13:03:56 Yeah, so I changed my title slightly especially for Pankaj's benefit.
13:04:02 See, obviously the puzzle of diversity goes way back and you know for Beatles, there's a lot of different things they do complicated things they don't all live in the same place, so on.
13:04:12 So one of the microbial diversity that people have been talking about is obviously that's much more of a part of the puzzle of understanding the microbial diversity, but to me that the most puzzling thing is why as you go down and scale you continue to
13:04:24 get more and more, more diverse I'm going to show one particular example of it. And so the crucial bit is that this is diversity between coexist in a single, single location so everything is directly almost directly competing with each other.
13:04:40 Now we are talking to most ecology friends they will say this you know micro dishes and there's just lots and lots of niches there, so I may be willing to believe in Micronesia, but I'm not willing to live in Jaco niches.
13:04:52 So Ayako is a particular unit that one over Jaco with a number of different genomes of abundant bacterial species of a single bacterial species is an inverse of the Octo.
13:05:03 So they obviously each genomics into different does not quite different needs.
13:05:07 So one possible explanation to really at the interplay of the ecology and evolution, and somehow happening fast enough that things aren't driven extinct.
13:05:17 Even though some of them to be competing together 400 million years and some here and some day and so on.
13:05:23 or is there some, some other explanations.
13:05:26 So, there's a related question which is on this evil part. Um, which is one of the points of a general expectations are about evolution, particularly if I have an evolution which is in an externally fixed environment, do I expect that to continue to slow
13:05:52 know the classic picture is it will reach some fitness peak, or and I think a lot of people here in bottles and zone will do it, or redo some stable ecology, or what. Okay. And there's some slight hint for experiments and Ben good can tell you whether
13:05:57 And there's some slight hints for experiments and Ben good can tell you whether they're that I'm completely legitimate in saying these are hints, or not, but they certainly motivate the question about thinking about the possibility of whether the general
13:06:11 behavior is perhaps not that the evolution should slow down, but maybe it keeps going. And so that that's actually the first part that I'm going to talk about Daniel, can you clarify what slow down mean the rate of growth rate slows down, or no so I can
13:06:22 think in terms of evolution so this is definitely asking about evolution, so I could mean say the rate of fixing of new mutations that doesn't doesn't slow down that's that's the impossible.
13:06:32 It certainly doesn't in Lenski, long term lines, and Ben's analysis of it, it certainly doesn't slow down nearly as much as one would think it does after the initial transients.
13:06:42 But of course you know they haven't gone quite forever yet. I think rich wants to get up in perpetuity so maybe in 1000 years we'll know we'll know more.
13:06:51 Okay, so with a question which goes a lot of you here of trying to ask whether something's emerged from the complexity and complexity in the sense of the features that sort of high dimensional, and I'll be somewhat precise in certain, certain context
13:07:05 and really one of them talk about sort of possible phases, what possible scenarios are the one could distinguish between them.
13:07:11 And in some ways the real goal here is to ask, what should one not be surprised by, you know I find this tremendously surprising I do and which but which things are will not be so surprised by in the sense that if you can find it in simple models, then,
13:07:26 that doesn't mean it's an explanation at all, but at least says, maybe it's not so surprising.
13:07:32 Okay, so here's the example what I want to give which is a particular caucus and I realized yesterday that all the substantive projects that I've been involved in on on microbes are old cyanobacteria on three that in three different things one of them
13:07:43 directly talked about.
13:07:46 talked about. The other day I would like to say in retrospect, that's a good sign of bacteria by far the most important organisms on the planet, especially them historically but in fact it was more to do with friends and other other connections with, with different
13:07:58 people. But anyway, Hong Kong because it is a wonderful example is their small small genomes enormous numbers of them in the ocean, they completely dominate the photosynthesis in the tropics, as against in the nutrient poor parts of the oceans, as against
13:08:12 if you go near to the coast. There's all kinds of phytoplankton which are competing with each other very complicated them. One more thing what they're doing is relatively simple they're, they're dealing with that planktonic they seem to get eaten by some
13:08:23 other little tiny plankton and so on.
13:08:27 So this is a collection of very closely related protocol because they were filtered for having very close.
13:08:34 Success sequence, basically, and the, and then looking at a bunch of them were taken from one location one sample order winter and spring doesn't seem to be much differences between them.
13:08:43 And this is all from single cell sequence.
