15:05:27 All right, thank you for sticking around at 3pm. 15:05:31 When it's beautiful outside. 15:05:34 So, I am tasked with giving an introduction to modeling community ecology and microbial ecosystems. 15:05:41 And that is a very daunting task, but I thought I should lay out my philosophical prejudices on the table before we start, because I don't think there's a single right way to do things. 15:05:52 There's just people who are good at modeling in various traditions and people who are less good. 15:05:59 And so you should just know. 15:06:03 Like, how this works. So just so you know what why I think maybe I don't have to convince this crowd but what what I find interesting is this is a quote from Sydney Brenner. 15:06:13 It's a really a one page, thing he wrote about touring, Alan Turing when he died. It was like some retro retrospective of him, explaining what Turing's contribution to biology were. 15:06:28 And at the beginning this is like the first paragraph. He has this kind of quote that really stuck with me, which which kind of I'll read it to you, it says technology gives us the tools to analyze organisms that all scales, but we're drowning in a sea 15:06:41 of data and thirsting for some theoretical framework with which to understand it. 15:06:46 Although many believe that more is better. History tells us least as best we need theory, and a firm grasp on the nature of the objects we studied to predict the rest. 15:06:57 Yeah. 15:07:04 Well, he was full of, I think, as he got older, he was full of these, it might be this one or it might be another interview with him but yes these are these are these are the kinds of quotes that Sydney Brenner was producing at the end of his life which 15:07:16 is kind of very funny because he was really a card carrying biologist right and a brilliant one at that. 15:07:22 The second thing that I made might be that I you know that's just generally something about theory and modeling in biology. I think the other thing is, those of you know me know I can't give a talk on ecology without registering my comrades. 15:07:35 One of them who just passed away last week. 15:07:40 Unfortunately, Vic Levin's, but anyway they have this book that's dedicated to Freddie angles, who might have gotten the details wrong but got the big things right. 15:07:48 And in it, you know it's a book from the mid 80s that had at least on me a lot of influence. 15:07:54 And I think their basic point was that modern biology is very very much, driven by what they call a Cartesian framework, something that based on the car but the whole idea is that we have to think about taking about relationships between things more seriously 15:08:12 instead of trying to break things into parts, just a part that's, that's what dialectic means in. 15:08:18 I wouldn't get killed by the philosophers, but that's, I can't figure out if it has more content than that and everyone tries to convince me it does but as far as I can tell that to the content of that the word dialectical that and sounding smart at left 15:08:30 wing parties. 15:08:33 Anyway they have this kind of funny, funny quote that I like to throw around which says that we have to think about the incorporation of the organism, as an active subject in its ontogeny, and in the construction of its own, the cooperation of the organism 15:08:48 as an active subject and its own and tagine and in the construction of its own environment, leads to a complex dialectical relationship of the elements in the tree I try out of the gene environment an organism. 15:09:01 And I think that has got to be really the goal. How do we understand the relationship between gene, which is the level of evolution, the environment which I think is often in modern molecular biology been neglected right like it. 15:09:14 you know, we spent a lot of time making model organisms, less time making model environments. 15:09:22 And, and, and, and of course the organism and. And the interesting thing about ecology, to me at least, especially, is that 15:09:32 it says do not raise all the way so you're gonna tell me when to stop. 15:09:38 Okay. 15:09:39 Do I have to hit the button again. 15:09:44 Nope. 15:09:44 Okay, good. So I'm done with my slides, because it's 3pm, on, on in the middle of the week. I thought we could slow things down a little bit and I try to do everything on the blackboard, and I don't know how I turn off the projector is there I just unplugged. 15:10:02 All right. 15:10:04 So I just wanted to. 15:10:11 Oh I got moved to Monday or Tuesday, and it is essentially was just going to be for the kids to try to understand how to write some Python code how to code up a simple consumer resource model, how maybe you can use the simulations to, you know, help guide 15:10:30 guide things it's just a very basic like we wrote a package, it is just essentially a rapper that Bobby around OD 45 and a very elaborate way but it makes it easier for many experimentalists to. 15:10:43 It just makes it easier to, you know what I mean you don't want to go into the weeds, the same reason I love Python and I hate see, like, I remember when I became a postdoc with Casey Casey, basically did everything for me because I just didn't know how 15:10:54 to do anything. So the difference between me. I don't know if Casey still does always coding, but like, back when I, in the old days, you know, I just wanted someone to write me a high level function in case you would like go worry about how memory was 15:11:05 being segmented. I don't know if those days are over. it makes us feel old. Doesn't it anyway. 15:11:10 But the point is that the point of that package is just to put a wrapper around OD 45 and, and it's just going to introduce some basic ideas about that. 15:11:18 So today is just going to be essentially none of my own work at all, but it is going to be a lot of my own prejudices, in the sense that I'm trying to curate to you what I think is one of the richest theoretical traditions, outside of physics, which is 15:11:33 this theoretical tradition of ecology and then particular community ecology. And so the outline of the talk is here. 15:11:42 You know, I'm gonna start with some introduction, some fundamental questions the intro is going to have a little bit more about what the purpose of models are some fundamental questions that people try to address in ecology, then I'm going to get to consumer 15:11:54 resource models. I think these two things are almost certainly going to be skipped because we're going to run out of time, which is the relationship to lockable Tara models and consumer resource models and when and when you can't think of them as optimization 15:12:09 of some objective function. And, and the relationship deliberate off functions and all this kind of stuff that's maybe slightly more technical I don't know what the audiences. 15:12:20 And then finally, I'll talk about how you take this kind of classical ecology. And I think this is something a lot of physicists have been involved with lots of people in this room have been involved in, you know Michael lots of people in this room, Michael. 15:12:33 Step. Everyone, how you can take these people have started to take these consumer resource models that were largely developed in the context of large macroscopic ecological theories you know rain forests coral systems, and try to adapt them to make, you 15:12:50 know, Casey just showed you a beautiful example of this and and and have used them. What do you have to change fundamentally to try to adapt these things to the microbial setting where I would argue, things like the relationship between environmental 15:13:04 environmental organism are much more fundamentally intertwined than one often sees in classical ecology where maybe one just studies a single traffic layer and ignores the interactions between things. 15:13:17 Alright, so what I'm going to tell you, essentially, as I said, it's a huge field to have one hour and a half I gave myself an hour and a half because it's the ICP. 15:13:28 And what I'm going to tell you a broadly speaking is about. I'm going to focus mostly on, which is what is niche theory. 15:13:37 And it's not because it's the best one, it's the one that I find most appealing. And this was largely, I think it has its origins and the work of Deke lemons and Robert MacArthur. 15:13:54 You know, 15:13:55 in a series of papers in the 1960s right so just a series of very very beautiful papers, while worth reading. 15:14:03 Many of you who might have seen me in the last 10 years probably have gotten my zip file of classic ecological papers that I was sending around when I got really excited about this like, seven, eight years ago. 15:14:18 And, and since then you know there's been of course a lot of developments know field. Stand still. 15:14:23 And, you know, there was a big contribution made conceptually by Tillman who's at Minnesota. He has a very influential book called competition and community structure that came out 15:14:39 in the early 80s. 15:14:42 More recently, there is actually like you know kind of two competing schools, though I as a physicist and outsider don't really see what the antagonism between these two schools is, but there's basically a very influential review by someone called by 15:14:56 Peter chessen, which is in 2000, if you haven't seen this it's kind of interesting. It's called, it's the annual review of ecology 15:15:06 and systematics, and you can find it because it's been cited a lot on Google. 15:15:11 And there's another set of books by chasing labeled. 15:15:18 That's called ecological niches, which is a lot about how you can use graphical methods to understand these things so I'm just I'm just putting these because I think it's hard to find reasonable references and useful things. 15:15:32 But these I would say will get you a long way towards understanding stuff. I should also add a lot of this talk is based on a review that I thought would be done by now but that I am writing to try to summarize this up from my own eclectic perspective, 15:15:47 with one ping who may be somewhere in the room over there and my former student and Arvin who's sitting next to him because my friend, Anatoly Pull, pull club Nick officer actually organizing the next program told me every review is better if you have 15:16:10 smart outside critic, so I enlisted him as someone who knows nothing and will tell us everything is shit. So that's his job. He's been fulfilling it well. 15:16:10 So, so hopefully that reveal will be done in a month or two and a lot of these ideas will be written I have some early drafts if people want to look at some of the sections and tell me they're all wrong I'm happy to send them out to you. 15:16:23 Alright. 15:16:26 So, These are some major references. 15:16:29 So, let me now 15:16:33 start first with 15:16:37 what we're trying to do, right. So, if I look at an ecosystem, a rain forest, a microbial community, a coral reef. 15:16:47 At first, they seem to have nothing to do with each other, right, because if you look at any organism, it doesn't really look the physiology, these are all different. 15:16:55 A biotic environments are all different. Everything looks completely different. So what does it even mean to have a theory or a model of community ecosystems. 15:17:06 And I think the goal of all this kind of theory that I'm going to tell you about is to focus on what I think as a physicist I would call universal ecological processes. 