15:01:34 Right.
15:01:35 Thank you everybody for being here, and the afternoon.
15:01:39 I'll start by thanking the organizers for this wonderful program, I'm having a amazing time talking to everybody.
15:01:48 And today I'll talk about some very recent stuff.
15:01:56 We put a pre print out basically just in time for this program. I'll mostly focus on that, maybe a little more if we have time, though. By now learned my lesson not to try and put more than one story in the talk, but we'll see.
15:02:13 Second, know were no more speakers have to wear masks now yeah so we're building a new format.
15:02:22 Previously, it's about talking to a room of people where you don't know what they're thinking, and now you also don't know what I'm thinking.
15:02:30 All right, so,
15:02:33 Yeah.
15:02:37 challenge for equal you with theory looking for the right variables. I'll start by just saying, if your question is short, given the microphone situation.
15:02:45 If you're asking it and you're not on zoom. I'll try to repeat it, and then you don't need a microphone.
15:02:50 If your question is long or you're not sure I'll be able to repeat it and get it.
15:02:56 Okay, I'll start a little bit by saying what questions, I find the most exciting and partly to justify, you know, I work on resource competition models on coach gave us a great introduction, probably by now, couple weeks ago.
15:03:12 I'll put in my two cents about why I think that's kind of a great sort of world to work in.
15:03:21 So there's this long history of trying to kind of bridge statistical physics with ecology and evolution. And for kind of obvious reasons right there's a lot of shared hopes and goals, which is, can we describe the system, somehow finding the correct course
15:03:39 greening, or given question.
15:03:42 Right, can we leverage some sort of self averaging to predict something despite knowing, not knowing all of the details, perhaps. And is there anything interesting that happens that we couldn't have predicted otherwise, are there any new behaviors that
15:03:56 kind of more is different style.
15:04:00 And all of this revolves around this question of, you know, finding great variables, and maybe you know some hope for immersion simplicity and I'll put a bunch of these things there.
15:04:08 And the things that are exciting for a physicist, is it possible ever that large and is simpler than small end or national communities that have somehow simpler than artificial and simpler everywhere and there's and big quotes.
15:04:21 What would that mean as part of the question. Right.
15:04:25 And so,
15:04:29 one question is well how we do it this is a very exciting hope and goal.
15:04:32 One question is How are we doing on that front.
15:04:37 And there's kind of the works our horse, the workhorse of theoretical ecology generalized lots of Altera type models is, you know, we I think we've had introduction to those as well you write abundances of your types, you know types, you know types.
15:04:53 There's some interaction terms.
15:04:57 There's this is an extremely general model you can implement all sorts of interactions in this way.
15:05:02 You can study all sorts of, you know, traditional ecological questions. Also try and merge this to evolution, maybe will allow the coefficients to evolve, or you know study speciation a trade off all sorts of really rich and interesting questions.
15:05:18 Um, but somehow for the kind of stuff I'm personally personal opinion, what I'm most excited about somehow feels like it's not really bringing us to, you know, the, the most interesting stuff partly because, well, if we're trying this model is about composition
15:05:40 compositional framework, and an issue with trying to predict composition is that will often composition, we see it's just not that predictable.
15:05:49 Right. And, for I guess the benefit of a few students we have in the audience.
15:05:54 There's this canonical example that everybody sites, and maybe that's not the best example but one of the older ones.
15:06:02 You know gut microbes we sampled them and healthy adults. So here's the experiment you sample, you know, nose, mouth teeth from bunch of volunteers.
15:06:14 And this is who we found and they are colored by Fila.
15:06:22 And what I want to highlight here, so of course of the thing to observe is that within sailor mouth. You know, you see this huge diversity between who's there.
15:06:30 And this is not the difference of like you know white rabbits or grayish rabbits. This is like Viola which are completely, you know, very, very far away from each other.
15:06:39 So is it hopeless.
15:06:41 So we kind of We know you're going to force the force and made of trees and other forces made of algae.
15:06:47 This crazy.
15:06:49 But then you look and you see that they kind of the both running for the synthesis.
15:06:52 And so, if you.
15:07:28 called overly.
15:07:30 So, over and over you repeat something you do hundred replicates, and composition is just not that predictable and function well like some example I happen to be involved in, you know, you take mice you feed them a diet with fiber, and you feed them died
15:07:48 without fiber, and if you feed them at night without fiber, the community loses the ability or declines and ability to process fiber.
15:07:58 And maybe that's something. One second.
15:08:02 Maybe that's obvious but there's something kind of pleasing about the fact that there's something something makes sense about that. Yes. Okay, maybe this is trivial, but I'm wondering about the distinction between the top and the bottom plots that like
15:08:15 if I posit for example that all of the things that you have in metabolic functions are present in roughly single copy and every genome.
15:08:25 Because these are situations where they're mostly hundred tropes.
15:08:29 What I get the plot sort of trivially meaning like to see what i'm saying,
15:08:36 well not, I mean, depends on so yeah.
15:08:39 With 50, you can just take 50 random Geno's.
15:08:42 If you have 50 species or more. I can show you, we have plots.
15:08:47 Yes, Yes. The answer is yes. Okay. did he answer.
15:08:51 All right, this is just the motivational slide like this is not what I'm right.
15:08:56 All this is to say that there's something, you know, it's kind of symptomatic that over this meeting I feel like we're, you know half the time we're talking about metabolism.
15:09:05 And why are we talking about metabolism, because there's something appealing to us about the concept of, you know, function being new thing we want to predict and possibly that we could predict.
15:09:15 Right.
15:09:15 And so the question is well when we're looking at kind of a lot of these, you know this side of the ecology Well, where is kind of where does the function come in here in our species in one and two and three, what do they actually do.
15:09:29 And that seems important to specify for example if only to talk about their evolution.
15:09:33 Right.
15:09:35 So that's a kind of brief spiel of motivation for why what I find the most exciting in this kind of resource competition framework, which is in some sense like the simplest way to connect composition to function in kind of really minimal way.
15:09:54 We've had a great introduction, so I'm not going to go through this in detail but basically the simplest model you could possibly write about the feedback between food and organisms.
15:10:02 Right.
15:10:05 If there's extra food organisms grow as they grow. They deplete food.
15:10:18 just a couple words on. So, the model as you write it, for example like bonkers wrote it's nonlinear, but if you let it rise it. So nonlinear is kind of pretty big difference from what we saw before, but you linear eyes that you get it's a very special
15:10:20 All right, the equations in a second for the specific framework I'll be using but
15:10:32 case of logical terror.
15:10:35 Very special in lots of ways. The framework I'll be using a special in even more ways than many.
15:10:43 It's your competition, although there's ways to for speeding right that's kind of easy but I won't be the matrix of interaction is very low rank.
15:10:53 Perhaps most scandalously there is a lambda function for the dynamics.
15:10:59 Absolutely.
15:11:01 Absolutely, yeah yes, so the one, I'll be using will be very special. In, including in this way, which gives you things like unique equilibrium which is of course not ecologically you know realistic.
15:11:16 And so, you might very justifiably be worried. Well, what are we doing then, if we're asking, same kinds of questions, but kind of the general ecological questions in this framework.
15:11:30 Are we just kind of looking under the lamppost here's the model we can have some extra analytical tools to work with.
15:11:35 What are we gaining.
15:11:37 If it were just that, that would still be valuable because there is value in like physics we know integral models can sort of give us some intuition which would then they break in different conditions.
15:11:52 But I want to argue that it's not just that, and specifically the sort of the value is that the explicitly functional description allows you to ask new questions about how composition is connected to function, and ask the questions from sort of both lenses.
15:12:09 So it's this interesting middle in between you know some hypothetical purely functional approach where we just talked about, you know, environment shaping fluxes.
15:12:21 And, you know, lovingly, sometimes called Super enzymes, which is not what ecosystems are, but then on the other hand there's this kind of what's called Terra type approach.
15:12:30 And this lives somewhere in between and what kind of questions.
15:12:36 I've been sort of taking notes a little bit from some of the discussions that were happening in talks over the past couple weeks, adding to my list.
15:12:44 It live in between.
15:12:45 So there's this question of what's the role of physiological constraints.
15:12:49 Right.
15:12:51 We've heard from Terry we heard from Stephen Ben was talking about some of this.
15:12:58 Something I find fascinating. And we also heard this several times. There's always ecology, somehow, at all levels that you look, there's somehow always ecology, and I'll draw this cartoon for people on zoom.
15:13:12 I'm not drawing anything profound. Just like a sort of wherever you zoom there's ecology. So let's say there's a population and maybe there's some dynamics of, you know this this time.
15:13:24 And this is kind of schematic representational population in abundance, and maybe one species is sort of taking over and then you look in there and you see well and they're also actually there's like, you know, finer dynamics.
