to kind of revisit These kind of classical models of ecology and community ecology that were developed initially by people like, you know Hutchinson's Levin's MacArthur Among the few Tillman blah blah blah the list goes on But I've been I've found these papers about four years ago and they really transform my view of the world But also in reading them now in the present age I realized there were real limitations that we have to overcome and I'm gonna try to argue to you that statistical physics Can help us overcome these limitations and in particular what I'm gonna talk about today are essentially work maybe Okay, what I'm gonna talk about today are mostly niche based Models and these kind of niche based models that maybe the most canonical example of this are these MacArthur warblers And so these are these two kinds of birds and you know The idea was how do they coexist on the tree and so there was detailed painstakingly Observations and the idea was that they figured out that one of these kind of birds lived up in the leaves Oh, thank you One of these things lived up in the leaves and the other one lived in the beak on the on the bark And so the basic idea was that each thing had a resource it was best at consuming and basically the these red birds were competitively excluded from up here and the green birds were competitively excluded from here and Given if we take this as our central intuition then it becomes kind of tricky to understand how we get these very complicated microbial communities and So the question is how do you get something where coexistence is generic or what's not and when we don't do this so The next quote is my first provocation Which is why are we so surprised by cooperation and coexistence right and Chris Marx dared me to put Donald Trump in here So I put Donald Trump in here And and so I would argue that we're really influenced by the world We live in and the world we live in is a dog eat dog neoliberal world and in particular You know this there's this very famous Margaret Thatcher quote as you know, there's no such thing as society There are only individual men and women and what Margaret Thatcher of course meant was that we have to look at the units That we if you want to understand the whole the only way you can think about it is by looking at the units that make it up Right is this and it is very much this idea that what defines society and the whole is competition at the level of the individual And then you know this this is just a this is just a quote from Donald Trump about cheaters And and we can make of why we're obsessed with these things But I would try to argue that you know a lot of evidence suggests at least in the microbial world That it should be pretty generic and easy to get coexistence right at least every place we look and the question of course is why and So and so what I'm going to try to argue from argue to you is a style of modeling that is not bottom up But top down and that basically uses statistical physics and the basic idea is that maybe to understand these communities We don't want to start building them up one by one So Jeff Jeff is okay with this because Jeff gave me an office for my sabbatical So but but we do have these kind of very different philosophical world views about how when things become simple So that I would argue there's three. There's two different ways to make a problem simple One is to break it up into its little parts and look at what's happening, but in statistical physics We know there's another limit where things become simple Which is in the limit of many many many things interacting together Right, and this is because largely things become statistical and we can use things like the central limit there and so what I'm going to try to argue is that You know if we start from a slightly different philosophical Prejudices you get what you end up with slightly different kinds of models and these kind of models are good for answering different questions Let's say right and and maybe it's worth exploring this opposite view where you don't go from the bottom down But the top up so um So I would argue in the strong form that we kind of have to overcome this cartesian fallacy We can't understand the community function by just understanding how the individual parts function in isolation And that secondly organized organisms modify their environment. We've seen that throughout this conference I think that's been a running theme and can transform the statistical structure of this environment And this is I'm going to argue This is especially true in the microbial communities because there's no trophic layer separation in the classic sense that you see in classical ecology and Finally, this is something Simon also did at the properties of large ecosystems with many species cannot be extrapolated from small Ecosystems because I would argue because of you get new emergent properties that come and especially this kind of environmental structuring so So Again the goal of this talk and I'm gonna show you Experiments that Albert was gonna dwell on a lot more, but there are experiments that end of all this bobbling Which is the goal is to build theoretical models where we incorporate the organism as active subjects in its own Construction of its own environment and a lot of these ideas are not mine. They're written by this very famous famous pair of evolutionary Ecologists and evolutionary biologists who have influenced my thinking more than anyone on this field And I will constantly refer to rich dick Levin's papers throughout this talk But I found this book quite quite provocative and quite interesting So here is essentially the outline of the talk We're gonna start and again the goal is gonna be to try to revisit these classical models in Theoretical ecology, but think about