15:17:16 So I'm not sure they ecologists would like those words, but there are certain ecological processes that seem to occur over and over again that shaped the systems, no matter which ecosystem you're considering, in particular, right and if as a former condensed 15:17:32 matter theorist I understand this well you know there's electron exchange there's anti firm magnetism. Basically all the world of materials that you see around you come from a few kinds of interactions you put them together you get this plethora of things. 15:17:44 The hope is to do something similar for community ecology. 15:17:47 Right. And so the goal is to kind of think about how do we lump these things that are clearly very different, what's common about them. Right. 15:17:57 And what's different about them. You also don't want to ignore all differences. And so this poses a big problem for models. 15:18:04 Right. And mathematic go modeling models theories, whatever you want to call it. 15:18:11 And so you have to think about, no model can be perfect no theory can capture everything. So you have to think about what the trade offs are in how you think about these things. 15:18:21 And so again I go back to comrade Levin's, who has, who has this kind of like very amazing paper it's the first paper in his origin, ecology and fluctuating environments, be compiled it in there, she has this famous book called ecology and fluctuating 15:18:39 environments in the first paper is this thing it's called the strategy. 15:18:45 It's worth while reading, especially if you're a student I think of model building 15:18:54 in population biology. 15:19:03 It's American scientists 1966. 15:19:12 Right. And, and the reason it's kind of interesting is because he basically lays out three basic kinds of models. So he basically says that, you know, you gotta have three axes along which you can function, one function is a one access is something which 15:19:30 he calls generality, meaning that the results you're going to derive or something that aren't just applicable to the say the particular system you're studying, but are applicable more generally, right, so this is something about results that can be inducted 15:19:45 Lee used on other things. Another thing he talks about his precision. 15:19:52 Lee used on other things. Another thing he talks about is precision. So this is really the statement about whether you're going to make quantitative predictions, very, you know you're going to measure things and how well you can make quantitative predictions or are you just trying to 15:20:03 make qualitative prediction. Right. 15:20:06 And the last thing he really talks about is realism and by realism he means how many of the kind of realistic biological processes. 15:20:16 Are you incorporating in your model, and there's always a tension between in any model between these three axes. 15:20:23 Right. 15:20:33 So he basically starts. 15:20:37 I think I can do this. right. 15:20:40 Sorry. So, and so basically there and you'll see all three classes of these models in in the paper in the projects, especially the students that are doing here. 15:20:48 And so the first thing you can imagine, is that you sacrifice generality, 15:20:57 To realism and precision and. 15:21:02 And so these classes of models are basically things where you say you build some very mechanistic model of a particular process, you try to really fit the parameters, and you try to make predictions on the short term, Right, so this is one class and modeling 15:21:19 and it can be done. Well, or it can be done poorly like every class of modern and this is something like, I don't know if we're doing is going to talk about parameter estimation, but this is, you know, maybe something like that to some degree or maybe, 15:21:31 you know. 15:21:33 And the point is that you don't really know how to induct what you learn about a particular system you fit it well you don't know how to go out to other things so for example I'm going to talk about nitrates and right so there may be something like the 15:21:44 stuff, you know, SEPA has been doing is falls into this class the second general thing you can do 15:21:53 want to say anything, and it always scares me in a physics audience. 15:21:59 The second general thing you can do is to sacrifice. 15:22:08 Ah, 15:22:12 realism to generality, and precision. 15:22:16 So, I would argue the best example of this 15:22:21 in population biology is actually population genetics, where you sacrifice, all the realism of biology. 15:22:29 Right, for selection coefficient, but you can make very precise coefficients, and it's applicable quite generally. 15:22:37 Right. 15:22:38 And and, but it's not very realistic, I would argue in any sense that it captures anything. In my opinion, much real about the actual underlying biology. 15:22:49 Yeah, good. 15:23:06 Do I think it there's specific to population, biology, I think it's always like, you know, the Ernest Mayer thing that like bio every biology is different, right, and so I think maybe realism in biology involves more abstraction than it does in physics 15:23:30 or it might be just that we have 600 years of physics, and knowing what the right thing to abstract is I don't know is the. 15:23:30 For some reason, he or you would argue that population biology is distinct from know biology or from. 15:23:39 There's some aspect of say numbers that you think is important. I don't think so. I, yeah. Ben Ben's gonna question about what were we mean by realism here, I feel like in, in, in how it trades off with with precision I feel like in physics we're used 15:23:55 to the idea that okay you can write down some effective model that great precision doesn't really make sense to ask whether it really embodies the ball. 15:24:04 So the idea is that you make this approximation which is nonsense, which is that the world is frictionless, but you can still get very general predictions and precision about it right like we we ignore friction in most of what we do because we think that 15:24:29 affects average out things don't matter for most of the things we care about. We assume things are near equilibrium, to linear response when they could be very far from equilibrium, you know, and in that in that sense it's not realistic that that's the 15:24:38 kind of thing he has in mind. 15:24:42 I don't want to get into real semantics thing but we make crude approximations in physics, often, and they, we still when and why that is maybe other people can say about i'm not i'm not sure but I mean it's true that like, you know, there's a reason 15:24:58 Galileo, you know, was so revolution was so revolutionary right yes I'm imagining a world like you're trying to understand these transitions by writing down a civilizing model we know the eyes and models and what we're actually modeling. 15:25:09 Yeah, somehow, that's okay. Yeah, I would say that's probably in the last class. 15:25:16 And that's the, you know, and the idea is we sacrifice. 15:25:23 precision 15:25:27 to general ism 15:25:31 and realism. And here what we're saying is that rather than to make quantitative predictions, right. We usually make qualitative predictions. We want them to be general in the sense that we don't want the answers of the model to change if we change any 15:26:00 settings right. And so, um, I would say what you were saying about the theory of phase transitions is and land out theories much much closer to the third one, then it's the second, I don't know, I'm trying, I'm trying to tell you that models are hard. 15:26:13 There's just no fucking, there's a free lunch. 15:26:17 You got to make some choices. 15:26:19 You just better know what your choices are I guess that's the point of it and I think this dichotomy I've found to be quite useful when I think about what I want to do when I want to model something, usually falls into one of these three things. 15:26:29 The purpose of my model. Yeah. 15:26:36 I would say niche theory, which I'm going to talk about is the most successful theory successful example of this kind of thing is I think it's been quite successful conceptually and making predictions, but kind of in Pooh poohed because in the, I would 15:26:50 say sociologically in the 80s and 90s. They became much more concerned with conservation, much more concerned with like managing habitat and clearly this, if you want to say how big should I make my habitat how many patches Should I make so that my elephants 15:27:05 don't disappear, or if I want to predict exactly how much the temperature you know how the temporary if the temperature rises two degrees you know what's going to happen. 15:27:14 This is not that useful it's just going to tell you, stuff's going to happen right. 15:27:17 And so I think sociologically, there's been a shift much more towards one at the expense of three. And I would say it's all ecology, in my opinion has suffered for it. 15:27:31 area and then our. 15:27:33 Okay, or I meant to say it the other way. Sorry. 15:27:39 Fine, but them I think one important thing we need to address is really what, what are the goals and what are the data you have to work with, because the parent and the What is he doing well in what is precisely one, one person is not precise or not and 15:27:58 And especially in this field and I'm coming from a cleaner world of microbiology, simple kind of microbiology and we did this heterogeneity. 15:28:24 going on or what is trying to explain. Right. It needs to be discussing contents of data. 15:28:30 It does need to be discussed in the context of data. 15:28:33 I agree with you because that was the first slide that right we have data, the use of theories to interpret it. I agree with you I'm just saying, depending on the data you have and depending on your goal you might want to go down one of these rights routes, 15:28:45 and you should just be aware that different models have different purposes. It took me, I know it sounds so stupid but it took me a really long time. I think I understand that from dead, like, when I became a postdoc is the first time I really learned 15:28:58 to look at data, that would be like, scroll down and sideways let's collapse it like IB I created that all to net right like I came from freakin high theory, the high end quotes. 15:29:14 Very quotes very. And I never even thought about connecting to the real world and then I showed up at Ned's group, and he's like showing me like simple models but he can collapse like read data in a way I've never seen before and that's, I mean yeah i 15:29:25 agree with you i mean i, it's almost second nature to me because of him. 15:29:29 I would say all credit to Ned, and, and, and so yeah i agree with you, you have to think about data, but your data is collected it may be difficult to any of this. 15:29:40 Right, I think you actually have the best chance at three because it's not really about data, because you're not trying to be precise. 15:29:58 Okay, how do you oh yeah i agree with you i mean i i don't have I don't have answers, I can just say in my own thing because I don't collect data. 15:30:07 I refuse to do that again following that I refuse to go open up my own lab. 15:30:16 So because it's hard, that's the main reason. 15:30:24 I don't know if that agrees with me but. And, and, and so I think what you will have to think very carefully what I would agree with is you have to think very carefully about what your model really predicting what it doesn't. 15:30:34 You can often fool yourself into thinking your model is actually being tested when it's not being tested at all so that's where I would say but you know theory has to exist independent of data in my opinion, you have to abstract, I guess I'm not from 15:30:45 the Rockefeller school that way temptation to build general purpose models but it's okay, but I think isn't getting to continue this Okay, can I comment on that because it seems to me that the one you 15:31:00 were done with intro. 