15:13:38 And then you look closer into any one of them and there's actually all these dynamics as well.
15:13:45 And how do we sort of think about that. So we heard from Ben, where, you know, within species there's still these strains that it seems like there's a correlation between them.
15:13:58 I tried really hard to exclude ecology from Lenski lines, there's a college
15:14:04 and sort of what's the simplest model for things like this.
15:14:10 Okay and then there's sort of this puzzle, which.
15:14:14 Well, we'll look closer and closer and there's still ecology, do we care, like those are details maybe we don't care about them.
15:14:21 And we know that those details really matter right there's lots of studies that show how the really fine distinctions, can cause a given strange to interact differently with another strain or with some environments will queue, right.
15:14:38 There's recent word from auto that kind of made made it, click for us when when we were kind of starting to think about this, showing how you look at, you know, abundance of some species, and it looks kind of maybe stable, and then within their, you see
15:14:54 dynamics between two strains that actually clearly interact with strains and another species and that is clearly participating in the interactions.
15:15:05 So, the closer you look.
15:15:08 You see all these distinctions that matter and just earlier today we talked about, like Andrew brought up an example how
15:15:16 sorry I'm kind of running a breath and ask
15:15:22 how within a population of yeast they're actually kind of finished typically distinct.
15:15:27 You know types that are heritable. So all of those details.
15:15:31 And that's really depressing for physicists because Okay.
15:15:35 All that matters. How are you going to ever make sense of any of this, and simultaneously there is the fact that well course green descriptions seem to work right and I talk a lot to Alvarado, who, in fact, tells you that for some situations.
15:15:53 Okay species is such a course concept. It lumps together all this diversity ignores it.
15:15:59 And he will tell you that actually for some situations what's reproducible is the structure level of families it's too coarse grained you have to sorry it's too detailed, you have to corresponding further and that's where you see some reproducibility.
15:16:11 So how do you kind of reconcile that.
15:16:22 excited that it's not just actually.
15:16:25 You might think that's very physicists hope.
15:16:28 Right.
15:16:30 And I've been talking to some, like, biologists who kind of share this picture of for example when we were studying organisms isolation a lot.
15:16:41 And what are we missing that way we're here to talk that started from that very slide.
15:16:45 One of the things you might be worried you're missing is some sort of complexity, like oh there's lots of things here that won't make any sense to you until you understand what they interact with in the real world.
15:16:55 And there's some hope well maybe actually things somehow make more sense in the natural conditions like what would that look like, what would that be okay.
15:17:05 So all of that is motivation. And I'll tell you about kind of one story, just very theoretical story in a model
15:17:16 that we've been developing to kind of get some access to some of these questions that I find exciting. This is work with a talented student of mine. Jake Warren, who often is on the zoom screen.
15:17:31 And so
15:17:34 the question. I'll start with is, what's the kind of simplest model for an evolutionary landscape as constrained by some physiological constraints. So the first thing on my list, like, somehow, you know, composition does matter for function there are
15:17:50 some things some functions go together in organisms and others don't go together and organism, what's the sort of minimum model to put that structure into a model.
15:18:00 And I'll build this.
15:18:02 Basically, out of resource competition model,
15:18:07 but I'll try to. I'll try to be a little kind of phrase it a little more generally, which is imagine that environment, think of an environment as some sort of, you know, a given environment provide some opportunities that can let you get ahead in life,
15:18:26 right, some opportunities that would increase your fitness and imagine that I could go ahead and numerate all of those opportunities.
15:18:33 And so classically in resource competition model that would be some maybe resources from which you can obtain your energy. Right.
15:18:42 But maybe it could be something more general as well, like for example and acumen stats. One way to survive, is to, you know, learn to stick to the walls and the wall space is kind of a limited resource, you learn to stick to it.
15:18:58 And you were the first one and you get a great benefits before a lot of you by now know how to stick, you're competing with them, or that niche. Right, so I here is my elusive notion of ecological niche.
15:19:11 And I will say that it runs from, from one to some parameter L infinity, which is suggestive notation to say that. I'll think of that number as effectively infinite, and this full kind of microscopic description, but I will conspire construct right now.
15:19:26 This is supposed to stand in for some unattainable microscopic full microscopic model of what's going on in my fat.
15:19:35 So that's why I'm trying to be more general because if I'm talking about carbon sources. There are many of them, but surely finite uncountable number.
15:19:43 Right.
15:19:44 If I'm talking about, like, oh you're in a batch culture, there's some phase at first, where it's like fermentation, and then you stick to you know you switch to maybe respiration.
15:19:54 If you learn to become a better like for a mentor, you can get ahead. You know at first, but then you know that phase gets shorter and you are competing with other good, good for mentors, those kinds of things you know trying to merging all of them it's
15:20:08 quite plausible that number is a very large, and B will probably never know everything that's on that list.
15:20:16 Who knows what factors might end up really important in the gut.
15:20:20 Right. So there's some microscopic model but that's kind of unattainable.
15:20:27 Um, and I think a phenotype has a simple binary vector of which opportunities it's benefiting from binary because that way I can think about evolution in this extremely simplistic way of mutations, which is a bit flips zero into one one and zero.
15:20:42 I end up responding to something like gain a function by maybe horizontal gene transfer or loss of function maybe just the loss of function mutation or something like that.
15:20:53 Okay. And I'll write the equation the second so I'll say that your niche, I has some benefits that it offers, and it is some declining function of the level of exploitation of that niche, right.
15:21:13 So, the equations are the familiar equations of that the tankers wrote, except I use kind of fewer indices.
15:21:22 For, kind of, much less general a bunch of things that I seem to be the same for all species are so kind of a particular simple model. And what is this.
15:21:32 So, kind of a particular simple model. And what is this. So, he has this benefit depends on the environment and the TI which is the total number of individuals that are trying to compete for niche by.
15:21:41 That makes sense so far.
15:21:46 So question is what is he again.
15:21:48 You mean this curly, the curly he, it's the environments which I'll define in a second.
15:22:02 So, for example, sort of, you know, purely metabolic view. This could be just kind of a community in a chemist that. So I'm flowing in some feed there's some resources in the feed inside.
15:22:18 Live some species, and in the outflow. There's some concentrations of those metabolize.
15:22:24 This would be the ah.
15:22:26 So, if I'm I don't have a stick.
15:22:31 Okay, okay.
15:22:35 Oh yeah, right.
15:22:46 Yeah, that'll probably oh yeah that's right because we have some people That's right. So, um, if I'm some phenotype what's the total kind of fitness so this implicit the simple assumption is that the benefits from different niches, I'm exploiting are
15:22:56 just literally additive which is of course extremely simplistic, but I'll put some interactions into these maintenance costs time you, which encodes How hard is it to be phenotype Sigma Nu I How hard is it to be benefiting from these niches, to kind of
15:23:15 bite you know machinery that requires How well does it play with each other.
15:23:20 So, if I am some investment of all I picture, these these concentrations of the nutrients in the medium. So this is the total food that I get.
15:23:30 This is how much I need to maintain myself, if I have any extra grow. Right. And then what determines the concentration of the food. Well, the total demand for that resource is the sum here, and I'll say that there's some function, which are bonkers was
15:23:46 exclusive dynamics where the resources. Right, I can write some explicit. You know the uptake rate of a resource and supply from outside. Maybe there's some, you know, external influx of resources, but I'm trying to be more general and include things
15:24:00 like you know other deplete double niches that are not necessarily metabolic, so I won't write explicit dynamics for the metabolites, I'll just say there is some, you know, environment is characterized by these declining functions.
15:24:14 What is the Hi, given the TI.
15:24:18 And I hope, please ask me things right this because this is the first time I'm talking about kind of this version of the story.
15:24:25 So, either it's all trivial or I'm just explaining something.
15:24:29 Both of those are very possible.
15:24:31 Yes, sir.
15:24:37 Question Is he must decline with ti.
15:24:41 Yes, I will sort of possibly that as being part of the model that in general, the more. So, these opportunities.
15:24:48 The more of you trying to benefit from them, the less kind of lucrative it is for everybody. Maybe you can decline slowly right but I'll say that it's declining.
15:24:58 And in fact, I'll say well whatever declining function has roughly, you know, least two key parameters where it starts. And where's the half point.
15:25:07 So, I'll actually take a specific form.
15:25:11 The value of zero I'll call it AI, where it crosses one half. That's that'll be my kind of carrying capacity and I. That's how much that nice can sort of support.
15:25:21 Yes, I got all.
15:25:28 You mean results depend on this like, if you had some sort of maximum that occurred in the middle of like at some intermediate ti would that for that mess things up or what things will be okay.