13:08:45 Now phone starts, I'm looking at the these things quantitatively the time since the majority of the whole group, most of them are similar subgroup of that sub group maybe 10 to the five years like that, on which state was a pretty extensive recombination
13:09:00 I'm gonna say more about that. The closest pair there maybe diverged hundreds of thousand years ago divergent about 10 minus three.
13:09:09 The ocean mixing times is claimed to be over 100 years in some aspects and certainly fast in the Atlantic in 1000 years globally. So these are globally competing on anytime scale, in which you can actually observe the divergence.
13:09:23 So we've been starting to look at, much more single cell data and this is particularly around a popular show in in appropriately rugged landscape. Anyway that's appropriate.
13:09:33 And the trickier is on a data from brew bed also Penny Systems Group, where there's a four to 500 single cells fully sequenced or 70% sequence typically take some of them that are randomly sample some of them trying to get to get more bigger, bigger variability
13:09:51 in them. And this is then showing the the distance some matrix is there that sort of useful one is to save the genes they have in common, which is rather a large fraction of them.
13:10:00 And look at this sort of distance between those users look at medium distance so you know dominated by the ones that are coming forward. And so here's on this scale here, and there's a particular group here highlight highlight to.
13:10:11 These are low light groups here, some of these ones here are called cynical cockeyed, but they're close to the low light protocol because the nomenclature is very bad by normal 16 s definition this whole message one is one species it's of water 3% 3%
13:10:39 They look at the cells which custom and looked at the ones I throw the previous slide that's some little bit of this bit in here, and it's almost completely uniform on here you can see slight shades of of variation and that's corresponding to basically
13:10:43 60 minutes.
13:10:43 If you go to distances more than about 1% phylogenetic distance is more than about 1%, certainly by the time you get different been here in here but actually by the time you get differences of the slight shades differences you can see in there, it's not
13:10:55 clear as any a sexual backbone left. The closest relative to the ones that had been sequence, you definitely see what looks like an asexual background, even though we don't entirely know yet.
13:11:04 But once you get to these bigger scales, this seems to be completely overwritten by recombination now pro quo or Cockers were for a long time a classic post the classic example of factory they didn't have much recombination except for in these little
13:11:17 islands a variable variable genes which they have a modest number of highlight ones which has been the most the most.
13:11:24 So there are clearly some dishes involved. I'm here. The highlight one highlight two there are definitely different features that they have. And then the low light ones leave a little deeper down, but within that it's not even knowing what the phenotypic
13:11:36 differences are between these were the clearly our clusters, and certainly not once you get within this and certainly not once you get within, within this, and I think if we start to look at correlations with various things in space and other things so
13:11:48 far at least haven't been haven't been successful. Okay, so that's basically the motivation can now I'm going to go entirely to, to, to theories.
13:11:57 The one thing just as you know how does one characterize the diversity almost all observations are of the phenotype but of course I would like that phenotype but we're once you get a lot of it, we're going to have to focus on statistical properties or
13:12:08 get very narrowly focused on particular systems like you know quite a lot of talks.
13:12:12 Here I'm really trying to disentangle those, but on these big picture one is it's got it's got to be physical property.
13:12:18 Other some universal features we don't know.
13:12:31 But once it be motivated by theory rather than just doing statistical analysis and principal components analyses which will mainly pull out, which group did took the data, we'd like to be able to sing or scenarios.
13:12:32 But there is a question here whether or not when there's a lot of recombination going on. Once you really be thinking about the diversity of the genomes, what should one think of being being thinking about the diversity of the legals in the, in the genes
13:12:45 that that's model clear mean there are combinations fast by measure of mutation rate, but it's not fast on time scale of what a load selection happens on, and a lot of spatial transport and things so it's not all clear there, what we should be thinking
13:12:57 in terms of.
13:12:58 OK, so the simplest characteristics are just looking at and local snapshot and looking at distribution of abundances people use all kinds of measures here and they have names I know dozens and dozens of them, the channel entropy which is loved by many
13:13:22 harder especially for organisms that all seem to be pretty much the same.