them in large ecosystems So we're gonna introduce to you some these classical niche paradigm of theoretical community ecology I'm gonna introduce you to the model that we're gonna study Throughout with many many modifications to try to make it applicable to large and microbial thing Which is MacArthur's consumer resource model And then I'm gonna show you how we are trying to basically turn that into a staff Mac model instead of thinking about MacArthur's consumer resource models with one or two species and one or two resources We're asking can we analyze it in the opposite limit where you have many resources and many species and then the last part I'm gonna tell you how if you incorporate cross-feeding You you you can get very generic thing you can almost Guaranteed coexistence and I'll show you some experiments at the end that Seems to suggest this might not be as crazy as it seems So so let's start with some classical paradigm of theoretical ecology or niche based theories And so Again You know theoretical ecology is an extremely well-developed field the papers are just absolutely brilliant I'm kind of sad. I didn't read them into until I was in my mid 30s But you know One of the defining things is this kind of niche theory which is the theory of competitive exclusion as I explained to you before The basic idea is that things compete for resources and everything has to be best at something And I think the most the simplest version of this and the probably one of the most influential is Tillman's r-star theory Which basically says that every species Basically has to be best at utilizing some resource in the environment and the experimental You know observations of these were largely developed using very macroscopic things birds trees grasses. This is a picture of some famous Experiments with grass that David Tillman did out in Minnesota. These are called the grass experiments They're quite influential in the 80s and the central intuition again that I want you to keep in mind Is that the number of species is strictly limited by the number of the limiting resources in the environment? And this is of course because of competitive exclusion Well, of course, it's not true. This is why yeah, go ahead No, I did ask for it. No Agreed I Resource is in the very general. Okay. I don't know I mean when you read Cheson or you read what the modern synthesis They they like to use a resource in a very general term like the ability to avoid predation. This is part of what I found I mean, no, I'm trying to give the simplest version of this, but yes, I agree with you if if if the primary mediator of Ecological interactions is the consumption of resources then this is this is absolutely temporal inches spatial inches Every every kind of thing that's going on So we're gonna think about these experiments. We're talking about we're trying to mimic steady state and where we're gonna do this of course, there's a Like I said very rich field. I'm giving Some caricature because I want to say even within niche based theories I think these kind of these kind of intuitions are quite quite limited it No, I agree with you. I'm not trying to bet All right, so so again, I Promise you this is really the only equations that are going to be in this talk But the basic idea of MacArthur's consumer resource model is Basically, you have some resources and They're consumed by each species and species have different preferences for different resources and the idea is that your growth rate It's just proportional to how many resources you consume weighted by some energy at minus some minimum cost You need to maintain yourself and the resources themselves can have some dynamics, but importantly, they're depleted from the environment So this is this is just one of the standard models that's been used and what's interesting Is that in the limit where the dynamics of the resources are quite fast? And they don't get eliminated you can show that this reduces exactly to these lot double-terra Equations that Jeff was using. Yes. Oh, yeah, there's tons of things that ignore. So this is No, no, God, no, it's a type zero recent response function as they say this is the dumbest model you can write down Everything independently eats things and they're all generalists Right is dumb is dumb dumb models don't mean they can't give you insight and that that's I mean No, no, it's not realistic at all and it's not meant to be realistic. I think that's that's kind of its purpose Right and the important point I want to point out is there's this contact concept of niche overlap Which basically says the more in these kind of models There's purely competition for resources and the basic idea is that the more similar the resources you want to consume are The more you compete with each other All right, so that's what I'll mean niche overlap. I you can assume. I know nothing to a first approximation except for what? Yeah, but I don't I that seems circular to me, but okay, maybe maybe maybe So the way I think every I don't know way the way I've seen it in the literature now I'm just getting scared There was that everything is gonna be wrong But I'll keep on pretending I understand ecology and telling you my interpretation of ecology Which is the physicist jumps in three years ago reads a bunch of papers and synthesizes it probably wrong interpretation of community ecology which is So so I you know There's these kind of Graphical ways to analyze these models that people are really interested in and what they are and the basic point in all this kind of stuff is If you look at it, you know one thing you can look at is the niche overlap here Which is how much things two species compete and so the way they do these things is they basically analyze these models in these Situations where you have one or two species and