15:25:40 I never played with that I actually think that a lot of the things probably wouldn't change much. Because basically the question will be running ahead there's a certain cost for carrying the straight and basically all of the game will be in the vicinity
15:25:51 of that point, if I can linear eyes it around that point, and it's it has some slope, that's basically all I need. But you know obviously if I'm talking about large fluctuations and, like, Yeah, but the first approximation.
15:26:12 That seems like a rather innocuous. I mean there's so many more assumptions of this model that that is not correct. So basically, even if you had some sort of some sort of like, actually affect things will probably.
15:26:23 Yeah, yeah I'm kind of staying away from that for now, worse.
15:26:34 Yeah worse is asking, so environment somehow is time dependent or does it depend on time only through your teas. So environment. So the immediate sort of vicinity of the organisms, the environment that organisms creed for themselves.
15:26:53 So the immediate vicinity of the organisms is created by two things the external parameters which are eyes and eyes and that's my environment sorry I should have actually just.
15:27:03 So this is what I call the environment, which is characterization of all the nations, how much what's the benefit if you're the first one to discover the niche, and how much will, will it support, will that need support until the benefit declines by a
15:27:16 factor of two.
15:27:17 That's the external parameters, those are fixed.
15:27:20 And then as the community does something bH eyes are time dependent, because somebody blooms who was very good at consuming this resource that depleted that resource that cause somebody else to start going down.
15:27:35 That is the internal environment which is time dependent external parameters are fixing.
15:27:42 For example, in some imaginary world where you call it just sits there without dividing. So, and it's not changing but it's burning glucose and is depleting the nutrient and whatever wasting everything away.
15:28:02 the environment here would not be time dependent.
15:28:04 So that picture would correspond to eat, I would then be that we can have the schema that picture right where he I was the rate of supply of the resource, which is constant and there's inside there's an equality that eats it, and it grew and population,
15:28:21 to some abundance until the depleted it to its own our star in the Tillman sense and that's been Strictly speaking, I can think of these EIS time dependent but they have time independent.
15:28:31 If you choose to feed them very regularly.
15:28:38 Ah, well you could make the ease time dependent and especially if you talk about like evolutionary process you can say what's going to happen if environment changes.
15:28:46 But I will think of the external parameters as fixed and then the rest of the dynamics is internal fixed is in the flux state tax.
15:28:56 Yes.
15:29:01 So this is my environment. And now I promised you the constraints. Right, that's the whole interesting part. So the constraints. I'll implement them by saying well there's this one letter here that I didn't define to yet, which I said that if you're a
15:29:03 Okay.
15:29:16 phenotype.
15:29:18 That is benefit you know betting benefiting from these two niches, which is maybe eating glucose and also sticking to the wall of the chemo stat.
15:29:26 How does the machinery for digestion glucose and the, you know, whatever it is I need to stick to the wall the chemo stat, do they interact in some way.
15:29:35 For some biochemical and physiological or some sort of constraints.
15:29:39 So the way I'll implement this here is to say, so yeah they kind of constraints, I want to say is, you know, the famous example nitrogen is not activated by oxygen, if you're trying to run both reactions.
15:29:50 That's pretty costly, because you need to invest into extra infrastructure to compartmentalize them right that's costly.
15:29:59 Or maybe, you know, something I learned in these two weeks, D natural fires do not ferment.
15:30:06 Why do they not from and I don't know, but if that's true, that's a JJ, that's the sort of the kind of constraints in the model that I want to put in.
15:30:17 Okay, so I implement this by you know the physicists way, which is to say that if I am a phenotype sigma.
15:30:26 What is my cost well there's some baseline cost of just, you know, replication machinery whatever that I paid no matter what.
15:30:33 Every trait I carry has some costs and traits interact, or simplicity pairwise.
15:30:39 And these JJ is implement these kinds of constraints.
15:30:45 And they can be positive or negative. So for example, you know nitrogen is nitrogen, oxygen or dinos requires on ferment. That's a large positive JJ which corresponds to a pair of traits that are costly to care together to carry together.
15:31:00 Or imagine that there's some branch pathways for two metabolites. If I'm eating this I carry this whole chain. And once I already carry all that to metabolize this other path, you know, carbon source which shares a large chunk of the pathway.
15:31:17 I don't need to invest as much I just need to add this little bit here.
15:31:20 So compared to somebody else who needs to do the whole thing. I can just add a little bit and for me it's less costly, right, that would be beneficial interaction, which would be negative JJ escape, reducing the cost, make sense.
15:31:35 Okay. And just because there's a lot of stuff on the page.
15:31:39 Yeah, so this will be the key thing for me, these interactions, and they're kind of the row.
15:31:45 This kind of framework has been explored before a lot in the context of kind of random costs.
15:31:50 Right. But I don't want random cost because I want to understand how you know the sort of hierarchical nature of communities within a family there's a bunch of general with in general there are a bunch of species.
15:32:01 So I don't want just some random phenotypes, I want the phenotypes to be structured. That's why I put in some structure, which here is the JJ.
15:32:09 Yes, sir. Yeah, so I'm just trying to put some mental picture versus GAJB she has a new sort of ingredient in your model. Would it for instance include the fact that if I'm using two nutrients, we chair a path part of the metabolic machinery.
15:32:25 So acquiring two of them together would be less costly than acquiring each one of them individually Right, exactly. So that would be, you know, not only because all the examples here, you listed are kind of negative interactions, if you have.
15:32:39 If you are denied or fire you are not allowed to have this but this would be a positive interaction, which would reduce the cost, yes I think that was Daniels question as well.
15:32:48 and let me give you some more examples so I'm really trying to in my head, think about this kind of more generally, and say also imagine that you live in a soil and nutrients come when an apple falls down.
15:33:00 And when an apple falls down it brings these three resources in some sticky geometry. And so, you know, with my niece she is eating whatever falls from the sky and forms of apples, it might make sense for me to carry the machinery that eats those three,
15:33:14 you know nutrients together. And so in my phenotypes the sample from the environmental see that on genomes. These three functions tend to go together in this patch of soil.
15:33:23 Right.
15:33:24 I kind of want to treat that as a JJ as well that's Association.
15:33:39 Make that a positive interaction, positive in the sense of beneficial interaction, they go together, right, just implementing this idea that some functions go together and genomes and others do not.
15:33:48 for it, not even kind of not even going to try to disentangle philosophy from biochemistry I'm going to say that's consider external constraints that shape the pool of available strains.
15:34:00 And I'll be asking, how should I be thinking about the structure in the pool of strains, can I meaningfully course green away some of the details.
15:34:09 And also like okay that's what I meant here but not metabolic trades in some environment, maybe there's a niche for being big and scary and a nice for being small and run fast call that a JJ, you know i'm just i'm not a theorist here so I'm like, do you
15:34:25 ever proven this, this term for being the most negative, in other words you you you need to make sure that I don't want to say negative never okay yeah so I think it's small enough that and if ever, it so happens that some configuration is negative icap
15:34:52 Yes, absolutely.
15:34:54 Okay, great.
15:34:56 So, because I want to pay the most attention to this and that'll be my focal point.
15:35:02 I'll simplify away a lot of other stuff, which I'll say that niches are otherwise. All the same, obviously you know that's just adding to the list of simplifications.
15:35:13 If you don't do that the model will have Richard phenomenology other things will happen. Let's not go there yet. Let's just say all the nations are the same.
15:35:21 And here just you know four units, I can scale, I can say easier as are all ones and zeros is some carrying capacity is like 10 to the 10 because bacteria and be done with it.
15:35:33 Yes, especially.
15:35:36 Now the reason.
15:35:48 Let's not go there Yes, and just focus on the role of these interactions.
15:35:52 So counting parameters in the model. There's that see, there's the chi zero. These I can just scale away but just choosing units mutation rates because I'm doing this.
15:36:04 It's an equal evil model for what I'm doing. It actually won't matter. Just because I will mostly be looking at
15:36:13 special properties of the optimal function, which we use for this purpose.
15:36:28 It's a mutation rate won't be a parameter that's kind of key here. It's just large enough for for the system to settle somewhere, as dictated by the JJ is.
15:36:39 And of course the model for the JJ again.
15:36:48 Ah, yes. Well, yes, in between so well okay actually.
15:36:56 So realistically I wanted.
15:37:04 So in a realistic population the population size is large enough at samples that mutations, so I don't need to worry about that, for me when I'm simulating this, and I'm doing this in this sort of strong selection week mutation regime.
15:37:15 I'm only looking at first nutrients. And so I could be trapped. If I'm only sampling a mutant at a time like one thing I'm doing this is to sort of go from equilibrium, equilibrium ecologically.
15:37:38 And that seems that that will trap me into more spaces into more states that are just not available by a single mutants, but not globally unavailable.