13:13:24 is a terrible measure generally, when you've got a very broad distribution of abundance. But of course we'd like spatial correlations temporal correlations correlations with fellow JD, and of course correlations with phenotype as well that's much, much
13:13:28 What do you see the timescale of selection, that depends on the population size and selection strength so how do you estimate that mark. Um, well you can say, okay, what's how small selection would it take in order to over 100 million years, to be able
13:13:42 to tweet or even over 1000 years right on things that divide once a day, and of course the population size come in if you want to come in there, but you can also ask by what direct evidence is in the data for some amount of, you know, close to selected
13:13:58 sweet just like the partial things happening fast. Okay this we're looking at much more now in the cynical caucus in the ones that never actually talked about, and was already clear from statistical things that there was a lot of stuff there couldn't
13:14:11 be explained without, without a lot of selection. So you only hit us you can sort of back out some numbers of it has to have been faster than a certain amount.
13:14:20 It's very difficult problem with a big population if you say it's everything is neutral and just drifting around, you can get completely different expectations for what the statistics of the snips and things look like so.
13:14:36 Okay so that I'm just showing this because it's the sort of straw man in some ways, um, so this is distribution of abundance of something. These are many different species diatom species which I'm sure to some of us are all are all equivalent, and they
13:14:48 look like it's a distribution of roughly like one over ends or linear on a log on a log scale. Okay, now this is a prediction of the theory of neutral college right to the theory of neutral ecology, it makes starting assumptions, there isn't any ecology,
13:15:03 that everything is ecological equivalent within some group no selection or interactions everything comes from stochastic processes and stochastic migration, but it has the advantage is the only theory of diversity in the college it actually has predictions
13:15:16 It's the only theory of diversity in the college it actually has predictions that are testable brother amazingly even data on sort of spatial distributions of things of trees in the western guts.
13:15:29 Some of you even probably know where that is. I'm will agree rather well. I've never gone and dug into how much fudging is done in, in, in fitting those but it's certainly it's not semi quantitatively semi quantitatively, but it's obviously ridiculous
13:15:40 obviously trees are different from each other and doing doing different, different things.
13:15:45 So, you know why on earth to the abundance cystic look as if they many, many of ecological grip, so it has to be something which emerges from the evolution and the actual the college if it's going to end up looking like that.
13:15:56 Many of ecological grip, so it has to be something which emerges from the evolution and the actual ecology if it's going to end up looking like that. But of course it would also like to ask about whether or not the things that are measured are actually
13:16:02 the right thing. Okay, and I'm not going to talk about this but if one of the analysis we did of the microcosm of the, the semifinals. And there's a lot of things look beautifully neutral neutral theory, but then you start probing deeper and you realize
13:16:18 this huge inconsistency is qualitative and quantitative. So there's a lot of things that sort of end up looking neutral. Okay, I'm going to give one. One example.
13:16:25 So that's I say is a general lesson but doesn't mean this is nevertheless and something's a phenomena that one would like to try to explain why does it sort of end up looking with statistics that are similar to similar to that.
13:16:39 Okay.
13:16:41 So with the basic starting point was is the observation that biology is very high dimensional.
13:16:47 Don't what do I mean by that, well, if I look at the the code microscopic scale I got the genome, but the genome encodes the molecular phenotype right so all the properties the proteins how they bind to each other how they don't bind to each other how
13:16:58 they bind to the finance on the dimension of that is huge even simple, even in simple organs.
13:17:04 Now you can say well I should be dealing with the phenotype but by the time you're allowed to change to two amino acids quickly, which bacteria can do by mutations, you can sort of make a good approximation of any continuous value with some phenotypic
13:17:17 property that you want. So, and of course I'm like I feel that is what matters to them, Madison. Then there's the organism phenotype which is the number of properties of the cell which affect how we determine how it's affected by the environment and how
13:17:32 it affects the environment, right so that's clear as a large dimension, you know, at least as far as the things that are important. Probably not nearly as big as this, and then these environmental space which of course are enormous number of chemicals,
13:17:44 but you know in some of the organism like the protocol caucus one might think, the number of chemicals around the environment that are really mattering is not that many.
13:17:50 So this is not necessarily huge Im dimension but of course if you're licensed organisms like each other it quickly becomes very becomes very Lord.
13:18:00 So, and then the basic kill and starts I mean it's following the things that punk movement so what is the complexity the biology the ecology and particularly the evolutionary history is the most crucial one.
13:18:12 I'm saying that any fitness differences dependence of growth rates on environment and so on, couplings other biology, they're all sons of positive and negative contributions.