15:31:04 I apologize. 15:31:08 All right, Let's get the equations. 15:31:10 But before I get to intro equations. There's also questions. So, these are you know I wanted to say what what are the questions that most people are interested in in this thing. 15:31:21 The first thing people want to understand is community structure. 15:31:25 Right. So what's the goal of these models. The first thing is to understand community structure, which is you know something, and community structure can be anything its diversity, which is, you know, a measure of, it can be richness. 15:31:39 It can be anything you can basically measure about the abundances or relationships between things and it's not well defined different people use different things there's huge debates about what's going on but people would like to have a sense of how is 15:31:51 the community structured. The second thing people like to do. 15:31:56 And Avi told me that he is, he's squirms every time he reads, he hears this. But the second thing people would like to understand. It's something about ecological function. 15:32:05 And what function means is very unclear, it's often in the eye of the beholder but you often have some property of the ecosystem you care about. 15:32:13 And you want, you would like to understand it. 15:32:16 And it could be something like how much biomass there is something else. And the final thing you want to do is often understand how these ecosystems respond to perturbations. 15:32:31 Right, so I would say most of community ecology is organized around understanding these things and often the relationship between these three things right. 15:32:41 If I more diverse. 15:32:43 And I'm perturbed in a certain way am I rub is does my function change or does it not change whatever the function I care about. We just saw a beautiful example of this in Casey's talk. 15:32:52 So these are the kind of I would say the three organizing kind of questions that most people are concerned with community section, a community college. 15:33:01 So that's what I wanted to say here. 15:33:04 Right. 15:33:06 And 15:33:10 I forgot something here in my outline, but this is what I would say, we're going to focus on. And the next thing we want to think about is, as I promised you through to be, or 2.5. 15:33:24 It's something about what processes are we seeking to capture with the comp ecology, but what ecological processes are generally important. Yes. 15:33:35 Yeah. 15:33:47 I think that's in the eye of the beholder it's an open research question is what I would say in all honesty, we know that this communities I structured we'd like to characterize them we have to decide what's important. 15:33:58 You know, they've running debates on what each of these things mean I'm just saying these are where the questions for the questions are measuring given some way of thinking about structure. 15:34:09 What is it, I don't know maybe people have better things than me whoever I mean Michaels read a lot of ecology, but my feeling is that people in the ecological community, don't actually agree on what these things mean, that's, I mean I don't know what 15:34:22 you want me to tell you I'm just trying to give an overview talk to a bunch of people about what what's what's going on. Yes. These are all ill defined. 15:34:29 But we kind of know what we, we kind of know a question about community structure when we see one. 15:34:35 Right. It's like pornography we know when you know when you see it like it there's a question about this. All right. 15:34:43 So what are the ecological processes that are important and all this stuff. 15:34:50 Right. And here I think the best review, trying to do this was actually a recent review by Mark beland. 15:35:21 I think is worth reading, and it's called a conceptual synthesis conceptual synthesis and community ecology. 15:35:25 As the quarterly review of systematics which I'd never heard of, but apparently exist, or really review. 15:35:33 Quarterly Review in biology, it's a different channel in 2010. Okay. 15:35:39 So while we're 3d, if you if you want to if you want to think about if you want to like actual coherent, maybe summary of what how ecologist themselves view this field I would say this is the best thing I've found, and the basic processes that are involved, 15:36:00 that people like to think about is what I would call in and what they do is they often make analogies with population genetics, but I think that's where the organizing principle is the first thing people talk about is ecological selection, which is basically 15:36:16 intuitive idea of how fit is an organism, born in a given environment. 15:36:28 The second thing just like in population genetics, you can have selection. 15:36:32 You can also have drift stochastic city. 15:36:38 Right. And these are just random effects that are important. 15:36:42 You know demographic noise environmental noise, things like that. The third thing that is central to all these things, process that is often really important is dispersal or immigration. 15:36:55 Right, so you have, you saw a little bit in Casey's talk again you have some regional species pool you have some other community things migrate in things migrate out. 15:37:00 And the fourth thing that ecologist usually also talk about a lot, but I've never really quite figured out why it's 15:37:16 put in is something they call speciation by which they mean evolution. 15:37:21 Right, so just like evolutionary biologists pretend ecology doesn't exist but they have to throw a bone in its way ecologist also pretend evolution doesn't largely exist and throw a bone in their way by listing speciation and all there. 15:37:41 things and I would say real equal evolutionary theory doesn't exist as far as I can help. Maybe people will disagree with me. So how does this all work together so here's my first equation. 15:37:49 And now we're just gonna have equations, after this. 15:37:53 Right. So it's worth thinking about what the structure of these models, often is. 15:38:08 Okay. 15:38:09 We're trying to put that up let's see if I can manage to put this up. 15:38:18 Oh, good. All right, So what is the structure of these models. so imagine, you know. 15:38:25 Imagine, I actually just imagine some kind of communities. Right. 15:38:30 And I have some communities, and I'm going to pretend you know I'm going to label them, they're well mixed on some scale on this community. So I have this is basically what's called the metal community framework. 15:38:42 Maybe I have some global pool. 15:38:46 Things can migrate here. So these are kind of well mixed communities, and the kind of structure of the models that are considered a niche theory, basically involve kind of a couple of fundamental variables. 15:38:59 So I'm going to often, right. 15:39:03 And IA as the population of species, I 15:39:14 environment. 15:39:16 Right, so the idea is that you have. This is just you take this little matter community, this little Team A, that's the population. In addition, what you often have are some kind of environmental variables, which, you know, which you can call whatever 15:39:33 which out through an abuse of notation I'm going to call resources, but really it's any environmental variable, and you have kind of these environmental variables at different places, and you kind of you know this is some kind of environmental variable. 15:39:57 Environmental a. 15:39:58 So now, I think the most general kind of model that people like to think about is I think about the change. 15:40:09 And the abundance of species, I in Section A. 15:40:15 And you can kind of say, This thing has a growth rate 15:40:23 that look depends on the local state of the environment. 15:40:27 This is the selection, this is what is often met my selection. 15:40:34 I mean are you know that's a leftover leftover notation I'll change that I try that made it didn't make it through this thing, right, plus some integration term 15:40:49 right this is immigration. 15:40:53 And then, often some demographic noise term, which is kind of a stochastic, the term. 15:41:04 So this is kind of, you know, something that would be familiar, even from evolution, it is actually borrowed from evolution. But the interesting thing about niche theory and I would say a lot of ecology is as was emphasized before. 15:41:21 You have to really think about the environment where you go on there's a question from Norah on zoom. 15:41:24 Go ahead. 15:41:26 And I hope you can hear me. 15:41:29 Thank you also for giving a lot of background, I don't have a nice background so I enjoyed hearing ecological theory. 15:41:40 And I'm wondering if, like the these models started out from a micro micro biologist, I don't know whenever I read ecological papers I. It seems like they weren't considering bacteria Rosie's. 15:42:00 Um, yeah. So, 15:42:05 yeah, I didn't mean to cut you off I'm sorry, ya know, so most of the stuff did not start off in microbiology at all, they were very much thinking about big macroscopic ecosystems. 15:42:15 And I think the goal by the end of this tutorial review is to show you how many people in this room have contributed to trying to just make little tweaks of these models, but somehow they fundamentally change. 15:42:30 I don't know, fundamentally, they qualitatively change some of the intuitions that people normally have about these kind of models, would say that, you know, they were largely developed to think about, you know, birds, eating rabbits, eating, you know, 15:42:50 eating, eating grass. 15:42:52 I mean that's the kind of thing that we're thinking about. 15:42:55 I don't know at least that's the that's what I saw in the old the old of reviews. 15:42:59 All right. 15:43:02 So the second thing of course is that you have, you know, the second thing that makes this kind of interesting, and kind of different from evolution is that you also have to think about what's happening with the resources themselves, and generally what 15:43:16 you can think about is that these resources 15:43:24 messing up my variables of a vector RA, like this, so they have some dynamics of some kind, independent of what the species are doing. and this is usually called the supply. 15:43:44 And then, the whole point is that the presence of the species themselves modifies the resource thing, a resource dynamics so this is usually this usually goes under the name. 15:44:00 You know this Q, alpha, a. And 15:44:06 So this is called, and these are going to these kind of general things are going to play an important role so this is usually called the supply. And this, in ecology is usually called the impact. 15:44:19 Okay. and here I've written it linearly and the species abundances but in general, you can imagine having a much more nonlinear term. 15:44:36 I mean, 15:44:39 yeah. Okay good, we get we can put it on for good. This is the most general thing, and no one gets all this model. 15:44:40 Nothing least have a life are going to drop the label a. 15:44:47 Right, as usual, as models too hard, right, we can't ever treat. Okay, well maybe we can. It's a rare Feat. When we can treat all ecological processes on equal footing. 