15:37:38 This is a bit of a technical thing but.
15:37:38 Long story short, we can talk about that separately but in for what I'll be talking about. We have a supplementary section on that but it won't be of course there's a lot of role for this.
15:37:47 I'll be specifically looking at questions where it doesn't matter.
15:37:55 Sounds like. Sorry, there's an extra parameter which is time, and is it fair to say you're letting time go to infinity such that mutation rate doesn't matter, basically, I think, yeah, sorry that that would have been a much faster answer.
15:38:09 Yes.
15:38:11 I'm trying to be a little sneaky about not actually postulating that I want the community to be it an evolutionary equilibrium, we can talk about that separately.
15:38:20 We're doing this a little bit, because that that's requiring a lot.
15:38:27 Turns out if you have enough, diversity, that sort of puts you in a place which is for our purposes, similar enough that that's all we need.
15:38:36 That probably didn't mean anything to you but we can talk about that.
15:38:40 Okay, so the key thing there therefore is, I think some value of this and that.
15:38:46 That basically will determine phenotypes that are our end up in the community, how much of a generalist versus specialist they are, you can think about that, like like that.
15:38:57 But the key thing is the model for JJ.
15:39:01 And that is where I'm kind of making the choice that I'll be sort of generating the phenomena I'll be studying, which is to say that.
15:39:12 Okay, like I said complete description of phenotypes.
15:39:16 You know plausibly arbitrarily long.
15:39:19 Let's imagine that I can order traits in some intuitive sense from those that matter a lot to those that kind of matter less and less in the sense of how strongly they interact with each other.
15:39:31 So, okay, maybe I shouldn't be using it as an intuitive motivation, let me just use it as a possibility. I choose Jay Jay's of this form.
15:39:42 Namely, I say that I draw every interaction, out of a Gaussian random distribution with a width.
15:40:00 That goes down as the maximum of the index inj obviously doesn't have to be a square matrix. I'm only something over pairs so it could be a triangular matrix.
15:40:03 This is just for visualization. So I'm saying that there are a few traits that interact strongly with everybody else.
15:40:10 And then as I go down the list, they interact with everybody but weaker and weaker.
15:40:17 So what's the intuition for that.
15:40:20 Well, yeah and technically speaking, I choose a sigmoid and the sigmoid has three parameters which is the height, the midpoint and how fast that goes down.
15:40:40 So, if this is my.
15:40:48 Ok.
15:40:52 For all elements on this, where the maximum the two indices is I don't know five.
15:40:58 I draw random numbers out of the same with, well actually technically I'm only doing this on the upper triangle, because I'm only doing this prepares, okay.
15:41:06 So secondly some over i less than jjj sigma, sigma Jamie.
15:41:12 That make sense.
15:41:15 Okay, so what's the intuition for this, for explaining that let me just show you what, what would be, let me draw 300 low cost phenotypes under a cost model that I described, where every trade just has some cost, but they interact with this kind of JJ.
15:41:34 Yes sir guy.
15:41:40 Easily GG matrix symmetric maybe I just didn't get it because you are shown there that something which is not symmetric, sorry, I just confused everybody got a JJ symmetric Eastman.
15:41:52 Yeah.
15:41:54 Sorry about that.
15:41:56 This is just a slide making problem.
15:42:00 Yeah. So, if I look at if this define some cost landscape, what are the minimum of that cost landscape.
15:42:08 And this is an example what it looks like.
15:42:10 For some random realization. The thing to see is that, well, the traits that interact strongly, there are only a few sensible combinations. Right.
15:42:20 And that's kind of okay do not requires a non ferment right but they may do this other thing, and this other thing, right.
15:42:29 So, up top here there are only a few things that make sense. And as you go down the list.
15:42:35 You could have something not have something right it interacts weekly maybe some, you know, it's not entirely random because it's still interact, but it's becoming more and more kind of noisy.
15:42:46 And so this will look a lot like some, you know, kind of like corn accessory traits intuition right, there'll be a bunch of types that are of this type, and then they may differ by this extra pathway where an extra flagella or something.
15:43:05 So this so far there was no ecology, this was I was just drawing kind of low cost phenotypes. And now, there'll be interacting,
15:43:16 Arvind says to state the obvious is not because of halogen Exactly.
15:43:21 Although, once I start running the evolutionary process.
15:43:23 Starting from some phenotype.
15:43:26 Actually over time I'll be running it I'll start from some criminal phenotype, and let it discover everything. It will be generated by for logic.
15:43:34 Now there's no reason for it not to discover the same phenotype, because I'm postulating rampant Corazon gene transfer. Right, but because it's kind of one moves away, each time.
15:43:52 Okay. So, basically this kind of model defines and kind of Daniels terms of fitness no escape.
15:43:56 It'll tend to functional associations will tend to also mirror the logic, but I'm not forcing that anyway.
15:44:00 So, this is kind of artists impression of growth rate of all strategies. Artists impression because this is absolutely not in many sense a two dimensional space this this massive hyper cube, which is what Dan was talking about.
15:44:14 And also, this is the physics audience. So, you know, I'm talking about minima of energies rather than, and I define them as costs I'm literally talking about the minimum costs.
15:44:27 Okay.
15:44:29 And I just want to kind of point out there kind of two levels of dynamics going on here. So these biochemical constraints shape this or physiological constraints shape this cost landscape.
15:44:42 Yes. under.
15:44:49 Andrew that is asking, What is the difference between us no escaping the landscape.
15:44:54 It's I, my understanding is that so landscape is fixed where there's no escape as you walk on it. It's sort of you are changing it.
15:45:02 And this will.
15:45:04 This will be the case here. So, um, so you have these physiological interaction that define this kind of rugged landscape on a hyper Cuban not on a plane.
15:45:15 But then you have kind of a level one dynamics which is you have.
15:45:20 Don't take these levels seriously, there's just like one thing that's happening is that evolution, kind of tends to discover the minimum right or kind of has some tendency for describing, getting you to phenotypes that are lower costs because lower cost
15:45:34 phenotypes tend to be more competitive.
15:45:37 But simultaneously.
15:45:39 You actually have multiple walkers on this landscape.
15:45:43 And they interact with each other because as you occupy some minimum.
15:45:47 You make it and you kind of become successful, you make a minimum less appealing for everybody else and minimum that are kind of similar in these directions you're over, you're using some niche that Nisha is no less interesting to everybody else.
15:46:00 so you're modifying this landscape as you're walking on it. Right, which is partly why just drawing samples from this ensemble is not what drawing organisms from the soil in this hypothetical world would be.
15:46:13 There is a logical dynamics on top of it, how they kind of repel each other.
15:46:17 So, what is, yes.
15:46:36 The landscape is burned in by the jij is yes, and what you're saying is there's essentially competitive exclusion in minima of this energy function. And that is the sense in which you're calling it a snow escape, but not to introduce another term it is
15:46:41 not a seascape, where the, where the minimum are actively moving in time because the jrj is are not time dependent. Yes. Yeah, okay. So maybe this analogy is more confusing than helpful.
15:46:56 What I meant to say is that.
15:46:59 So, the thing is that this. The cost is not directly, your growth rates or your fitness, because your growth rate depends on your cost, and the environment.
15:47:14 Right. So, everything else equal, if you're less costly. You will be more successful, but for anybody, my growth rate is determined by my cost plus, how much the Nisha is I'm interested in.
15:47:26 I'm benefiting from our depleted. And so as others in the community, be, you know, bro and die and whatever the change the availability of the kind of availability of those niches, which changes my growth rate.
15:47:42 Okay, thank you so fitness in that sense is determined by everybody else the cost landscape is fixed once and for all by the JJ.
15:47:51 Okay.
15:47:53 So, so I showed you what some low costs phenotypes look like. Now let's look at what the dynamics look like in this equal evil, kind of model. Now that I actually run interactions.
15:48:05 Here's an example. Just, you know, pick some random costs. This is every. So what do you see is x axis is time.
15:48:16 Y axis is population abundance. Each color corresponds to a phenotype.
15:48:22 When a phenotypes kind of seeds off another phenotype for this kind of big flip. It's a new color.
15:48:28 And the thing that you see is that there's a lot of dynamics where there's this strange kind of a little bit of strange turnover, but it looks like there's a pretty, sort of, there's one band and another band, right.
15:48:40 So if you squint it looks like there's a coexistence of two types and and within them strains are kind of replacing each other, which is kind of what I wanted.
15:48:48 Right, I asked you how do I generate the simplest model with this kind of hierarchical
15:48:56 dynamics and this is what
15:48:59 this is kind of the mirror.
15:49:01 The flip side of the Phoenix low cost phenotype is being, you know, there are few defining traits or the beginning and then a lot of these small traits that can swap in and out as the environment that kind of changes by the other inner types around you.