13:18:21 Okay, why is that well if something and mutational change was always good to the organism, it would affect the dense population, a long time ago. Everything is conditional upon the conditions, and the evolutionary history that particular denomination
13:18:34 genomic backgrounds.
13:18:35 backgrounds.
13:18:46 And this is particularly true when you got very close relatives, which is what we're talking about here. So the key character then is to approximate this by the randomness and then of course the physical property there, and then hope that some kinds of
13:18:48 universality in higher dimensions, at least in reality in the sense of talking about phases, but if you have some certain set of properties that you can you know argue that that exist, and then some robust way.
13:18:59 That doesn't mean that applies to any particular system, but it does mean that when you see certain features you might expect the whole of other ones to follow, like in just a simple way properties it's solid like metals or metals or insulators once you
13:19:10 know certain things a lot of other stuff.
13:19:14 follows, so.
13:19:17 Okay, so what are the basics, I want to get to the simplest condition of where there's no spatial gradients or temperature variations in the external environment because the evolution ecology can drive and drive those.
13:19:29 And then we want to ask whether or not. Ecological feedback can generally cause continual evolution so the second question that I asked, even without the person that we got the simplest problem, one organism which is gradually, gradually evolving, without
13:19:43 booming a diversity, small population.
13:19:45 But then what happens in that case, then we can ask, turn off the evolution and say, This is evolution with a little bit of ecology. This one is good.
13:19:54 This one is ecology, with no evolution at this point, and whether or not you can sustain extensive diversity wanted there. And then of course I'm like to combine them can evolve and continue to, and then one here which is like these dimensions how much
13:20:10 is actually needed to get high diversity. Right, so the classic example of resource models, is the amount of diversity that is the number of resources.
13:20:20 Okay, so the first the first one is this one here. Okay, so this this is one where now the trivial caricature which is done in courses and books and so on is you have a phenotypic landscape and that landscape is two dimensional because that's all you
13:20:33 can draw.
13:20:34 And then you have fitness pizza in and maybe many different fitness.
13:20:53 if it's if it's better than it takes over and I got the next one. It's always basically clock. So let me evolution is roughly deterministic the appeal on this landscape.
13:20:59 So they just have a crude model of this and what I mentioned it now, however, is dynamics in high dimensional landscape.
13:21:11 One too complex high dimensional high dimensional landscape, and there will ready. Intuition based on low dimensional landscape state.
13:21:14 Okay, in high dimensional landscape or exponentially many effects stable fixed points several points second one is data points and so on. And what happens is if you look at the evolution in these just uphill, the fitness will keep going up, it has to
13:21:27 the index of the points you're nearby will gradually go down, they'll get closer and closer to being stable, however, and this is a crucial point, the trajectories never commit to getting to a given peak.
13:21:42 You can't say okay after some time I know which Pete they're going to go to, they get closer and closer to the borderline stable peaks, which dominated of the, of the maximum, the most of them are borderline where the eigenvalues.
13:21:53 As soon as soon as you say that they almost flat in some directions, you know it's going to be very sensitive to the perturbations, of course, because all those titles that you're going by which control the damage.
13:22:04 it's also sensitive to initial conditions and everything else.
13:22:07 Okay. Mutations make it stochastics to cast a gradient descent or maybe a little bit of tunneling and so on. But the things which are known and the mappings to sort of thermodynamics and say that probably doesn't make a big, a big difference, the deterministic
13:22:18 one is is will give you the central features can ask. So most of this intuition as far as I can gather comes from the peace.
13:22:39 with all the saddles dominating, so I'm going to come to this. So the first thing I do when everyone does is you do, you do a model on high dimensional sphere and deal with and I'm yeah well what I'm okay.
13:22:51 OK, so now but this is now I'm of course not what goes on. Generally, we've got the fitness is a function of the phenotype, and the environment.
13:23:00 Oh.
13:23:01 And I can just say this is the this is the growth rate if you're in a competitive situation is your growth rate minus the mean of the others.
13:23:08 So this is a generally a complicated function.
13:23:12 The problem is with so much literature still and even people talking about it, they tend to use fitness is if it's singular even in spite of the fact there's got to essence of the end.
13:23:20 So I proposed I want to change the word to fit now, then the very least one to talk about is a function of phenotype genotype and the environment, and I'm even though I'm strongly against using omens, the things I'm going to try to sneak this into a journal
13:23:33 I think probably by using old fart on a method for publishing papers.