15:44:58 So what different theories end up doing is they end up choosing certain processes and emphasizing those. 15:45:06 Right. And niche theory, largely is a theory of selection supply and impact that ignores stochastic city and treats immigration in the most superficial way like you just have a big pool and things can invade. 15:45:29 There's other another very prominent theory that is the equivalent of tomorrow's neutral theory, which surprisingly wasn't written down until 2001 which is called Hubble's new theory of neutral biodiversity, which ignore selection completely ignores resources 15:45:45 supply and impact completely, and just focuses on stochastic immigration. 15:45:51 And if you are interested as a physicist, there's a nice review by the part of our people buy a most marathon, and these guys. 15:46:00 I think I have the reference somewhere here for niche theory, which is this kind of this. If you want to understand a neutral theory which I'm not going to talk about, which is basically a theory that completely ignore selection and just focus on drift. 15:46:15 You can look at this kind of nice red blob is 15:46:23 2016. 15:46:26 And it's a veil at all. I think the last author is Amos maritime I don't know if he's the last author he's definitely on there some years on there, a bunch of people, it's worth worth reading it so this is neutral theory which I'm not going to talk about. 15:46:40 All right. And of course there's interesting questions about if I turn on stochastic city and I have selection Do you continuously go over from something, don't go continuously over we wrote some papers on there. 15:46:54 Do we claim their space transitions, without. 15:46:56 I mean, it seemed right to us in the particular model we analyze, but there's all kinds of questions about how you what happens when you turn on multiple of these processes. 15:47:06 And of course, what do you have competition between two of these processes that are both strong, we understand things much less than we do. 15:47:11 both strong, we understand things much less than we do. If we just focus on one. 15:47:14 Yeah. 15:47:25 Alright can depend on and I just put a demographic noise there I mean you can you can put anything. It's a D squared at this just looks like demographic noise I look honestly this is 15:47:41 not a black hole I want to get into is this is like this is not a good. 15:47:45 I in fact because I'm going to ignore this term for the rest of my talk so I definitely don't want to. I definitely don't want to go into this thing right so I'm going to focus on niche theory which is basically, Roughly speaking, 15:47:59 this 15:48:02 right so that's what niche theories about. 15:48:04 All right, let me, let me, let me now send this up and get this down. 15:48:14 So I think we're done with ecological processes. 15:48:19 I'm doing okay on time. 15:48:21 So now let's think about how we start analyzing these. Right, so the most famous example 15:48:32 of these kind of niche theory, kind of 15:48:38 models are these classic models that were largely developed by Levin's and MacArthur, which are called consumer resource models. 15:48:48 And in a consumer resource model. 15:49:01 And 15:49:01 you kind of have this, you make a bunch of simplifications even compared to there. So the first thing you kind of do, is you assume, and I'm going to drop this a index because I'm only going to consider one well mixed population because that's generally 15:49:16 how it works. I, I'm gonna drop. I'm going to say that the interactions the growth rate of a consumer only depends on what resources are present there. 15:49:31 That's the first general approximation that the thing that dominates growth is not some non resource mediated interaction, but it's actually primarily driven by resources. 15:49:44 Right. And this turns out to be competition for resources. 15:49:49 I think in the microbial world this is actually probably much more justified, than it ever could be in the context of which the context in which these things were developed originally. 15:50:00 The second thing we're going to do 15:50:04 is, again, we're going to simplify this, at least for the course of these things. Again, and just focus on an impact vector that again. 15:50:17 Just depends on where in resource space. 15:50:21 You are right, so this is impact 15:50:26 is resource dynamics. 15:50:33 Okay. 15:50:34 And so, what a lot of consumer resource models have been interested in is asking about. 15:50:42 If I throw a bunch of species into an environment, when can they stay busy coexist. 15:50:50 Right. And what's interesting about all this stuff is you can do it all with graphical methods. You actually don't have to solve any equations. 15:50:58 And that was kind of the inside of Levin's that was built upon with Tillman, and why these things are so robust. So let's ask, you know, on this simple question. 15:51:09 So, let me let me give you some examples. Right. So, a lot of stuff that you're going to do in for the students are going to do your classes is going to be about how do I model, you know these kinds of functions here. 15:51:23 What do the resource dynamics look like in the absence of consumers, you know, can they be serially diluted. 15:51:31 How does the growth rate depend on resources. Can I measure model this with a Nicholas Menton equation are different things. And there's you know there's kind of different names for these kinds of things there's called type one growth type to growth but 15:51:44 essentially, you know, you want to ask how does the growth rate depend on our, and there's you know kind of linear response function so you can treat it like it's linear, you can kind of treat it like a Nicholas Menton equation which is basically something 15:51:57 that looks kind of like that, you know, and you'll see very many different kinds of versions and depending on exactly what you want to model, you're going to change how this goes. 15:52:10 but their stuff you can say that's independent of all these choices, which is kind of interesting. 15:52:12 And that's what I'm going to focus on in this in this tutorial, and hopefully you'll get experiences and see how people make these choices, otherwise. 15:52:21 All right. So, imagine. 15:52:26 You know, I have to resources. 15:52:29 So there's certain objects that pop up all the time. Right. And what I'm going to do is I'm going to imagine, 15:52:40 asking, What can all these species coexist. So there are certain objects that are really important in all these ecology and the first one is the concept of a zero growth. 15:52:53 No client. 15:52:54 So if you ever see this. 15:53:01 It's often called the zg, and I. 15:53:04 And this is kind of really interesting, it's just basically the idea is that if I look in resource space. There's a set of resources for which gir or species AI is going to equal zero. 15:53:20 Right, so it just says what what combination of resources. 15:53:24 Do I have zero growth. 15:53:27 Right. And in particular, one often thinks about this in two dimensions but like you see that the first thing you can say is that in order for species to intersect. 15:53:43 The zg and eyes of different species. 15:53:51 Must intersect. 15:53:53 Right, because in order to add one of my coexist I mean coexist at steady state, because that's what niche theory is largely concerned with. 15:54:01 Right. I know that for the species to exist. Basically they all have to have zero growth rate. And so these things have to intersect, and that sounds like a trivial statement, but it actually gives you the competitive exclusion principle, all at once, 15:54:15 because if you think about it, if I have, if I have an ecosystem with. Let me call them s resources. 15:54:25 I mean, species. And I have a thing with resources with em resources. 15:54:31 You see I have is functions 15:54:36 that are variable of that our function of em variables. 15:54:40 So generically, unless you do something clever like Ned did 15:54:46 generically, you are going to have at most. 15:54:52 You know, the number of species that survive as star always has to be less than I am because generically you can't have more than that many functions intersect. 15:54:59 Yeah. 15:55:01 Yeah. 15:55:08 00 I messed it up. 15:55:12 Oh I messed it up. Thank you, did I even copy this out of a book. This is like my Princeton biophysics club, zero net growth. I saw Klein, I don't know. Okay, ZNGI, oh yeah that makes much more sense that sounds much writer. 15:55:27 Thank you. That's much better. It looks much right here, to continue my good grammar. 15:55:39 No, absolutely not. 15:55:40 Absolutely not. 15:55:44 In those cases, nothing I can tell you about stability of the, the US criteria, if I can tell you some open questions so we're going to get to some open questions very quickly. 15:55:53 It turns out in more than two resource dimensions we don't know, obviously the stability we only know it, they only have proof or two resources. 15:56:01 So we don't know right but in theory, if I have only two resources I can tell you. 15:56:05 Yeah, he had a question. 15:56:18 Alright, so, so let's say I have a stable set of case species. 15:56:23 What is there some obvious, simple conclusion I can make about any subset of those case species, will they necessarily, you can graphically, maybe maybe I should go to a real example and then you can see how it how it how it works. 15:56:40 You can sometimes, depending on the shape of these lines right so the whole idea is you draw the shape of these lines on a plane, and then depending on what the shape is you might or might not be able to say something I have something I have an example 15:56:52 in a second, that tries to explain this. 15:56:57 The second thing you can realize is that this is the statement that if I want all these to be zero. And I don't want an AI to be zero, they all have to intersect. 15:57:06 That's the first statement. The second statement 15:57:10 is a little bit more, non trivial and it gives you a lot of geometry is the statement is that if this is zero. 15:57:17 Right. Let me call this the supply vector, evaluated at this intersection. 15:57:24 Right, so I have someplace where they intersect. 15:57:27 That's a potential stable point and I can evaluate the stable, the point, the vector here, evaluated there so that's my supply at that steady state. 15:57:37 Now look, geometrically at what this thing that's geometrically what it says is that the ends are all positive. 15:57:47 So it says that this supply vector has to live in the cone spammed by these impact vectors. 15:57:56 I'll make this less clear become more clear for you at, hopefully I'll make it more clear not less clear but with an example. 15:58:04 But it's the statement, the second statement is that, in order to have coexistence. 15:58:09 The supply vector must lie in the cone span by the impact factors. 15:58:16 I'm not going to write that all that down because we're into an example. 15:58:19 And the third thing which again gets the bends question which is an open question is that that just tells me there's a steady state where all these things can coexist. 15:58:27 How do I know if it's stable or not stable, and you would think the answer would be no. 15:58:34 The answer as far as I know, someone correct me is completely unknown outside of two dimensions. 15:58:40 In, in two dimensions, the answer is the impact of each species, must be biased toward the resource that has more impact on its growth rate. 15:58:50 So, meaning that you should consume or change the resource that limits his growth more than all the other resources. 