ask what happens so here, you know This is the kind of kind of phase diagram. I would call it in physics that you can get so here on this x-axis You have niche overlap how much they you know compete for the same resources here You have basically intrinsic fitness differences and the idea is that the bigger the niche overlap is the smaller The region of coexistence right the more similar the fitness of these species have to be so over here Species to exclude species one here species one excludes species two and in particular if the niche overlap is zero That means they occupy independent they consume independent resources so they can always coexist If the niche overlap is one they compete for exactly the same thing and you always have competitive exclusion Right, so this is this is kind of what's going on and there's another version of this I won't tell you which is There's a way to that this picture is exactly the same as that picture But the thing you want to take away is that species must I mean the end goal of all this way people have Summarized is that species must compete with more with other members of its each species than others Right and on another way of saying it is each species must have its own limiting resource so And and I want to emphasize that most of these intuitions when people say things like this They basically analyze these things using two species or two resources. There's very few works I look through everything where you don't have well mixed Things that I could find we want to do this in the large large thing limit so So I want to point out what I think are the limitations of thinking about this way for the current paradigms of microbial community ecology And the first I think is one that's also experimentally true it's not clear that intuitions from few species scale up to complex ecosystems with many species and You can have the emergence of new behaviors and for those of you because there's a diverse crowd There's this one of the great theoretical physicists of the 20th century. Oh, he's still alive Phil Anderson, but wrote this amazing piece in science more is different Which is essentially an essay arguing about emergent properties and the basic idea is the constructionist Hypothesis breaks down and could when confronted with the twin difficulties of scale and complexity the behavior of large and complex Aggregates of elementary particle It turns out is not to be understood in terms of a simple extrapolation of the properties of a few particles Instead at each level of complexity entirely new properties appear and the understanding of the new behaviors requires research Which I think is as fundamental in nature as any other But the basic idea is that you can't understand the whole by understanding taking apart the pieces and then putting them back together And so the question is how much does that hold even in these classical simple dumb model? Which is the MacArthur consumer resource model, right? If I consider many many species and many many resources The second I think important thing is that niche-based models Often focus on a single trophic layer so they think about you know all the herbivores But you know microbes they don't each eat other animals They exchange small molecules that produce and eat them and so niche-based models assume a trophic layer separation That's no longer true in the microbial world. You really have Generically the thing is that you're not eating other microbes You're eating small molecules and I'll try to convince you that completely changes the intuition that we kind of try to implicitly hear it from these things Yeah Okay, but I mean that small molecules diffuse far there Okay in well-mixed cultures, right? So if I grow something in liquid culture, no, I agree with you So the question is how much geography I have nothing to say about geography at the moment Even though I live next to Carol, which is really really depressing, but it's true But yeah, I agree with you. So I'm not gonna tell you about spatial structure I'm gonna think about the dumbest model and show you even in the dumbest model things changed dramatically is Is what yeah? Yeah, right so viruses are different layer, right? Yeah, no, I agree with you. So it's a viruses and bacteria is a classic trophic layer separation So I'm gonna just go to think about all the bacteria in in a thing. I agree with you Your statements are all correct. Okay, so the first thing I'm gonna show you Oh, I'm doing okay on time is I'm gonna show you some work that we've developed with Madhu and Vani At Harvard who's mostly a neuroscientist But it turns out these techniques are things across things and Guy Buhnen who just started at the Technion and he's Really he's really he's really a smart physicist thinking about this stuff So if you if you're in Israel, you should you should look him up. He's really good And so the basic idea now again is that there's actually two regimes where things get simple One is when I consider small number of things But the other thing other place where things get simple is when I have many many degrees of freedom And so what we're gonna try to do is analyze this stupid model not in the limit where I have two species and two Resources, but where I have infinite number of species and infinite number of resources and I fixed the ratio between the two Right and this is what goes by the name of mean field theory in physics But I've been told an ecology mean field theory means something completely different from what it means in physics So I'm not allowed to use that word Okay, someone told us it means something completely different. Okay, so the idea is again, right? This is just drawing from a Gaussian distribution You see eventually everything looks like a Gaussian if I start drawing numbers and that's because