13:23:39 The.
13:23:40 Okay, so, but the population has changed the environment so I've got a single population in saturated it changes the environment, and we're going to particularly be interested in the cases where don't we change a little bit right because we want to ask
13:23:50 the question, in principle, go to the change by the by by a lot of ways, then would not surprise by a simple model which Michael associate model of where you're going uphill but the snow, and you change the invite the landscape as you go along.
13:24:05 So these are going to be high dimensional and caricature, this is random. And for the first round of calculations exactly the ones that I'm Pantages is referring to have simple high dimensional landscape with nice physical properties which are sort of
13:24:18 very and biological even in the characters.
13:24:23 Okay, so this is if you look at this dynamics here of going uphill and this is the adaptive dynamics, particularly Michael w who I was looking forward to directly here but I guess ended up not be able to come up, so you have a again environment you have
13:24:36 So you have again environment you have a mutant that Newton is invading in the environment everyone's already there. If it invades then it'll tweak the fixation, and then you'll change it.
13:24:48 And this means that the dynamics are now of the evolutionary trajectory is no longer gradient descent.
13:24:51 Okay in the some magnitude you can define it how big this feedback effect is in terms of second reference. So what we're particularly interested in what happens when this feedback is very small.
13:25:00 So if I've got settles, here's a saddle with no feedback then of course that determines which way the trajectories go is that coming towards it. But as soon as that's the feedback, and if you're coming towards this.
13:25:10 You of course unsettled the movement bit and you can make it going other direction. So it's clear that in detail the trajectories in which way you're going to go is going to be affected by this feedback.
13:25:19 Okay. However, if you get near to a maximum.
13:25:23 And then you're putting a small perturbation on your spiral into something slightly different, but you'll still go towards it. There was not a little clear that sort of overall qualitative features are affected by a small amount of feedback.
13:25:36 Okay, but in fact they are and this was anyone can do an exhaustive exhaustive analysis and simple models. Any feedback, the limit of high dimensions, any feedback, no matter how small gives you Red Queen dynamics and evolve forever without slowing down.
13:25:51 There's initial transients where it slows slows down, and the definition here you can say the rate of the mutation fixing, or you can say you're a parent increase of fitness in the environment which you are now, so you can keep on that can always be positive
13:26:08 because the environments changing. Okay, and this is the sort of fitness floods and you can get a sense of that, by how fast mutations that come and fix, how many come and how fast they fix it so you have something which is you know roughly a measure
13:26:19 of a measure. Now there's in a very different regime than like Minsky's experiment with a big populations a lot going on at once, but one can certainly imagine in principle, being able to track attraction.
13:26:30 Okay, so basically what happens is short time the fitness goes up with things playing the roles and it goes up, the indexes will go down, long times on the timescale which diverges of the power of delta it forget to history exponentially wanders all over
13:26:44 the phenotypic space. And this you can analyze it by dynamical midfield theory, which gives you which gives you enough simplification, then you can start asking you how general, This is punk he really did.
13:26:58 ones that some big family of things which their, their general, but can we make something which a little bit more like the biological caricature and asked whether it still work there.
13:27:17 So this is the question from this part of it, which is the how much complexity is enough. And what do I need.
13:27:19 Okay. So supposing I have a situation where you know maybe his profile is a good first approximation within one group of one group of protocol because I've got a pretty simple fitness landscape.
13:27:31 It's got one peak in it.
13:27:33 It interacts with the environment, but my environment is not very complicated the number of chemicals I'm changing is not all that many, but I if I change the environment, slightly, then if I if I then evolve my phenotype changes like that'll change the
13:27:46 environment slightly. So the coupling to the environment is boring is only one peak I kind of anything.
13:27:52 However, the organisms are really complex. The How am I going to caricature what's going on in a cell, what's going on inside the cell is I have in terms of my non molecular phenotype so this isn't the molecular phenotype, but this is looking at the growth
13:28:06 rate in environment conditioned by phenotype act of something which can be slightly different which is, which is why.
13:28:14 So this is a part here, which I'm going to say I'm going to caricature everything inside the cell as a very large number of nonlinear constraints involving all of the components, and they can just be pairwise things that's fine pairwise interactions with
13:28:25 him, so I can think of this as being all of the like all the binding energies between the bunny friendship between the proteins, so I've got some of a large number of those, you know, to make it tractable one does a number of those of order, the dimension
13:28:36 of the nano phenotype so the number of the nanoscale and property, and my couple of the environment here is something which just makes me a line along the one for directions.