15:58:58 If you can show that for every species. 15:59:02 Then you can also show in two dimensions and only tool resource dimensions, but as many species as you want. 15:59:09 That is also stable. 15:59:12 In general, when we run numerical simulations I can just tell you, it seems to be true in arbitrary dimensions. 15:59:17 As far as we can tell, but there's no proof. 15:59:21 There are no in five if you don't have not to the third statement I don't think there's a non counterexample there there's places. 15:59:32 Yes. 15:59:35 Know the rule for when it's unstable rule for what it's unstable. Yeah. 15:59:40 Yeah. 15:59:49 Yeah. if I perturb the species abundance a little bit. 15:59:53 Will it will it stable. 15:59:56 As a fixed point of the dynamics. 16:00:05 Are you. 16:00:15 Yes, I mean it is, we can get chaos, or 16:00:23 no I agree, I agree with you i mean i'm just saying like you just know that fixed points unstable and the dynamics have to end up somewhere. Alright, so let me do an example of how this works. 16:00:36 Graphically, let me do a couple of examples. 16:00:38 And then I'll talk about the microbial world. 16:00:47 Okay. 16:00:51 I'm sorry, give me these review lectures I was talking with Daniel is torture you never know if you're talking above everyone below everyone, you should be going faster you should be going slower you should be emphasizing everything so I tried my best 16:01:06 I 16:01:06 tried my best to span. 16:01:09 Some, some whole in this in this, in this in this, in this space. 16:01:18 So let's do an example one, 16:01:24 which is the classic MacArthur's consumer resource model 16:01:29 car. 16:01:31 Where's consumer we source model. 16:01:34 So MacArthur's consumer resource model is essentially DNIDT goals, some, and I time some growth rate. And the idea is that you have a bunch of generalists that can eat a bunch of resources. 16:01:54 Extract so basic idea of this thing is that imagine having a bunch of resources, 16:02:00 each species is basically defined. 16:02:16 That tells you about how much things will grow. 16:02:19 There are some maintenance costs which was talking about yesterday or some death rate at which species die. 16:02:21 RDCI beta which are their consultant consumption coefficients, how much do they eat of each resource, the resource has some weight. 16:02:26 And this you can lump in or not lumping is basically something that's, you know, a species specific thing that says, How do I convert convert the energy. 16:02:36 I consume into a growth rate. 16:02:40 Right. 16:02:42 The second thing, because, again, this wasn't about the microbial world that MacArthur was they were talking about. 16:02:51 Right, is that you imagine that in the absence. 16:02:56 In the absence of being eaten or anything else, whatever resources you have are going logistically right so this is like maybe bunnies are eating or anything and grow logistically. 16:03:09 It's usually some other thing you're predicting something. And then, the point is now I have to think about it impact. 16:03:17 The impact vector is basically I deplete these resources 16:03:25 by consuming them. 16:03:31 So, what's interesting of course about this is now I can write down. 16:03:40 Zero growth, no clients or zero, no growth ZGZNG eyes, zero net growth is the death of me. 16:03:51 That's me. ZNG eyes. Right. 16:03:54 And we know that the ZNG eyes of this thing are essentially going to be straight lines, right, this is essentially by set this equal to zero. It's a straight line and resource space so I draw. 16:04:11 And I have two resources, but a special case where I have two resources. I draw this thing, and I can get two lines so this is a species one. 16:04:22 And I think I have color. 16:04:28 And I have species to 16:04:34 go. 16:04:43 This is just for the resources imagine there's rabbit, that are imagine there's grass, that's growing. 16:04:57 That's this equation, that's the resource depletion right. 16:05:02 This is just the growth of the resource, independent of the depletion. 16:05:09 Yeah, it's a it's not externally supplied it's just a self renewing resource that has logistic growth. 16:05:15 Right. Yep. 16:05:18 Is that I do something wrong. 16:05:23 Yeah, yeah. These are the bunnies. Right. 16:05:27 These are the grasses. 16:05:29 Okay. 16:05:32 No, it's just a two traffic layer system to traffic layers. 16:05:35 Right, bunnies. Eat grasses, grass grow to some carrying capacity. 16:05:42 The bunnies kill the grasses, it's more like sheep. I guess sheep and grasses, I don't know, 16:05:52 let's see I mean what why don't I will I'll get to mythical creatures soon like. 16:05:57 Right. All right. 16:06:01 So, they says resource one and resource to I draw these things. And already The first thing you can figure out from this thing is that actually this region here, the inner convex Hall. 16:06:22 Right. 16:06:22 What's going to happen is you start off with some resources. 16:06:27 And they're going to get depleted. 16:06:30 So I start anywhere I start off with some initial condition. 16:06:35 I start off with some resources somewhere, and they start getting depleted, because they keep getting eaten things start growing. 16:06:43 And eventually, I will never get inside this region here, because things have stopped growing. 16:06:52 Right. And it doesn't matter, Casey coming back to your question since I have more chalk, I can say, depending on how these intersect. Right. 16:07:03 But if I make something like kind of like this. 16:07:09 Right. If I imagine have a third species that does this. 16:07:27 You know that at least on an ecologically unenviable sense, this is not somewhere that can be a stable fixed point because if I allow a small amount of immigration it's not on the inner hole and then the feasible region becomes this inner convex, If you 16:07:28 can go through these things. If you can measure these things that you can do it it's not it's not super thrilling but it is what it is. 16:07:36 So, this is the first thing I'm going to come back to my simple example of two things. 16:07:42 This The first thing you can say, and now you know in order for these species to coexist, they have to sit at this point right here. 16:07:54 And now you have two vectors, which are here, these kind of impact vectors CJ, right, that basically tell you, in which direction or the species depleting the resource. 16:08:10 Right. 16:08:12 And I can do some math but I'm a rough time so what you can show. 16:08:18 It's like a one line calculation is that the impact of vector. 16:08:24 In this particular case because it's linear is always perpendicular 16:08:30 to the 00 ZNGI. 16:08:36 Right. 16:08:39 So since it's always perpendicular, I can just basically draw the vector here. 16:08:47 I can draw the vector here. 16:08:51 And that's basically how it's impacting these things, this is like really the direction of the depletion. 16:08:57 And I can basically the second point I can make is I can make this kind of cone 16:09:05 that extends out from this kind of potential coexistence point like this, and this is this cone that said that this function here, which I'm Paul h alpha, our star evaluated at this point here has to lie in this cone. 16:09:27 And so what basically happens is that, if I can calculate this supply point here. 16:09:34 And it lies in this cone here. 16:09:39 What happens is that if my supply point lies in this code here. 16:09:47 Then the species will coexist. 16:09:51 Right. 16:09:52 So here, species coexist. 16:10:02 What else do I want to say, right. 16:10:04 If I'm over here. 16:10:06 Right. 16:10:07 If I'm over here. 16:10:09 Let me call this one the white species species one wins 16:10:15 I'm over here, the purple species that consumes less resources, wins. 16:10:24 And so from here you can see how the region of coexistence. 16:10:27 All right. 16:10:30 Depends on what the environment is initially saying. 16:10:37 All right, so right now I just drew this with straight lines. But the power of the theories of course that I didn't have to use straight. 16:10:43 Yeah. 16:10:46 Yeah. 16:10:55 rrH of alpha of our star. 16:10:59 Yeah, 16:11:06 your resources. 16:11:08 Yes. 16:11:09 Yes. 16:11:13 Yes. 16:11:15 Yes. 16:11:18 Yes, That's basically what it is like is your initial point in a certain place and didn't collapse down. 16:11:27 And, and, and, and, yes, yes. What Sergei said, hopefully the people on zoom also heard it, if they didn't. Sergei his point was that that this HFR star is kind of like, where your resources were before the species ever invaded, then you ask, what happens. 16:11:41 All right. 16:11:44 Yeah, it's maybe a dumb question but. So with this picture. Yeah, I just haven't asked the same question as before, so you have any Jeff of our star, let's say a three species. 16:11:54 Yeah, and it exists in the cone of all three species. Yep. So what's the scenario where it no longer exists in the cone of two species. If not, you can draw them when their lines, it would would lines it's harder but when you get non convex function so 16:12:11 essential resources is like, so the next example is essential resources, essential resource, right, so here. 16:12:20 This was basically a theory of generalists because I didn't care which resource I got they're all equally good for me. 16:12:26 That's basically graphically what this line means, and I can write line, you know, example to imagine I have kind of quasi essential resources, right, that Mike ZNG eyes are going to basically look much more like this as a function of resource one, and 16:12:45 resource to right, basically saying, 16:12:50 right, because then exactly essential resource is something where I die if I don't have below it so you know it's some approximation to something like that. 16:13:02 And I can do that again, you know, with essential resources so I have, you know, a curve like this. 16:13:10 And then I have a second curve. 16:13:15 You know, say like this. 16:13:18 And again, I can you know, draw impact vectors. 16:13:23 Once again, 16:13:28 swimming, there are five of them but it really doesn't matter that they're orthogonal anymore. You just have to have a fixed angle, I'm not going through all the subtleties you draw these cones again. 16:13:38 And once again, 16:13:42 you can kind of figure out where coexistence happens. 16:13:48 And why things don't happen. 16:13:51 Right. And the reason this is useful to answer Andrews question is now I don't have to think really about what the exact functional form is, I can say, if I change the shape of these things, how does the intersection change and how does the cone change. 16:14:07 Yes. 16:14:15 Yes, We're going to get to that in a second. 16:14:20 Oh it does a fundamentally fundamentally because the supply point depends on what's sitting in a fundamental way so that that's why microbial systems are kind of interesting. 16:14:31 So that that's going to be the last 510 minutes of what's going on right 16:14:39 now the science is about fact that you're producing resources. 16:14:43 Yeah crossbreeding and all this stuff. Right. 16:14:49 Yeah, yeah. 16:14:52 Grass myself or producer. 16:14:54 No no I mean I mean, there's many. 16:14:58 We spent a lot of time thinking about this, I how what parts of these things generalize but you can very quickly convince yourself that the supply point is not a simple thing anymore. 