15:49:17 So I also because I'm running the simulation I can also tell forever phenotype who would, who would derives from.
15:49:24 So this is not an a technical philosophy, this is just the tree of descent. I'm just showing it here so you see that there are these very deep branches, which are of course sustained by the ecology, right.
15:49:35 I'm showing this because there's there's these big branches that correspond to the bat bands, but they're also very small abundance one at the top, which corresponds to that one, which has a very small niche, it's a very low abundance.
15:49:50 But there's something that only it can do and it persists forever.
15:49:54 And all of them actually in this case share their common ancestor at the very beginning. They diversified, and then they persist.
15:50:03 Okay, it looks to me also that the timescales are getting sort of your rising descent curves are getting flatter so in other words you are at some point you will run into the situation where you novelty will be just too slow for Yes, this is not a solution
15:50:21 to Daniel's question of does evolution can evolution run forever remember this isn't a model where there's a global level of function, it will converge to a final state, right, and all that is in some sense very boring.
15:50:38 If I were asking questions like coexistence of types, and I'm very explicitly asking a different question, which is, these phenotypes will exhibit this diversity.
15:50:49 Certainly certain structure of the trades I'll show you in a second. And my question will be, which details are negligible, which can be coarse grained away.
15:50:58 Yeah.
15:50:58 So So trying to connect this to your to the minima you showed before, how does the number of minimal compared to the number of species.
15:51:06 So, there are some.
15:51:11 So the fact that you see these kind of four branches.
15:51:15 Think of them as they're four of these kind of minima of the first few traits that really define if you kind of sensible combination that are very hard to break within them.
15:51:27 You have lots of freedom of in the other trades whether you have them or not have them, and some of them are still more sensible than others in a given environment.
15:51:35 So there's some you know diversity in here, which is changing over time. So that's kind of the, the whole picture is that it's not like a model with our five minimum their for their fights PC.
15:52:00 It's precisely the situation where Okay, it looks like there's this type you zoom in, you see that they're in this family there are 15 general and then you zoom in and there you know, Five to 15 ZSK so quick question first.
15:52:04 We've been thinking about this this sort of similar thing with with Daniel long I guess I'm curious in in these figures.
15:52:10 How much of this should I be interpreted a little colors as ecology sort of at all levels, like you said, versus just evolution like we might see in, you know, use population like if I turned off the patients after generation 600 would many of those things
15:52:26 go extinct or what they sort of coexist forever.
15:52:31 Yeah, so let me make a comment so first of all yeah this is kind of.
15:52:51 not going entrepreneurs like sweeps. So at any given point here you can stop and see who will equilibrate and coexist.
15:52:56 So the to the four big branches are ecology, a lot some of the diversity within is not get a college if I wait some of them will be out competed right of course.
15:53:04 But the point is, so there are a lot of kind of ways of asking like a lot of work in this kind of models, where the question is trying to explain diversity.
15:53:18 Right. So there's all these types of coexist. How come right what's the mechanism establishes that. So here, I'm going to kind of make clear that I'm instead of this being something I'm trying to explain.
15:53:31 I say that this I started this is my starting point.
15:53:34 By construction in the smaller remember my L infinity goes to infinity. I postulated arbitrary number of niches.
15:53:41 So by construction, an arbitrary number of types could coexist here.
15:53:46 So my question is not How do I explain it school existence, but given that the school existence exists.
15:53:52 And let me kind of take that as evidence that maybe there are lots of niches and maybe I don't understand all of them, and maybe I'll never understand all of them.
15:53:58 How can I course can of course green the diversity, what's the right variables remember this starting question, are some kinda like, and what I showed you there's these core traits and accessory trade, and they're kind of look noisy.
15:54:12 And I ignore them, or what questions can ignore them.
15:54:15 That will be the question I'm asking.
15:54:17 And for now I'm just setting up the just the intuition of what the model looks like. Yes, Andrew.
15:54:22 So if you look at this picture, you could construct a world where it looks a lot like the picture of the Lynskey data that Ben good collected, where you have persisting ek types and you see sweeps within them.
15:54:39 Do you think that similarity is interesting or coincidental.
15:54:45 It's part of what we're hoping to do so. Specifically, like there's a lot of questions that the kinds of questions that Ben was asking about this Lenski lines are not in any way solved by this so for example, you know, how do you get the situation where
15:55:02 you keep getting new mutations at a comparable rate. It doesn't decline, right here, like, I think Sergei pointed out there, kind of magnitude of fitness effects that remain keeps going down.
15:55:14 Right, so some of the puzzles that that analysis was trying to explain specifically for Lenski is not here. However, there is a lot of work where we're trying to understand for example the structure of who's in entries.
15:55:26 And how do we put ecology in them.
15:55:29 Then pointed me towards some paper that, like we can postulate that occasionally, you know, a new niche is discovered and colonized, and then there's some rate at which of extinction or something and ask what kind of trees that creates.
15:55:45 That is not a very rich generated model, because those niches don't interact anyway. Here they do. And so one question would be if we learned to understand the structures that this kind of simple framework generates with a few parameters.
15:55:58 Would that give us any more handles on quantifying or characterizing, you know, real trees comparing them and saying, Oh, this parameter is very different when I'm trying to fit the tree of insects, from the tree of mammals and what does it tell me, or.
15:56:13 So with bacteria, there's much more recombination have to worry which is not here.
15:56:18 But yeah, this is something that I would love to talk to somebody about when knows more about this than me.
15:56:27 This would be an exciting direction.
15:56:29 I think I have to restate Ben's question because I'm not sure I totally grasped your answer. If I how much of this within eco type strain coexistence is a result of the hierarchical structure of the way you built the JJ is and how much of it is coming
15:56:46 from continual mutation.
15:56:49 Yes, so precisely because for their first pass of this we didn't want to worry about that.
15:56:56 I'll just say now imagine that I run this for infinite time.
15:57:00 And because my model was deterministic, there was no room for like older, like, it's one of the very exciting directions to add something like your fitness mutations, but for me I said this phenotype has this cost.
15:57:11 If this is what you're doing.
15:57:13 This is your cost nothing you can do will ever make you better, right.
15:57:18 Then there is such a thing as final endpoint of this process and eco evil non unavailable state.
15:57:26 And that will be I'll be constructing things I study out of those sets of strange.
15:57:36 Again,
15:57:36 there are many.
15:57:40 So, because I work in a model where there's the up arrow function.
15:57:46 It's there is only unique true not available one.
15:57:50 Now, there could be multiple.
15:58:01 Well, but it is convex here it is a convex.
15:58:10 No, it is yeah so for whatever whatever JJ is whatever costs, it's still conducts optimization. Now, and that gets back to me to what were the mutation rate and sort of like important parameter not.
15:58:20 If I sample enough phenotypes, like, so if I don't sound on the phenotypes I could get trapped into a locally non available one that is only not available by first means empirically.
15:58:33 When I run this, basically you know I start from different colonial states, I converge to almost the same final states, almost the same because they're very slow modes at the end, or.
15:58:46 Yeah, we can talk about that more basically for, like, I'm trying to be very careful there, but for practical purposes. There's one final state in a given environment.
15:58:57 and I'll talk about this in a second.
15:58:59 Also this is just a picture. And the whole point is, let's learn to sort of quantify the picture in some way. So maybe after I've discussed this slide, maybe it'll clarify some of this.
15:59:10 Because now if I look at the final equation equilibrium state in a particular run in an environment. This is what I look at what is what I see sorry this is when we will clear, every row Yeah, every row here is a phenotype.
15:59:26 And you see here 27 coexisting phenotypes in a particular run.
15:59:31 This was the community that established phenotype as the Yeah, he strained.
15:59:39 I'm so glad I didn't try to put two stories in this because I'm
15:59:46 okay. So, observation is that kind of.
15:59:52 Now this is not just sampling low cost phenotypes This is actually the final kind of state of the community, but it still has some of this nature of, you know, they look similar, or more the traits, there's like a few sensible configurations the beginning
16:00:06 and then they paid search kind of started looking more noisy. Is there a way to quantify that.
16:00:11 So as an example, the ones I highlighted there, those are seven traits seven strains that if I looked at their genome.
16:00:22 And I use the kind of.
16:00:24 I'm not that, you know, I'm not aware of all the factors as well, that are relevant for the community. I made a list of the first 20.
16:00:32 And if I only look at first 20 I can't resolve.
16:00:35 Right. So, and actually they start differing something like position 2020 25th position is the first where they differ, so I will say that they belong to the same Belle Starr type, where else stars 24 that level of detail.
16:00:50 24 traits.
16:00:53 They behave, they are in the same class.
16:00:55 And then if I zoom in really closely past Trey 24 I'll see some distinctions.