13:28:45 This is the single peak. Now I'm adding the simplest possible feedback here with a dimension of the environment comes in and I just got a product of a response and they.
13:28:55 What do you call it to matrix, I don't know the effect matrix in the response matrix wherever the role is in labeling the number of the chemicals Neva simple as possible one, this can't give any advice or anything interesting except for little spirals
13:29:09 the stable fix. However, you can show that if the system is sufficiently constrained. The simplest is you take this to infinity, then you've got a lower dimensional manifold, that everything is moving on.
13:29:18 And you can ask me what happens there and there's a critical value with a over the end for Fiction autos.
13:29:26 If it's sufficiently constrained, you're in the same phase same as all the classes I had before you get this Red Queen evolution which continues forever with arbitrarily small duration I call this up on here, opportunity small values of this, of this
13:29:37 premise.
13:29:38 Can I can ask a technical question just just one just one, but if you're under constrained, then it'll tend to go towards the the stable.
13:29:49 Yeah, just to be clear D is not an extensive variable in your analysis No, I mean, of course you want does the analysis on the assumption that d is low, but it turns out this quantity here which doesn't have any interesting structure anyway.
13:30:00 It's small, it basically some give some of the effective noise, and at least in my level of understanding of it. That doesn't have to be that doesn't have to be high dimensional as long as it's enough to give you things that are approximately looking
13:30:13 random. But the thing is, the X is moving all over the place right so you doesn't matter really if your randomness when you're over here with similar to what it was when you ever here, because all the constraint parts of different, so I'm pretty sure
13:30:24 this you can do with the DB order one.
13:30:31 I say but that's the level, nobody understand these high dimensional things what the finite large The effects are like for example in the simple models, how, how strong you have to have the feedback.
13:30:42 Before I get into this this continual evolution gets chaotic dynamics, if it's very small venue will.
13:30:48 It's not going to. It's not going to do with any fine ID because then it will go towards because there's no such thing as a marginal peak in finance.
13:30:58 It would help me at least enormously if you can provide some sort of a rough caricature of what you have in mind behind those variables so I can see that, for instance, you, you, you are sort of referring to the consumer resource models and some new ones.
13:31:16 For instance, yeah, yeah And would it be, for instance, an example of your model, if I have an environment in which the resources are flowing between multiple micro environment now I don't have any I don't have any micro environment.
13:31:30 Now, Michael, everything is well mixed to this point, I see everything what makes my, and I know how many cold you I've only got one type there. And then I get beneficial nutrients that coming in, it just affects the environments like there's no there's
13:31:41 no anything what would normally call ecology I'm calling it ecological feedback was it is the sense in which you're changing the changes of your, your.
13:31:58 You know paradox that well, how did you overcome the competitive exclusion principle that there's only one type so there's no one to exclude me.
13:32:01 Then there are no micro environments nicer not special temporal, everything is where everything, everything is simple.
13:32:17 Right. There's only one side this is this is purely looking evolution with no diversity I'm going to come to now I'm going to come to the diversity piece it's still one species yeah sorry I'm not just one species it's one cone gets a mutant that if that
13:32:19 takes over then you have another clone and that's it. It's really the absolute simplest simplest possible which is the simplest adaptive dynamics I mean they, you know, Michael and others also do it after dynamics when you've got some diversity downstream
13:32:31 question maybe Is there any other any qualitative differences between the Red Queen dynamics that you observe when you put the complexity inside the cell vs.
13:32:45 I mean, I don't know what those would even look like but no at least at the level of things that I can work out, and I think that's sort of general, I mean the weird thing is even though this is just a little tiny bit pushing it it's sort of runs over
13:32:57 the space of the constraints still. And it's really loud region with with the, with the constraints.
13:33:07 Yeah, I don't I don't think there's going to be anything which is intrinsically that different. It's not, if you tried to make an estimate of the dimension the environment by trying to measure properties environment as you were following along, you could
13:33:20 find that that was, you might find that was quite low dimensional estimate an environment that would be this D. Okay, so there are some things there if you try to measure some other properties of the organism which is measuring everything inside.