16:15:09 And in fact what you have to do is you have to intuitively. It doesn't matter if I had time to talk about all the optimization, if I optimization stuff the lip you're not function stuff, the relationship to lockable Tara. 16:15:21 Lot of it I figured out with one thing we we spent a lot of group meetings on my board trying to understand all this with Bobby and went during that I could tell you more but I just felt it was better to err on the side of introduction for the students 16:15:33 then the tell you all this stuff. Yeah. 16:15:36 Yeah. 16:15:42 fact that you're using these geometric pictures and say the functional form doesn't matter. Is it implicit that you're supposed to use these models to ask steady state questions at the end. 16:15:50 Yeah and you shouldn't trust, you know, transition things and just yeah I don't think they have much to say about changing environments. 16:15:58 Even though Levin's also was obsessed with Junior I mean you can try to make these geometric things that you can imagine, if I change resources between two things were coexistence happens I mean you can ask very basic questions. 16:16:13 Right. But you, it's harder to say something about non basic questions right you can actually ask if I'm here how big a change in the resource preparation, can I get without killing my co existence. 16:16:25 So for example, that kind of question. 16:16:27 Right. If I fluctuate in this call that I know I'm not killing resource coexistence this, for example. 16:16:34 So you can say something. 16:16:37 It's harder in high dimensions, I would argue, you know. 16:16:41 Yeah. 16:16:43 Just a bit about this HL fight our star. 16:16:47 I think my understanding of it is not that it's the supply. At times zero before and you know, rabbits come in but rather, when you're at steady state. 16:16:58 You know the resources are being renewed at a certain rate or one has been renewed at a certain rate or two is being created. Yeah, yeah. So, basically what we're looking at is another vector. 16:17:16 Yes. And this backpack another point, more to our two more to our bond or somewhere in the middle and only when it points somewhere in the middle. Do you get coexistence. 16:17:17 Wait, did I say initial. Yeah. Oh no, no, it's that steady state. That's why you evaluated and our star so yeah, he was saying something about you know before any rabbits. 16:17:30 I think I 16:17:30 think that that's not the correct interpretation before rabbit. 16:17:35 Nine any any any model that it's the steady state supply right. 16:17:40 Yeah. 16:17:41 Yeah, I don't know what I said. Sorry. 16:17:44 I'm tired. 16:17:47 I'm so all I want to tell you is that this theory exists, you can read it. 16:17:53 You can modify it, you can put many of these lines here you can get many of these cones, it's often the first thing you should do if you have quality, if you have experiment, till date on coexistence and low dimensions. 16:18:05 This is nice thing to do, because you can always try to reverse construct what you think the growth milk lines must look like if you have many, many different resource supplies and Bobby did that with. 16:18:18 I wasn't involved in this stuff my former postdoc Bobby actually managed to interpret a lot of data with a collaborative Michigan State using just the simple graphical arguments we thought we would he thought we would need all our fancy physics machinery. 16:18:30 It turned out just these kind of simple graphical machinery can help you explain many MIT explains much more than you think it would naively as it seems so simple, is what I would say it's a good first pass. 16:18:44 Just a question about the generalization, if the resources are competing with each other so if I think of them as being, you know, two different grasses that are growing. 16:18:52 So then your equation for the resource that I must get a bit more complicated, does that, yes, that kills everything that fickle arguments are that that kills everything that if it's a strong competition among the resources. 16:19:01 Yeah, it kind of kills it, kind of, it kind of kills this things except for in very fine in very fine tuned things. So it depends on how the competition is if the competition between resources is actually induced by a third Trump declare that you've integrated 16:19:16 out, then you can still make it work. But if it's really like some thing where it's not a marginalization over other degrees of freedom that behave very similar to these degrees of freedom that I don't know how to do it. 16:19:29 So, basically what I'm saying is if it's a three traffic layer system, where the resource interactions are done by basically ignoring one of the traffic layers integrating it out you can save this graphical argument because it's really actually a three 16:19:42 traffic layer thing but you can't get for general interactions at all. 16:19:48 That's what I did that's that's the essence of it. All right, I'm almost done. 16:19:52 So this is my last little thing. So this is basically just to tell you, give you a flavor of how this works. 16:19:57 So last thing I wanted to just say was, how does this modified for microbial ecosystems. Right, so I'm, I'm on page 10 or 11 so I am really almost done. 16:20:12 I'm not going to try to drag you out, or things. So there's a lot of people in this room who have contributed fundamentally to try to like kind of think about how does these kind of intuitions which I must say that the low dimensional to species to resource 16:20:30 intuitions if you read an ecology textbook. That's what they say, even when they analyze complex ecosystems that really is where the intuition of ecologist come from, even when they're thinking about very big ecosystems. 16:20:45 And, in particular chessen has insist. In his review says that every species that coexist in an ecosystem. 16:20:53 You know must impact itself more than an impacts compete with itself more than a competes with other people. I've never found a mathematical proof of that statement, if someone knows one. 16:21:04 They can tell me. I think it's dogma. 16:21:07 But, but it's a good first approximation. So a lot of this stuff is about the microbial world. 16:21:19 And the question is what goes wrong with this simple fact that, you know, problem is the first thing is, of course, this these theories were largely formulated imagining bunnies eating grasses and things like that but microbes. 16:21:35 Mostly, 16:21:38 mostly small molecules and not each other. 16:21:45 Right, so we have to think about God, 16:21:50 Not other organisms. 16:21:55 The second thing is that, at least you know my dogma, is that micro because they're eating small molecules and because metabolism is always producing small molecules. 16:22:06 This kind of impact. Right, has to be modified dramatically because metabolic secretions 16:22:19 basically create resources, as opposed to just depleting them, which is the main thing that is basically been intuition of Mitch theory. 16:22:29 And the final thing is that I don't think you can really think about a low dimensional resource space anymore because there's always so many small molecules and. 16:22:41 Admittedly, many of these intuitions kind of fall apart and you can kind of see that because if you ask about random intersections of planes and dimensions. 16:22:49 They do very non intuitive stuff right high dimensional geometry, or high dimensional complex halls and behave very differently from low dimensional convex hell so this is basically the basis of half of machine learning, I would say. 16:23:04 Right. So, I think it's inherently high dimensional. 16:23:08 It's my claim. 16:23:11 This one, these are Marvin. 16:23:12 And so you have to modify these kind of consumer resource models. And I think the main thing that happens 16:23:24 is that once again, the kind of models people are writing down of various degrees or complexities that you still have consumers that grow. 16:23:34 You still have some resource dynamics that you choose. 16:23:40 But now, in addition to a depletion term. I think the best way to think about it is that you have to separate out to new vectors which is the production 16:23:55 and a depletion term. 16:23:59 And the reason this becomes a little bit tricky, as has been pointed out is that the effective supply vector. Now depends on the species that are present themselves in the abundances of the species. 16:24:16 And you notice here we could largely ignore this abundances of the species they really weren't that important because you just wanted them to drive you to the edge of this convex. 16:24:29 prototype. 16:24:29 Here you have something fundamentally different. 16:24:33 And there's many ways you could parameter eyes. 16:24:38 This kind of different thing. 16:24:40 And I'm not gonna, I think it's late, I'm not going to go through particular models of different kinds. But I want you to see qualitatively what's going on right qualitatively we can't just think about this contracts Hall anymore, because the species 16:25:02 button this is the supply vector is very intertwined with the abundances the presence of species that are present. And you can do many, many things with these consumer resource models for example us in our group, often think about this in higher dimensions. 16:25:11 I think SEPA is going to show you some two dimensional three dimensional I don't remember how many equations you have in your paper two or three dimensional versions with nitride and nitrate. 16:25:22 I often think of what I would call the third model class up in, you know, mother. I've been thinking about the low dimensional what I would class one. 16:25:30 But what's interesting is that this kind of this framework seems to be flexible enough to capture many things and hopefully you'll you and you saw Casey. 16:25:41 I never see I don't remember to include Casey because I'd never seen that those models until until like an hour ago, Casey showed you an example where he just added a little bit of stochastic city to these kind of things and use random matrix theory, 16:25:54 but they seem to be quite robust, they seem to be able to explain many large scale patterns that you see. And I must say much better than I thought I was going to show you a bunch of examples on my computer but I think Casey already showed you that kind 16:26:08 of dumb models seem to be able to reproduce, I mean the only point was to show that dumb models, what I would call kind of naive, I don't know dumb but naive models with lots of random matrix he seemed to be able to predict predict predict many large 16:26:22 scale statistical patterns in these things. And I think it's because the fundamental structure is really about just supply vector self organizing and impact self organizing and, in particular, I didn't get a chance to talk to you about optimization. 16:26:40 But it turns out that you can generalize this picture by basically asking for self consistent supply vectors. So you say here's a supply vector, let me pause in a random supply vector. 16:26:51 Let me flow to the edge of the thing. Let me, update the supply vector and go back and forth. It's like an expectation maximisation algorithm. 16:26:59 And so there is more geometry. 