I have some kind of Simplicity when n goes to infinity and so the price you pay is you talk about micro macroscopic quantities like pressure and distributions Instead of thinking about individual things. So if I want to describe a gas of particles I can't tell you anything about the position, but I can still tell you about Macroscopic quantities and the question is can we do something like that in ecology? Where I can't tell you anything about any particular species, but I can tell you about macroscopic quantities And so the basic idea is going to be again. We come back To this, you know, you know, you we come back to this kind of thing and we basically draw Consider the case where the number of species and the number of resources is extremely large and then we just draw All the parameters I need lots of parameters So I just draw them from a random distribution and this is something that may introduced already in ecology Almost 40 45 years ago, right? So I'm gonna draw these with random matrices and the hope is that I'm studying typical ecosystems And so in order to understand what's really a result of biology as opposed to what's a result of you know Some very detailed biological interaction and what is a result of just having large diversity Communities we have to understand what you get for free for just having large dynamic, you know diverse communities where everything is drawn randomly and so The quantities that we really turns out we're gonna care about is this kind of growth rate I'm gonna replace this whole thing with a growth rate and what I'm gonna do here is say that the resource has some effective caring capacity So I have some baseline caring capacity that I would have in the absence of all the species and what happens is the presence of these species actually just Changes this to some oh changes this to some other number and the important point for all our observations Is that this growth rate is a sum of many many many terms and this caring capacity Effective caring capacity is also a sum of many many many many terms and so what we can do is We can say the growth rate should actually be well modeled by some Gaussian distribution Because it's a sum of many many many terms and the effective carrying capacity should also be well modeled by some kind of Gaussian Approximation it turns out to be a truncated Gaussian for technical reasons. I'm not gonna tell you about and What we're gonna and for the physicists in the thing This is a two-step cavity method for self-consistency things. It's used in spin glasses and it's been used in Hufffield model and compressed sensing It's actually quite a technical calculation But the basic idea is I take my ecosystem and I throw in a new species and I throw in a new resource And this is an argument that Levin's and MacArthur were running already in the 60s But now you ask self consistently. What's the probability? It's gonna survive and Since every species is the same as every other species in a random ecosystem You can self consistently solve for means variances and things like that And so let me show you what happens what I want to show you is that you draw these kind of coefficients from different distributions so you can draw them from you can draw them from a binomial distribution where the ci alpha the Consumer coefficients are binary. You can draw them from Gaussian distribution And you can run numerical simulations for all these nonlinear PDEs or you can solve these kind of self-consistence Equations and for things like the fraction of species that survive the fraction of resources that survive The mean number of the mean abundance of the resource the mean abundance of the resource the mean abundance of the things Any statistical quantity you can come up with you can actually calculate that analytically which was very surprising to us because these are a bunch of nonlinear PDEs that are coupled and So what we can do Yeah, I mean odys odys odys not linear odys. No, no, I just said the wrong thing All right So, you know, I'm not going to show you all the calculations and technical things But one of the interesting things that you find once in that once you go to a large ecosystem You can generically ask Are the properties of the isolated ecosystem different from when the things are there? And so on the left-hand side what I plotted on the x-axis is the fitness of a bacteria if it was introduced into an ecosystem by itself and on the right and on the y-axis is its final abundance if in the presence of everyone else And what you see is there's some correlation which we can calculate analytically But there's a bunch of stuff. That's high fitness that goes away. There's a bunch of resources that go away There's even things that flip sign And so what you get is generically even though you can say something about the whole ecosystem By thinking about things in isolation Actually, the ecosystem is sufficiently engineered that you can't actually make the correlation you get is about point six Right, so it's true that good things on average do better than good. That's great, right? And Other things do badly and in particular there's things that it turns out that you can you know You can you can have things that have you know that won't survive without the environment that do survive when the environment's there And all these things but all these things about environmental engineering when I was thinking about this got us thinking a little bit more About how we can modify this for the microbial world, right? Because here the only way you can change the external environment is just by depleting resources But imagine how much more dramatic the environment on engineering would be if I also produced small molecules, right? So before Before going on I you know I just wanted to argue that what we did