16:01:00 So this is kind of a course grading scheme that is suggested here Yes,
16:01:11 sorry yes I'm, you can tell this the first time I'm giving this talk. So, this is so I take these dynamics.
16:01:20 I wait for infinite time,
16:01:23 have a coffee, see what the final non unavailable state is of this community given this realization of biochemistry. This JJ is we should pick once and for all the random realization that's my world.
16:01:36 Okay, so in that world in the environment where only shows are equally available right, what are the phenotypes that coexist at the final state. So here I have 40, mile star is 40, sorry not all star.
16:01:52 The Infinity the sort of microscopic description is 40 resources so I can't have more than 40 strains coexisting in this case there 27 of them, that happened to coexist.
16:02:13 structure to them, which is what I was trying to capture and I'm asking how do I quantify this. And one way to quantify this is so I said let's define these acorns grading scheme, putting them together into what I'll call L star types.
16:02:23 So if I only look at the first trait. Well organisms could have it or not, there are two types.
16:02:29 I look at first two traits.
16:02:31 Therefore combinations and all for I think our president no actually three or present. So there's three types with all star equal to.
16:02:38 And as I look at different L star, how many.
16:02:43 I'll start types are there in the community.
16:02:46 And I see that well for a large plateau here. I have this number of all star types. And then, of course, you know, at some point I start seeing more and more details of course I can resolve more and more types.
16:02:58 It's okay, maybe you know Is it true or is there any sense in which that is somehow the correct level of course green, that's the kind of question I'm trying to motivate and this kind of actually you can do these kind of things with data for similar kinds
16:03:14 of things like people look at how many you know if you wish to use our within you know if I lost everything by 99% 98% 87% How does that grow, not exactly this but that's kind of the way the connection.
16:03:34 But,
16:03:35 yes, yes.
16:03:38 But ok, so this kind of looks a little bit like, Oh, you know, that's, you know, one of those types of the bottom was kind of like a call line and call I can sometimes be resistant to this thing and not resistant to this thing this is the kind of intuition
16:03:47 I'm trying to put on this.
16:03:49 But, you know, there's more to this intuition so if I'm if I'm sampling material from the soil.
16:03:55 I look at the material here and then I look at a different patch of soil different types of soil, and my expectation is that I'll be getting, you know, I'll keep discovering new and unique strains, but they'll be variations on the few types that I saw.
16:04:10 Right. So, with that motivation and to get away a little bit from this notion of evolutionary equilibrium. Let me do the following let me look at, I don't know, 50 similar environments.
16:04:24 So I start with my environment, my golden environment. We're all niches are equally available. The way defined for you. Let me know perturb it a little bit.
16:04:35 In 50 different ways, and in every urban environments that was my different passions of soil, run this thing, and get a collection of strains, and then pull together those strains.
16:04:47 And this will be my strain pool defined by the environment, which I will then take that strain pool and put into my golden environment of interest and ask how they interact there.
16:04:59 So technically you know I never required evolution equilibrium in that environment, but you know that's a little kind of, can I just clarify environment you mean a different realization of gij know Jay Jay's.
16:05:13 yeah. Very good, thank you for that question. I should be I should have us like slide like emphasizing that JJ is, that's my biochemistry fixed once and for all.
16:05:22 I don't change that okay environment is availability of like the benefit from a given niche and see. Second, your parameters see know so those are my eyes and he is.
16:05:37 This is my environment. Good. So I'm flowing in this chemo side and flowing this much glucose and that came.
16:05:44 Second, they're not all the same no or not and not all changed together in one environment, where they change. So in those 50 environments, I'll fluctuate them around that, yes, I should find a more concise way of saying that but yes, thank you for, I'm
16:05:59 glad people are paying attention.
16:06:02 Question. So, right now, in this last blog. Your niches are about 75% field in other words you have about 30 pieces out of 40 niches. Yeah, but that must be a function of your ruggedness of your landscape, you have you tried playing up with gh making
16:06:21 jG amplitude larger and see for example yeah if Jay Jay's or as I make JJ is weaker and weaker. I'll get saturation, that's pretty much the regime we've used to study.
16:06:32 And that's precisely the reason I want to go away from, but also I don't care about how many species coexist because remember, I'm thinking of 40 is going to infinity.
16:06:39 And so how many types of existence not really a problem and in fact, I'll just go ahead and look at my 50 environments, go to all those strings together and call it a strain pool and now the number of threads in my stream pool is of course no longer limited
16:06:51 by 40, because in every environment I may be getting slightly different strains, but I'm putting them together, and I'm saying in my universe. This is kind of like the strains I encounters and experimentalists I you know sampled here sample there.
16:07:07 These are all possible strains that I saw. And I want to come to this and say, Well, look, there's the CO y and Pseudomonas.
16:07:15 And I don't want to be hunting down all the details going to make any predictions without, you know, paying attention to absolutely everything. So in the right block, your eyes are different in each realization right yeah you assemble them uniformly or
16:07:29 something, I keep he is the same for simplicity, they're all ones. And I vary a little bit the caring capacities and I with plus or minus 10% each and independently.
16:07:38 That is technically a parameter of course yeah and you still get an exponential growth. Right. Again, in the total number of possible strains, yes somewhere else, because down there, that that diversity is very unconstrained it's very sensitive to environment,
16:07:53 everything can change. And so now there's no longer like a plateau, but it still has the structure that first there are few types, and then beyond a certain level it just explodes because well of course it explodes, you can have this not have that right.
16:08:05 And so the question I want to ask. And I'll maybe give you have time to give you some of the answer.
16:08:12 Can I ignore these details.
16:08:16 Right. Is there a sense. And the answer will look like.
16:08:22 The answer.
16:08:24 Yeah, so the answer in this model will be kind of interesting, which is that we, sorry, can I guess I'm confused about two things so on the left side, this plateau and L star is a trivial consequence of how fast your jij is fall off as you move away from
16:08:43 00 along the day I go. Yes, you could predict that basically just by looking at the number of large entries and JJ right.
16:08:50 Yes. Kind of, yeah, yeah, roughly, okay, yeah. Okay, and then can you just explain one more time what happened when you went from the left side of the slide to the right thing.
16:08:59 Yeah, so here I take my environments, and I modify a little bit the availability of the niches. So the intuition is that the trace down there like the tail end traits are very, they're very easy to gain or lose, right there very controlled by the kind
16:09:14 of by the environment. That's this intuition will become more precise as they go, go forward. But if the in the environments, there's more of that resource.
16:09:22 Right. Some strain can easily pick like pick that up and depleted, to the.
16:09:29 I'm not sure that's helpful. But, yes, so those train those.
16:09:38 Okay, let me put it this way. If I take my original environment. And I give it a make a small perturbation here and perturbing everything. Let me just give it more of, of, you know, increase nice 3737 is one of those very weakly interacting issues.
16:09:53 I just pay the cost for it. And if the benefit and the environment is larger than the cost, I pick it up, and I'm better, right. I'll do that.
16:10:01 that's very easy.
16:10:04 Now, If I do this to trade one.
16:10:09 So those later traits are very sensitive to environmental things they're easily gain and loss. If I do this to trade one, I can just easily flip trait one because drink one interacts with all these other things.
16:10:19 And so, that's not going to happen there's still only a few combinations of the traits early on. So as I changed environments I'll get a lot of diversity in tail and traits, but none of the beginning.
16:10:33 just can't see it because the y axis got blown up. So, yeah, so Okay, number of types, is a very sensitive is not a great measure if I looked at least at something like entropy.
16:10:44 This is immediately increases by one. If I even have just one blip and some particularly environments where the first traits changed enough that.
16:10:53 But yeah, you have you have the right intuition.
16:10:57 Sorry, that was possibly more details than.
16:11:02 Okay, so high enough to announce what the kind of the the endgame here, which I'll actually I think we'll be able to get for most of it. But the question is looking at these plots, it's tempting that I set this whole thing up for it to be tempting to
16:11:22 call. Oh these are kind of details.
16:11:25 Is there a sense in which that's true, and I can ignore it, and the corresponding description, be a sensible description for some questions, what we'll see is that the answer in this simple model is still kind of interesting, which is that for some questions,
16:11:41 you can ignore them, not for others. But for the questions when you can ignore them.
16:11:47 This requires two things. First, it requires that the strains that you're studying remain in their natural diverse ecological context.
16:11:58 University College with other strains, and in close to their native environment.
16:12:06 So that's the kind of phrase that I'll try to unpack, you will see that I kind of engineered a little bit the model for that to be true.
16:12:13 Right.
16:12:15 Basically by making all these niches equally lucrative.
16:12:19 But interacting in different ways.