16:27:02 I don't quite haven't quite worked it out, but it's also quite powerful because these models also in large scale you can solve them very easily so I guess that's all I want to say, it really was a review introduction lecture, I did not try to add any 16:27:17 research of any kind in here because I didn't feel like it was appropriate. So, if you want to talk about these technical things we've wasted, way too much of our time in the technical weeds on these models, and we're happy to tell you about how you relate 16:27:33 these random matrix theory and other ridiculous things like that. 16:27:38 Okay, thank you. 16:28:09 Thanks. Um, so it strikes me there's actually maybe a fourth thing maybe we want to think about in the microbial world I'm curious to get your opinion on it which is the fact that I guess the growth rate could depend on resources in the past to just curious 16:28:09 whether you had any thoughts about sort of organism or state and physiology how that might sort of factor into this world. Oh, I think, life histories, this is this is Nick Levin's one of his classic points that we do things in real time, instead of thinking 16:28:23 about time delays. 16:28:25 I would say that's probably much more dramatic. In the macroscopic world that it is in the microbial world. 16:28:33 Life histories, I don't know, is there a microbial life histories whole field of research. 16:28:40 Right, so we found, like for example in Alberto and Josh and the stuff we did that, like, even though these colonies are doing dioxins shifts over large period, you can see it in the OD curves because the other docs shifts, because we let them go out 16:28:52 to 48 hours. 16:28:55 And they seem to consume everything. The generalist model actually on the timescales off which we want to predict steady state seems to do pretty well i don't know maybe Josh can comment. 16:29:04 I mean that that that that I mean, so we. 16:29:12 Yeah so time very is i think i think i would call that much more. Yes, there's all, there's a lot of stuff with time varying environment. So time is absent spaces absent. 16:29:22 They obviously obviously matter. 16:29:27 Yeah. 16:29:30 Yeah, I know you come from the Stanford school where everything is there's no steady states in our, in our in in in our experience. 16:29:42 Everything reaches a steady state and I was so happy to see Casey's data because it basically all this stuff I've been saying dogmatically as as as truth, at least there's, I have one piece of evidence. 16:29:53 What I don't think it's published yet at least I didn't notice that on the archive yet, but maybe it is. I don't know what to say yeah I mean, yes, I know there's a lot of chaos and dynamics obsession. 16:30:04 I haven't seen it is my is my feeling. 16:30:12 Well the stability you completely ignore multi stability. And I think it's, you know, you don't see much in the gut, but you see it in other communities, and it's perfectly well described by the consumer resource models without going into chaos or Yes, 16:30:25 complex dynamics. 16:30:27 Yeah, I guess my, my, my prejudices that multistep. Yes, yes, I think, in lower dimensional dimensions, it's more pronounced than in higher dimensions but yes multi stability. 16:30:38 Everything exists. It's just an introduction, I just wanted people to learn some words. 16:30:44 I'm sorry. 16:30:47 What do you want from me I'm trying to summarize 40 years of really great research, and like not doing justice to how clever the ecologists where that's all I was trying to do. 16:30:56 I was just trying to tell you that. Here's this rich ecological tradition that many of us are much less familiar with, then we should be that, that's all I think that's what I wanted to say to you. 16:31:06 That's it. You know, can I will Yeah, yeah, you should take more questions that I'll say thank you for a beautiful introduction. 16:31:14 Talk, and I wanted to add that I have two beers and a bottle of wine. And so if you want to get together at like nine tonight on the patio. Let me know so not just sitting lonely by myself but also, if we need more beers I can go get some. 16:31:34 I have five beers to contribute so don't worry we'll be fine. I think me and Josh still have one whole bottle of whiskey between the two of us left. 16:31:46 So one thing I wanted to ask you skip lockable Tara entirely but I wanted to get your take on like, given the fact that microbes basically always interact through like sort of the chemical space you know the resource competition or interactions, or lockable 16:32:00 Tara models ever really useful as sort of our first starting point for microbes, do you think are the only really useful sort of simplifications of a starting sort of consumer resource model. 16:32:12 I think they're useful Jeff has proven me wrong after getting into lots of fights with him, that he can at least. 16:32:17 Jeff gore and he get fixed up with lockable Tara and I told her you couldn't. So, I still maintain you can't do it in higher dimensions but yeah of course they're useful. 16:32:26 I think part of, I guess, in that rain part of the dogma, I would say is that people claim that lockable Tara models are consumer resource models in the limit of fast resource dynamics that's absolutely mathematically false lockable Tara models are linear 16:32:40 response. 16:32:43 They're really linear response around a steady state of resources and species so they're linear response models to second order. And, and that's it. That, that's why only like, kind of, kind of technical thing I want to say about that. 16:33:00 Yeah, yeah so that's why they work, right, like, just like in physics linear response there seems to work way beyond it it has any right to work. I would say that's the kind of second model where you ignore friction I'm talking about so he's like, how 16:33:12 with it. we're just gonna do linear response theory. 16:33:16 And we know that linear response theory somehow seems to work for all this stuff it shouldn't work for, and I think that's what Jeff has taught me lockable Tara models are that's my running interpretation. 16:33:35 You're asking the most stupid theorists here. 16:34:00 stationary say you're talking for too long for the zoom people. So, Boris is asking me how microbes die, which is probably the most misdirected question in audience like this when Terry and Sam, and other people are sitting here, I don't know how microbes 16:34:14 die but if you told me I'm sure I could add a term to my model that's all I could tell you. 16:34:19 You don't think so No. 16:34:23 I'm not convinced of that I know your PAGE PAGE PAGE believer, I haven't seen the data that says that's true. 16:34:30 Yeah, I guess, minus may not even be a well formulated question but I guess, given that you want to use this sort of model to try and understand some level of complicated data. 16:34:40 Is there a systematic way where if you start with, say, I can measure 100 metabolites, and you put everything in that this can actually reduce it down to the relevant variables and some useful way, and likes telling you what to throw out saying stop measuring 16:34:54 this it's useless for you, so that as an experimental list. Can you at least like, teach me how to better measure what I need to then understand what the community needs. 16:35:04 What I need to describe for the community but my short answer is no longer answer is, I think what the models are good for is they, especially when you start drawing things from random matrices the at least you see a lot of patterns that you think are 16:35:19 non trivial, or at least very deeply biologically motivated and they're just generic things of self organize things that feed and eat each other. And I would say the vast majority of stuff, and you can, I mean, Sergei, and actually have some kind of thing 16:35:36 with a bioinformatics package you are you can talk to them. 16:35:42 It relies on a database so I'm skeptical, but you know, that's my. It's better than a lot of stuff I did, which I know is wrong so like, you know, in that sense, it is what it is you should talk to them they know much more. 16:35:55 I don't know I can just tell you the stuff we did with Alvarado with Josh. 16:36:00 We design those experiments, very intimately tied to these kind of models because they have to think about some stuff we wouldn't have thought of so at least second order. 16:36:10 It helped us design, some experiments because the model was very intricate in the experimental design but no I think what resources I care about what resources I don't care about, I don't know. 16:36:19 The only thing I can tell you is that we know that generically and all these models, we have some proof that, if I have nn species, right, then I must have at least two M intermediates that I care about. 16:36:34 That's the only proof. That's the only thing I can tell you generically that like, you know, a general species will pack half the niches. That's the maximum packing bout. 16:36:43 I don't have anything more to say than that I we I wish we did we've thought about it a lot. Josh is the right person to talk about that Joshua would have much much better things to say to me. 16:36:58 I'm gonna Echo, and what they're asking about the temporal aspect in the stationary phase and the dead space and all that. I think I know many people are looking at these models. 16:37:15 Going to steady state, and it was very interesting, interesting properties and these are great starting point. 16:37:21 But I think that commitment to steady state is way, way, way too premature. 16:37:26 The, um, yeah so so okay next week I'll describe in one of our studies on a simple, very simple proceeding, and just see all kinds of temporal dynamics that's happening you know during what what I thought it would just be simple about how many how many 16:37:46 species. 16:37:47 I know you're gonna last it right so the is also what we can study in details are few species yeah so I don't think you're gonna tell me, my check or whatnot. 16:37:59 In a long term it's gonna be a steady state know and also I just think that things are simpler, I think things look like I am dogmatically tied until people prove me otherwise, to the theory that most healthy ecosystems don't mean field. 16:38:15 The way they look like mean field theories that like, just like mean field theory and physics is something that could be a means to be a dynamic field of the point is that the important biology in involving stationary for the cells are not growing most 16:38:35 of time, right. I understand, but if you average over many stationary phases and they're not described by these. 16:38:37 I agree with you but if I average over many, many dilutions, and many many you're stationary phases. 16:38:41 Right, can you question it but I just think that dioxide shift is one place where we know that this looks like a stupid model. 16:38:48 But you average long enough, and they look like generalists, even though they're temporarily segregating what they eat that we know from experimental data I don't do any of the size Josh, I don't remember it's all avarice. 16:39:03 Yeah, you can do it theoretically to, you can also, we also check Hey Josh, we, we, the Royal we meaning Josh, 16:39:13 trying to explain it ultimately you want to try to explain, okay just exist as many species, right, that if you. 16:39:30 Of course, every time a cell dies, you know, thousands of metabolites and you've got enough, then conceptually we don't have the answer. If you want to go into more details into mechanism then the you need to actually to take some other biological reality. 16:39:38 I agree, okay so here's the question, the way I view these models is, these have the minimum amount of mechanism and ecology you need any pattern I can explain with these dumb models with random matrix, there is something where I would say there's not 16:39:50 too much biology. 