is on a technical level We have a way of doing a statistical mechanics of this MacArthur consumer resource model We can match all these simulations analytically which kind of shocked us and the properties of I said of individuals in isolation can differ Significantly from those in the complex ecosystem and the practical Implication of all this and I'm going to try to convince you is that we always want to build things By characterizing each individual part But maybe they function very different in the whole than they do in the individual and that's true even this dumb model Where the interaction where it's been chosen to minimize the interactions between things, right? This is the best-case scenario for non interacting things so So what I want to do is now talk about how we're extending this to microbial communities and the stars of this kind of thing It are Josh Goldford who's Daniel's student will help me with who did some of the experiment started the initial experiments Has done all the analysis and then see who's sitting somewhere in this thing who's been doing all these experiments in Alvaro's lab And so what we've been now thinking about is You know as I said before there's no clear trophic layer separation bacteria eat small molecules Not each other Not each other's and of course bacteria killing each other also releases small molecules and so what we want to ask is Cross-feeding means microbes construct their own environment and implies we no longer can think of organisms in a fixed external environment And so we have to think about how they change the environment in other things So if this is quote I like the incorporation of the organism as an active subject in its own tonnage And in the construction of his own environment least of a complex dialectical relationship between the elements of the tribe of the gene environment and organism And I think we've always kind of neglected the environment and so even in these models We've kind of neglected the environment and so what we can do is We can just take the original consumer resource model Where everything just competed and just add a simple term that says that when you consume things you also produce things Yeah, absolutely Yeah, I agree, but I think it's impossible to avoid that in the microbial world. Whereas you get out But usually you just focus on our trophic layer, right? That's the way I read the literature No, no, of course the question is is it the okay? The question is can we make a reasonable ecological theory without taking into account environmental engineering? Which a lot of these kind of chase labeled and all these kind of guys they kind of assume fixed environments and and and and and and and so okay my only point okay, I agree with I Don't know philosophically all I can tell you is we took this model We've never seen this done and we just added one little term that says in addition to consuming resources. I can produce resources right and You can just here. I'll just show you simulations, right? So you take you know kind of these things and you put them in a single externally supplied resource and you ask What happens so in the absence of cross feeding if you have a single resource in the environment You get a single species surviving in the presence of cross feeding as soon as you allow cross feeding Generically no matter how you choose the random matrices no matter what you do as long and you enforce some energy balance It seems to be that you can have very complex communities living on a single resource It's a it's a generic it seems to be the norm and not the exception as soon as you even allow a modicum of cross feeding a tiny bit of cross feeding right and more out more over if you you know look at the results the Structure of the community is shaped by the external resource. So for example here what we did is we just for each community We took the co-co Coefficients that it consumes CI alpha weighted by the number of things there and we just did some dimensional reduction And what you see is that resource a kind of clusters here resource be kind of clusters here Resource see kind of clusters here if you look at the consumption rate of the resource You know it kind of you know if you put it in resource see you consume the metagenome It's much more likely to consume see just very obvious stuff But you get these kind of things, right? Yeah, yeah In this thing is just in these resource types. They're all pretty they're just random They're just randomly chosen everything is random. So all that all that's true Is that the species different species have different coefficients for consuming resources? Oh here? Oh, no no here It was if you put it in an environment with resource see then you enrich for things that each see that's it This is just a statement saying that I throw a bunch of species in randomly that some of them will survive that in the surviving species I Am obviously if I'm in environment if I put in resource see I'm enriched for things that have That can eat resource see here. It's saying I here I took all my things and through them Right different communities in three different resources a b and c So each one is a different simulation each each little point in there different species survive in each simulation because because it's all done randomly and then you ask What's the structure and the structure you see is that is That you things group by resource Otherwise the same They're just randomly drawn. I mean there's some distributions. We're drawing everything from it. Yeah, they're all the same everything is the same This is the no model right everything is the same everything is random. How much of biology can it explain? Yeah Okay, so It's a species I can consume resource alpha and produce resource beta. That's what what I added Before you