13:33:31 You would then say Well no, that's a very high dimensional thing that is evolving. It's like you know evolving under low antibiotic resistance like Dan Henderson's thing.
13:33:39 So unfortunately couldn't come where you see all kinds of different routes in the same cells that you do completely different things at the molecular molecular pathways and stop it isn't just variant within that would depend on what you what you look
13:33:52 at.
13:34:07 So I'm just trying to get intuition for what exactly is high dimensional, what are these constraints we're talking about just as an example the I should think so these quantities the actual the why I mean those, so they have, you know, I wanted the end,
13:34:20 caricature of I've got a few amino acids, with some numbers and I, they can bind or not bind and this constraints and any qualities and so on in there so but this is this is the caricature, but it's trying to get a bit at punk edges question, if I take
13:34:33 something where I say the complexity is associated with the cell. I'm not in a complex environment. This is a really simple environment. The detail ways I couple of the environment and just some projection of the all of the microscopic properties, some
13:34:55 them affected more some effective little, a little bit and so on. But it's just a projection, and this is just a simplest form and this is not meant to be realistic at all. It's just asking, Can I get this by a caricature with all the complexities inside the cell, meaning
13:35:01 the cell, meaning the number of molecules required to describe the metabolism could be a high number in Thailand, but the number that are secreted outside and exchange it's a much smaller number that really matter outside is gonna be a long time but but
13:35:13 only a few matter of to dominate right because of course if I saw saying this MIT very many of them right there are only a few dominating the effects of them, full of exponentially with the listing ranked list.
13:35:23 That's sort of cheating thing that's really high dimensional, but I think inside the cell it's not cheating because I.
13:35:34 It's hard to mention, but it really is everything in that right if you do an evolution experiment where you're trying to improve something which you think is your metabolism, it often does something different.
13:35:38 It's not just even just metabolic enzymes and it really, you know, so there's that but I say this completely a character you shouldn't take it seriously.
13:35:53 to sort of picture in my head how this population evolves in the low dimensional space, should I be thinking that it.
13:36:01 It won't look like it's climbing forever because something will fix and that will change the molecular constraint which will then alter the environment, or the low dimensional, you can't, or is it like sort of just running around mental space is a projection
13:36:13 is a projection so I would take something which is a high dimensional thing projected low dimensions it'll look random. Just be some correlation time, but it's going up and down or well I mean there isn't this quantity here is going up and down the pentagram
13:36:26 well in the limit depends on your limit because you're summing up a lot of things that only does that by square root of the use of like effect, but yeah it's going up and down.
13:36:34 Yeah, okay, because there's not there's not a, the content you're maximizing keeps changing. So the business some there's no, there's no early often a function here and this is one of my messages I'm even put in capitals, at the end, right, it's things
13:36:46 in which is an optimization principle, you're going uphill all those things are extremely special. And as far as we know if things are complex any perturbation away from that changes in court.
13:36:57 And this is this is the simplest example of this, first, then can, and then turn to the diversity.
13:37:11 So, I'm just struggling to understand the constraints. So, I don't want to spend more time, this is not totally realistic model, I know that it doesn't it but here if you wanted to constrain the system was is unconstrained the system which of these things
13:37:24 would you would you change.
13:37:27 This is the constraint, this is all the constraint. Okay, so the the, but it's a, it's just a caricature to show that there is that where you need the complexity right was sort of the goal.
13:37:37 I wasn't I wasn't wasn't clear on it.
13:37:39 It's not meant to be realistic but it's these does interesting questions about sort of why do you get stock will keep on going and so on that, that I don't understand it will cause then the gets interesting you add this what you would like to do you believe
13:37:51 in these. And if you allow finite jumps rather than if it doesn't well jumped, then you can get coexistence and there's conditions for coexistence that again Michael Douglas book that a lot, so you get what's called evolutionary branching and diversification,
13:38:12 Hey, this time when I support stop putting more assumptions in the model in particular what you replace. Once you replace this by. It's not clear whether the dental Tennessee's high dimensions encourages or discourages diversification.
13:38:21 The thing let's look at so far actually discourages it, everyone is going along carving out an environment which is good for them. And even if you try to compete with, you know, something which was in your future, they can may not be able to invade you
13:38:32 because they were further in the future. And it's not clear that the conditions under which it's. This will give you this kind of thing will give you diversification.