16:39:52 And I would say, the way I read. 16:39:54 When I read papers. I see the opposite, I hear very mechanistic explanations of things I can produce with random matrices, and dumb models, or at least very naive models. 16:40:06 And so I don't believe the mechanistic explanation because there is no mechanism here. And then that way I think it's a good diagnostic it's just like, I started condensed matter of physics I have something I do the main field. 16:40:16 I measured the exponents. If it doesn't read that I have to put something else in. Yeah. 16:40:27 Yeah. 16:40:35 Somebody pours food into this niche, and it is growing in the steady state. And there is flux of stuff going through, whether 16:40:50 Well, somebody's speeding your regularly, and you can dispose of the waste. 16:40:56 Right now, take some microbial Matt, I don't know anything about them. So, please. 16:41:04 And I would imagine that this is much more resource limit that situation. 16:41:08 There's energy for sure. 16:41:10 Right. 16:41:11 But couldn't exist mostly in the steady state recycling stuff repackaging there, stuck in a metric flux balance. 16:41:28 You know, and just take the energy from life dissipate the heat and do their business in that column closed circuit effectively. So how much can be done by recycling. 16:41:47 But this is certainly not a question for a model. This is a question for an experiment no 16:41:54 conceptual thing you know why we get into this frame of mind of living in this open system flushed with nutrients. Maybe we should be thinking a little more closed systems and recycling. 16:42:09 Maybe all the bars you should join the conversations were having yeah i mean i mean I mean we I agree and it's harder, I. 16:42:18 It is recycling a little bit, but like I think what Boris really means is, I think there is this very deep idea of how do you set up sustainable fluxes at high rate, you know, which honestly SEPA we we had a zoom call at the beginning of the pandemic, 16:42:33 and we. 16:42:33 It was the pandemic and I had nothing intelligent to say I mean today, and it's a hard question. Yeah, I agree with you. I think it's to me the most profound question if you'd come from whiskey yesterday evening you had heard me babble about how we should 16:42:45 really stay close to ecosystems. 16:42:50 Taking the earth is a closed ecosystem we've got 3 billion years of carbon isotopes that tell you a lot about how carbon is being cycled between auto traffic and hetero traffic populations. 16:43:01 And that seems like a really rich data set that I'd be curious if you're doing anything else. 16:43:17 That's not. 16:43:21 Josh, 16:43:21 Whatever I produced from that analysis would be wrong so what I do is I say Josh. 16:43:26 Is there something interesting we could do. And he says, whatever, but misunderstandings are stable cycles of resources just given a population volume in a popular yeah so we're trying to do something much simpler that Josh. 16:43:39 Josh. Josh just grabbed the microphone explain how you wanted to do carbon 13 stuff, and see if we could do something, but I don't think it's happened yet. 16:43:50 You need them. 16:44:03 So, take some label the phosphorus. 16:44:09 How many 16:44:12 generations of DNA to answer that particular phosphorus lives in between so entering the system, and falling out into the sediment. 16:44:27 Yeah, I don't know about labelled phosphorus necessary. 16:44:33 Not from oh yeah you should I 16:44:36 mean sure, why not I mean they you know it's it's stable and the timeframe of the experiments so you could track it and you know, I don't know if anyone's done that I certainly haven't heard of that especially not with phosphorus but it could be really 16:44:47 interesting. 16:44:50 I'm sorry recharge 16:44:58 roughly how many, but that's why I keep asking you about our microbes that. 16:45:04 Yeah, right. So the question is, how long has it stayed in. 16:45:16 Remember, in the math and ecosystem in 16:45:16 the passage between, between cells. 16:45:21 I don't know if I'll time to present this data but we've measured the rate of carbon cycling and an auto Trove header Trove sealed microbial community and I can report to you a number of moles of carbon cycled per unit time as a fraction of the total 16:45:33 biomass in that system so that's so that's tending towards what you're what you're looking for. Now the question that remains there is, you know, it's a very complicated system that we put in there, and we don't really understand, you know, building a 16:45:49 model that looks like this from the bottom up of that system is going to be next to impossible, I think, is the system is too complicated. 16:45:56 So what we're talking about Josh and punk edges you know what are the sort of generic features of the systems that sustain those cycles metabolically. 16:46:06 But that measurement you know maybe I should try to put that in my talk. 16:46:10 Give it given us. 16:46:14 Yeah, I'm not sure. 16:46:19 Rachel. Thanks. 16:46:21 So, one thing I mentioned ask is that same principle, there is no reason you know we can add in this equations. 16:46:31 Just a death term right and light coming in. 16:46:36 And there is. So, you know, I'm actually going to extend this and the other thing I want to point out is that, In essence, this is not the dynamics Let's bounce houses democratized version of the same equations where instead of having those terms as matrices, 16:46:51 the you have, you know, calculations based on FDA. So I'm, I don't know, you know that's something we can talk about off of. I know you think about this, you know course grading and so on but how can we bridge these two things right it's it's it's the 16:47:07 same equation just with very, very different source for, you know how you compute this terms. 16:47:19 I was hoping this was going to turn into a proper Kitt talk where I never have to talk again. 16:47:25 That's the best kind of catch up talk where the speaker just sits down and everyone just. 16:47:29 It's the first time it really felt like the old days. 16:47:33 I you know we've talked about this a million times i don't know i don't have an answer you, you know, my, my feeling is my, look I everyone knows my dogmatic feeling you ever if you put enough things in you average, and it's all going to blur out roughly 16:47:49 speaking, whatever like, I don't know how we would Bridget, I think we have to try to do it, just so we understand, because I think FBA is the closest we're going to get to the complexity of biology and FBA as you pointed out, as everyone knows, it's 16:48:03 still very far away from the complexity of biology. 16:48:08 My feeling is the kind of things were limited by what we can measure. So, giving back to the beginning of the talk, I feel like the kind of things we can measure right now are very crude, and don't really probe the biology very well. 16:48:20 They're kind of the stuff we can measure is really much more this random matrix theory stuff right like you know auto measures modularity we can produce reproduce that with random matrix theory seems to be very much something about but metabolism you 16:48:30 see succession that seems to be something very much about metabolism, but you put in generic random agencies you get succession on a single resource, you know, So all I would just say. 16:48:41 Unfortunately, despite how amazing the experiments are, and they're really amazing they blow my mind on a regular basis. 16:48:48 We're still an order of magnitude away. 16:48:52 In measurement ability, from where we can really start probing the real violence. 16:49:04 I guess we would really like to measure the flux is to see how off you are I mean I think that has an obsession with measuring these flexes since like when I met him I I kind of feel like you're right i mean maybe, and Rachel. 16:49:17 Rachel Josh, everyone here I see on the left hand side of the room wants to measure flexes, and I think it would give us a lot of, lot of insight, at least quality, we don't even know qualitatively what the flux is, I would say look like in different 16:49:32 environments, right, like the main thing is what's the relationship between environments and flux is, what's the relationship between the metabolic niches that are set up, and the external flexes, we don't, We don't know I have lots of speculations, but 16:49:46 they're literally that there's speculations I don't know maybe people have a better answer that's what I would like to measure. 16:49:52 Can we come back to Boris's comments and questions in connection with experiments. 16:49:58 The something which has not been done very much except for just long term starvation experiments going back to cold and Fingal is trying to just mainly feed a bacteria with the life of their siblings. 16:50:14 Now I mean in principle we could do that where you only put an energy with light that pumps protons on like it and actually see what, see what goes on so you an intrinsically a very rich, rich environment but you're not adding a small number of things 16:50:26 artificially. 16:50:30 And then what has the fluxes of everything that's going on on there and everything's being recycled. 16:50:36 Yeah. Yeah, I agree I mean I think we would like to understand some of these big ecosystem level cycling. I think that's my intuition, but it's really, you know, not my intuition, it's really like I talked to a bunch of people I respect and they all tell 16:50:56 As the thing I think we need I'm not the right person. But it's not clear what needs many organisms if you feed an organism back to itself with the first we know that will evolve a lot, and you'll get a lot of differentiation and Tony was talking about 16:50:58 me the same thing so I just adopt it. 16:51:04 different, different things but it it somehow seems in certain conceptual way simpler than a lot of the things people try to do with with communities, but it's always got evolution mixed in. 16:51:16 But I don't believe that you can separate evolution in ecology anyway from microbes so 16:51:24 yeah okay that's that's a debate I won't get into with you again. 16:51:33 I don't really understand how we kind of ended up discussing the you know what happens in Super closed ecosystems because almost never the ecosystem we deal with is closed. 16:51:44 And instead of thinking about hard about how bacteria die or what makes them die let's just think they're just being diluted the dilution term is here in this model, it could be constantly solution that could be cereal the illusion like in a god or somewhere 16:52:00 else. And then this consumer resource models will give you a perfect answer without being anywhere near a station restate the bacterial constantly be growing and being dealt with it so that's not sure why. 16:52:15 Just because you have a gross dilution cycle doesn't mean you're gonna always have a steady state. 16:52:20 Well, if you don't, then you deal with it but even, even in this cycle. Well, what if you have an email step, which you're constantly feeding with these nutrients. 16:52:35 Well okay so cereal cereal dilution again, it's not a problem at all. 16:52:42 For most pieces. 16:52:49 Well, look, look about look at the material communities around us the gut is constantly they would you agree, right. So, it exists in some kind of steady state where you don't need to think about the oceans are being saved us in any way. 16:53:11 Right. And then they're being washed away. 16:53:14 I mean, it's a slow drain, but when they grow.