16:12:21 But I think that thinking about this model is still kind of instructive in this way, it's kind of engineered to be a particularly, you know, interesting example, in a way, but I think that's kind of an interesting theoretical exercise.
16:12:39 So,
16:12:42 but first. To do this, to talk about, when is the course greening Okay, what does it mean, I need to somehow define what it means for course greening to be good.
16:12:53 Right. Actually what is it was raining in this model. So the whole point of this is to make it possible to ask those questions and Cleveland quantitatively, even though it's a simple model which we can then build on.
16:13:06 So, what I described for you so far.
16:13:10 Is this unattainable level of kind of microscopic model. Think of it this way right the Infinity factors that are relevant for the community. It's kind of like I'm looking at a leaf and a leaf is this in the community living on the leaf is an all these
16:13:24 crevices and there's water occasionally and all of that really matters potentially.
16:13:29 Now there's no way I can ever construct a microscopic model that takes into account all of that.
16:13:38 As a modeler all I have access to, is an Iraqi have ever more detailed models with the understanding that I'll never get the whole thing.
16:13:44 So, to construct the sort of hierarchy of course grading schemes.
16:13:48 Let me think of, I have this parameter which is level of modeling detail, which is, which has never quite infinity.
16:13:57 I forbid l from being all infinity, which will allow me to settle infinity to 40 knots, you know, million.
16:14:05 So, yeah.
16:14:11 That would have been good.
16:14:13 When I do this one submission.
16:14:15 Okay, so I have like a completely naive model the leaf and the slightly less naive model of the leaf right but I'll never get the full thing.
16:14:24 And so, in my world here.
16:14:27 For every description that only knows about the first l traits.
16:14:31 I have my biochemistry defined.
16:14:36 Up to L traits. I don't know about trade helpless ones I don't know how to interact with anything, but my matrix JJ, I look at the first L by all components that defines me and approximate model for modeling level of detail out.
16:15:02 I can you know look at the pool of what I'll call l strains that you know this model predict would exist in this environment. Right. And all the way until you know this, some very complicated structure at the end.
16:15:08 Now, within any model.
16:15:11 I can now ask, Do all details matter.
16:15:14 And I'm kind of trying to play both games here, right. So, typically you would think, how do I evaluate a corresponding description, I have the Microsoft model, and of course green model, and I should just compare their predictions in the for close enough.
16:15:26 I call my color is green good.
16:15:29 And here and trying to kind of remember that actually.
16:15:33 What makes this kind of game interesting is that you you don't have the full microscopic model, and you'll never have the full microscopic.
16:15:41 They're always these unknown unknowns. And how can we deal with that. And at least in the simple model we can sort of try and deal with that.
16:15:48 So, are any L.
16:15:53 You can look at different levels of course grading and say well what if I take my, you know matrix, and only look at first trade I only see two types.
16:16:01 Is that enough. Well probably not enough. Right. Okay, let me look further.
16:16:06 Now of course, for a fixed L.
16:16:09 The larger L star you use, the better your predictions.
16:16:15 Under whatever. So of course, this requires me to define some metric of how happy I am.
16:16:20 So for a given question.
16:16:22 Let's say I have some way of evaluating whether level of course grading L star is good enough for my tolerances within the model with parameter L. Okay.
16:16:35 And for any L, including more details will always make predictions better.
16:16:40 But the key question is not that.
16:16:44 What makes a chorus greening ballad, is whether for a given L star. As I increase, l, my predictions are still good enough.
16:17:02 Yes.
16:17:03 Yes. Oh, I see. Sorry, I forgot to repeat the question So Daniel is asking, but the British was always getting worse because your model gets worse.
16:17:10 And that is, of course, absolutely true in general.
16:17:14 In this model because.
16:17:20 So, in real life is can only be approximately true that may be describing up to here is sort of good enough.
16:17:28 In this model, it can actually be sort of rigorously true.
16:17:31 You can include extra niches that you never knew about, and not spoil your predictions.
16:17:39 At least approximately this is I mean analytically this will always be, there's a little bit of a tail end of some topics there.
16:17:46 This will hopefully be.
16:17:49 This is not an exact political statement, this is more of this. What I'll show you is simulations and I, I, you'll see what I mean.
16:17:58 So, just to finish that thought.
16:18:02 Imagine that I had some criterion, which is now the question dependent criterion that will tell me if at some level of all star.
16:18:11 I'm satisfied by the quality of my predictions or not.
16:18:16 So there's some line here that I'll say, Well, you know, obviously for any l using L star equal l will be good enough. Because that's the full description of that model.
16:18:30 Right.
16:18:30 But the question is, what's the sort of aesthetics of that line.
16:18:37 So, Question.
16:18:42 Admit scores greening if, for a given sort of tolerance. If this curve has an asymptote, as you go. And mine meaning of asymptote will be a sloppy meaningless and I run a simulation.
16:18:59 And I see that it saturates, this will not be an analytical state. But if these kind of hunter lines, you know, carbon look like they have a limit here that tells me that if I want this level of tolerance on my predictions.
16:19:12 This L star is good enough. And as I add more and more components to my model, it doesn't break that right and this is what we do is modelers. You say, Well, I'm trying to understand this metabolic process.
16:19:25 It probably doesn't matter exactly how many flagella the thing has. I could include in the model and show it to you. Right.
16:19:32 We typically won't make those choices. So this is kind of that idea, but kind of formalized in this way. Does that make sense.
16:19:42 Yes, the only place I know where you can do this well as thermodynamics, and there I just asked about extensive and intensive quantities.
16:19:51 And this is exactly the opposite of that. And so I'm just confused.
16:19:59 It sounds like a kind of question that we should have in the break after this, because I don't have a snappy answer to that.
16:20:08 And there's a big chance that you'll confuse me as well. So let me just show you what what do we have and then we can take it over over here.
16:20:16 Yes.
16:20:22 The question is.
16:20:26 So the question is what do you mean by asymptote in this particular case.
16:20:29 Yes, so all I mean is, I'll show you some simulations, and I'll sort of tell you. Maybe you agree with me that essence was look different.
16:20:40 And so the this whole value here is, you know, in some sense, making these statements, more precise, even more precise in this kind of simple model like this there's some trade off between well in this model it might actually be it's true sometimes it
16:20:54 will never be in any real situation so here I've kind of got content with just the simulations to kind of spur this conversation and let's see what comes out of the conversation.
16:21:03 Right.
16:21:05 But basically distinction is, if I see this, that okay you know in this model for l equal 10 five traits was enough.
16:21:15 But if I added five more factors that I forgot to include. Oh, now I need 14, and if I included three more. Oh, now I need 17, right, that is not of course variable question.
16:21:28 Right, that's what I'm trying to set up.
16:21:31 Okay, so, and all of this. These are contour lines of some function, q quality of course greening of model with a level of detail, l coarse grained to the level of detail star, which I now need to define some examples of that to try that.
16:21:50 And, Oh man I have seven minutes
16:21:55 in questions, because I know I'll have like 10 of them this is just to discipline myself and Sergei.
16:22:01 Okay, so I'll do the following. I'll define.
16:22:13 And then I'll go straight to the conclusions and we can talk about everything else afterwards.
16:22:18 So, basically the final take home from this will be in this contrasting between the two possible interpretations of what a good chorus greeting means.
16:22:20 I'll define two criteria for this course granting because that will, I will then show you these slots that will look like like this.
16:22:28 And, you know, the model is wages simple, the definition of what a you know this asymptote is not going to apply beyond the simple model, but the value of the discussion will be maybe in that sort of possibly slightly more generalizable take.
16:22:43 So, what are possible.
16:22:46 I'll claim that their least two ways of thinking about what a good course branding might be.
16:22:53 Imagine that I'm looking at. Okay, this is a community.
16:22:56 And I say oh here's a possible of course grading Let me pull all reddish types in one beaker, bring these types of bluish types and call these my three species.
16:23:05 How do I test. If that was a sensible course grading. What are possible criteria might require.
16:23:12 So, option one is what are called reconstitution test.
16:23:16 So imagine that I want to ask. Okay, I want to describe the soil as saying that what lives in the soil is, these three phyla. And that's all I need to know.
16:23:30 One way of testing that would be well if it's true.
16:23:33 Let me go and take a representative of this file and that file and that file, bringing home, put them in a petri dish in the environments mimicking soil and ask what do I get.
16:23:45 And I do this over and over with different representatives.
16:23:48 And if I see that I kind of get similar results, and maybe that was a valid course breathing.
16:23:55 Right. However, imagine that well okay I say it's a colon colon bathroom this thing.
16:24:01 And I bring them home and somehow. Occasionally I get this answer and occasionally gets that answer.
16:24:06 And that'll tell me that oh there was something about what I call the Nikolai there was some distinctions there that I wasn't allowed to ignore it matters because it matters what the community assembles and so there's some detail there that ignore that
16:24:19 I shouldn't have.