couldn't produce a resource So now I take resource alpha and I produce resource beta and I have to enforce energy I didn't feel like writing the full equation. I have to enforce energy constraints on all these things But it's not that you're just pumping in more energy to the system. No, they're not they're not any different They're not any different No, you just can consume things and produce things and they are the stoichiometric coefficients of how many of alpha do I eat and How many of beta do I produce? That's it. That's all this But then I'm looking for steady states right there's some dynamics associated with this So resources can get depleted resources can get produced and you do this Huh, I don't know. Maybe I can explain to you afterwards material I'm not I'm not quite sure but all I want to tell you that if this is zero then I only get one species surviving And if it's not zero, I generic they get lots of species Alright, so Alvaro is going to tell you all about these experiments And then she has a poster that you should go see but you can ask, you know the The claim should be that our known models shouldn't be that it's really hard to get coexistence on a single resource But it should be really really easy if there's cross feeding and so you you know They did these experiments that they'll tell you much more about but they basically isolated this leaf and soil samples all around Boston New Haven You basically passage them for 14 days hunt 80 to 160 generations Grow them on many many many many carbon sources. This is the list single carbon resource things Alvaro again, and she will tell you much more and you can ask what happens and I'm not going to dwell on this data But what you should see is that all these things have lots and lots of color in them And that means that generically what you have here are some sugar sources Here you have some relative abundances and what you see is it's indeed true that generically in these communities that you isolate You grow them on a single carbon source in M9 media and You do get generic coexistence. It just seems to be generically true Right and Alvaro will show you all of the experiments Nancy's poster has all the little things checking everything and all that stuff I don't feel comfortable, but the one piece of other data. I'll show you is Now you can just basically take we do 16 s sequencing so that we don't have a true metagenome But we can use this essentially this pie crust program But any other version of this where you take the 16 s map it to a species ask what genes it has in it And so this is essentially some proxy for the metagenome and you can ask what happens You can do some dimensional reduction on it and you see indeed again the metagenome segregates by What resource you put in so all the glucose communities here These are eight, you know eight many many communities from many many different places They all go here all the citrate communities go here, you know all the leucine communities go here and indeed you're enriched You know in a community where you're in you know in leucine You're in drip, you know you're enriched for leucine degradation and it's exactly like our model that actually had no biology in it at all Right that was just drawn randomly Everything was drawn randomly so you could make a very deep biological story of what what's going on this interaction that interaction But you seem to get this kind of structure for free in large communities Right at least that's you know all the provocative stuff is my ideas I'll rose probably gonna get up here tomorrow and tell you that I'm full of you know I'm completely wrong, but that that's my take on how I interpret his interpret their data, right? And so What I want to tell you I mean I'm out of time and this is what I wanted to tell you is that you could take this Classical model from community ecology the consumer resource module Which would tell you that it should be very hard to get coexistence you put a little bit of cross-feeding in Any small amount and what it tells you is that actually no no no coexistence is completely generic and so and It leads to qualitatively different behaviors and the reason is that in this cross-feeding model You can't separate out the organism from the environment you're taking into You're generically incorporated the idea that the or you can't talk about organisms without the fact that change the environment they live in and So you know one way of summarizing this is bacteria construct their own niches and need to think about the environment and species Together on equal footing and we actually have a much more if you're interested in ecology It's very a rich place We have way of putting thermodynamics into all these models so we can ask if I put a total amount of energy into this Models what can happen? We have intriguing results that suggest that thermodynamic efficiency that you can partially order steady states based on thermodynamic efficiency There's tons of stuff you can do with these things and they're all with random models Right, so there's a lot of structure that emerges when you consider large models even when you choose everything randomly and That's something you know we should kind of know so here are the acknowledgments you know and So Madhu Advani helped me with this first part, which is this technical cavity calculation Josh and Nancy who's over here, and you should really talk to did You know the second part of the project is really theirs Alva is going to tell you all about this tomorrow and Carol helped us make the model better I wrote a really crappy version of this model and Carol fix it for us Daniel as always Is is one of the most artistic and interesting people to have as a colleague it's a real pleasure and these people gave me a lot of money Thank you very much