16:24:20 That's where and I have little asterisk here. That's where the existence will open a function is very important for me.
16:24:28 Because, you know, in any sensible model of ecology, you could get this just because the alternative steady states, all sorts of things right here because it's a simple model like that.
16:24:37 I can attribute. If it's, you know, if even identical phenotypes can assemble two different things. I need to disentangle that from the fact that I ignored some details here, if they were really interchangeable they should have similar to the same thing.
16:24:51 So I can uniquely attributed to porkers greening.
16:24:54 So, how variable those abundances are, that could be a metric, of course, granting quality under this approach what I call reconstitution test, which seems like a sensible thing.
16:25:06 Right.
16:25:07 Okay.
16:25:09 Now, Here's an alternative approach.
16:25:13 And I'll call it leave and leave one out test which is possibly about a name I don't know if you can come up with a better one. Please tell me which is, here's another thing which would also be sensible.
16:25:26 In terms of when is it okay to group strings together into the same unit.
16:25:32 I want to attribute, I wanted to be sensible to say oh this community is missing any call I normally in this community there would be a Nikolai Nicole I could be any of any number of strains right but somehow oh here there's a niche for equal I don't
16:25:50 get tested like this. Let me, assemble a community leaving out one of the my star types, right, one of my types that I'm trying to test if it's a meaningful course grading or not.
16:26:02 And then say, Well, okay, if I try to add. What I think is an equal lie, but different representatives of equal lie.
16:26:11 What do I get.
16:26:13 And maybe I'll see some reproducible invasion by all of them.
16:26:18 And then I'll say, well, maybe they they behave sensibly similarly enough, it was sensible to group them.
16:26:24 Or if I see that some representatives can invade others cannot invade. Right. Everything is very different. I'll say well that's that's very.
16:26:31 I'm missing something important.
16:26:35 So now I'll flash it to you the plot for those two things.
16:26:43 Okay, and I don't, I won't have time to explain why that happens but I'll go through this quickly so remember that the things was, this is kind of my criteria for telling if something is Chris green have or not.
16:26:55 So for these two tests of invasion rate of a missing strain behaving as a function of Ll star, and this reconstitution test lol star. This is what you see, this is great out to remind you that I say that, you know, that is unattainable I'm not allowed
16:27:10 to sell to to actually 40.
16:27:13 What do you see here is that you know you are you are allowed to ignore some of those tail and details for predicting who can innovate.
16:27:21 But for the reconstituted community to behave like original community. You need to get all the details right. So basically, this is kind of in this model, kind of, you know, addresses, or reproduces, if you will, this will seem like a paradox which is
16:27:37 that grouping strains into corresponding units can be justified under some questions under some criteria, even though, you know, in this sense all details matter you can show the results will be different depending on which train you got, but you know,
16:27:52 to answer this question. It's okay to group them together.
16:27:56 Why does this happen. This is basically a short answer is that the tail end traits in this model become effectively neutral in the environment of the assembled community specifically.
16:28:10 If you had enough diversity in there.
16:28:12 And some of you know we worked like with, like with me, this idea of you know a phase where you know shielded phase environment, community creates its own environment of interactions or we can, we can have this is kind of that phenomenon.
16:28:27 So, okay, I will need to skip this basically leaving you with a puzzle.
16:28:36 Ah, ok I can probably say this quickly.
16:28:38 So if you have if I'm looking at phenotype.
16:28:41 And I asked, Should this should I lose that that talent.
16:28:50 Okay.
16:28:53 Yeah. So, let's say care we trade, I and I'm in a diverse community.
16:28:59 What's the cost or benefit of losing that talent race. Well, I no longer get the benefit HIV but I no longer pay the cost for the trade Chi, and if it's a weekly interacting trade.
16:29:11 And so this term, basically doesn't matter. Then, the cost is equal to benefit if hi is basically Chi.
16:29:21 And if I allow evolution dynamics to go in here and ask revolutionary equilibrium.
16:29:26 Hi would be driven to chi, and the only non trivial statement here is that if you have enough diversity evolution, you know you don't say that evolution is happening in your beaker, but there's enough strings there that they know how to populate those
16:29:37 niches. And that was some results from, you know, what we did with Ramey but also recent paper with Jacobo release group. They call this a functional attractor state for weekly tracking traits, they're driven to this place, which is a place where carrying
16:29:53 or not caring that trades doesn't give you obvious benefit or penalty, right, because it's kind of a modular trades in the sense that it doesn't interact with everybody else.
16:30:03 So that's very briefly. The reason why this happens in this model, I have some example here, which is basically that this is the traits where you remove different I'll start types, but all of these aren't affected.
16:30:17 Sorry, this.
16:30:19 I'll just talk through this and this is the explanation for why you can ignore them for the reconstitution test.
16:30:26 While you can ignore them for the invading strange test.
16:30:30 And very quickly. Why don't you.
16:30:34 Why can't you ignore them for the constitution test that is very simple.
16:30:37 If you look at just logical terrorist style interaction between two traits.
16:30:42 This is the simple math.
16:30:47 That's some over I own issues matter of the matter equally. You see that that's where I said that I, you know, the example is one engineer because I said that all the traits that I don't know about.
16:30:58 I postulated that they all potentially matter equal to the community.
16:31:02 Some of the traits I don't know about maybe very important.
16:31:05 Right. And yet they can be negligible for some questions, that sort of thing not true.
16:31:09 Okay, so then I will.
16:31:12 There's a sanity check that if your traits are truly neutral you're always allowed to ignore them. All of these things have asymptote.
16:31:19 There's thing about home Environment Matters.
16:31:23 There's a lot of hopes for the future.
16:31:25 There's this is the second story which obviously I didn't get to.
16:31:30 I'll just read the take homes.
16:31:33 So the specific ones is that the big exciting hoping here is kind of this question what is the right variables.
16:31:42 And I sort of showed you this framework that based on resource competition that allows you to describe interacting phenotypes in this hierarchical way, increasing level of detail.
16:31:52 If you wished, or reducing it if you wished, which allowed to make these questions.
16:31:57 quantitatively precise, at least in the simple context, and of course it's very simplified context but we can build on this.
16:32:05 And so, hopefully it kind of address these questions of how physiological constraints affect the structure function relationship.
16:32:14 Within this model. Okay.
16:32:17 This is a very strange description can be adequate for some questions. Even though it's grouping together strains that you can show depend differently.
16:32:26 Under the circumstances, kind of, you know, mirroring this paradox that experimental observed.
16:32:33 This is the part that didn't really show you. Well I briefly ran through this and it didn't really show you that. But that's that's in the footprints.
16:32:43 And I just want to finish on this which is kind of the bigger picture a little bit speculative but in this field. Felt appropriately appropriate for kind of ATP still talk any description of an ecosystem is always of course green.
16:32:58 Right.
16:33:00 We will never know all the unknown unknowns.
16:33:03 And so, We have no other choice but to hope that some programming work.
16:33:10 Right.
16:33:13 And so okay I pitched this as you know that's for me is the exciting question that systematically constructing and evaluating this for screenings. How kind of in a question dependent way is ultimately kind of the challenge.
16:33:27 Oh, Wow, okay.
16:33:30 Broke up the middle sorry, but the take home from this story is that when we assume that of course green unit is meaningful when you say okay, this is this species and that species and that's how you know, meaningful level.
16:33:46 What might we mean.
16:33:47 And I feel like there's this kind of theoretical exercise suggests that there's a distinction possible here.
16:33:56 The default intuition is that we're grouping together individuals that should be similar enough are interchangeable enough.
16:34:04 And I would argue that this is, this is what I call the reconstitution test in this discussion. Basically, I can replace the species by any representative of that species to a sufficient level approximation.
16:34:18 I think what am I argue that this is basically assume by all compositional models, this is what we mean when we put in one dot.
16:34:25 Right.
16:34:27 But that's where the paradox is coming from because probably given the sort of external evidence.
16:34:32 This is probably never really true.
16:34:34 Unless like if you, you know like, auto as this recent paper, you have to go to something like hundred base there's differences and already count them as different types, because you can see them you know experiment, interact differently.
16:34:48 And this sort of proposal is maybe that's not the only way of thinking about what makes a coarse grained unit meaningful. For example, maybe the right way to think about a species equal lie is a place and some theoretical sense, it's like a beaker and
16:35:08 it's written Nikolai, but inside is the entire kind of diversity of strains that we call I.
16:35:14 And then the quite the statement is that if you mix this diversity, with diversity cold. I don't know, sort of bonus, you will get some reproducible outcome, as opposed to any strain here and any stream there and tracking the same way.
16:35:27 And this is a model where it's not.