13:38:45 Do you have to selectively assume niche like things or can you get it without it. So I'm going to talk about another way of getting without. Okay. So knowing and ago.
13:38:53 Go away from the evolution and say let me look at the ecology so I'm gonna look initially large number of things assembled together, and then go from there before you move on.
13:38:55 That's a, that's an open.
13:39:03 Can I ask one question about the pure evolution one if you thought at all about sort of opposite limit words sort of a single clone you have a bunch of freely recombining illegals does that change the picture, totally.
13:39:30 you're, if you really are free of recombination so your fitness is coming from the distribution over the frequencies of each of the levels, and then you're looking at the evolution of the illegals then each Leo's evolution of might be pretty simple.
13:39:33 And so the factorization assumption.
13:39:36 You have to ask and it may be that as soon as you break that slightly.
13:39:40 Then you, then you get the interesting things coming back, but I haven't thought about that that's an interesting question.
13:39:45 Daniel, can you just restate the conclusion so you analyze this model, and you concluded that with arbitrarily small feedback and so as I called it planners after arbitrary small feedback, you start evolving, you slow down.
13:40:00 And then you just keep going at a constant speed forever. By any measure you want to what you call it slows slows down and then just keep on going. It's deterministic kale.
13:40:11 I there's no noise in here this is deterministic chaos. There are in the high dimensional face space, little pockets or the maybe little pockets in which there is a stable fixed point there, but they were very small fraction of the faith based volume,
13:40:25 and so we very likely to find.
13:40:27 so we very likely to find. If you do find them, and then the environment changes for other reasons, then you make then you'll get pushed off and go anyway so then it's that's very probably unstable to a little bit, but nonzero amplitude change and under constraint one stable fixed
13:40:41 point that means.
13:40:43 Well, if you know if I increase this, or I decrease the amplitude of how stiff I'm making the constraints, or I decrease the number of constraints. And there's another phase where the simple, practical, with whom I built that you've got one stable fixed
13:40:56 point and it converges exponentially. Okay, it spirals into it because of the feedback that.
13:41:02 But that's a transition exists in the land of landscape models to you put one direction which is preferable at some point you lose all of the complexity, as obviously you know special to these dimensional models.
13:41:14 Okay, so now we want to ask about this bit and the most basic out to look at diversity is one species but I'm going to really consider to provide a bit of it with closely related subtypes, and this is now work with done with a Tish Agron our Google Michael
13:41:31 fierce now at Facebook and Aditya. Mahadevan now in Santa Barbara, I'm somewhere okay back there. Yeah.
13:41:38 The.
13:41:40 So, I'm in different environments appropriately.
13:41:45 So the normal Exactly. No, just go back back to me, normally one right sit in terms of people call it so the number of species. I prefer is for selection but with a number of alpha so I've got large number of taste species here, and then the normal way
13:41:59 I've got some growth rate I've got some carrying capacity, each. And then as an afterthought I try and interact.
13:42:05 Right.
13:42:06 And this is a this is a problem it's not if you're dealing with very different species but if you're doing things that are very close. This is clearly not the right sort of way of prioritizing prioritizing.
13:42:24 So we're going to modify that a bit, but then look at you know no stochastics the no spatial structure and literally no evolution. Initially, and so one of the possible long term behavior as well as the modal gnosis focus I can have a stable community
13:42:30 of see coexisting types that the fixed point where some of them are zero unavailable means all the others are at zero, and the end with a stable stable fixed.
13:42:40 So I can have a single community if I've got three. Three types here or two possible different ones that I get by stability, so I can have that.
13:42:48 By the time I, I can also have a limit cycle.
13:42:53 And this is now an unbeatable limit cycle, but I can also have and it's actually going to be important, something which is unstable to near extinction, where you sort of spiral, you get closer and closer to extinction because at some point the fact that
13:43:04 populations finite, you can't write down oh two ears and one of them go extinct. Depending on this list it could be that one either one that goes on goes.
13:43:13 So this is sort of this sort of hetero clinic orbits where they getting bigger and bigger. And this is a very important thing that will see once I get start looking.
13:43:23 With a bigger than three chaos is possible, and you can sort of imagine stable chaos where things are sort of going around maybe occasionally going down to low frequencies, but it's basically stable, or chaos it's like this, where it's chaotic, but things
13:43:35 like more and more things are getting different, and eventually the cancelled Diop because most things have gone, but can I ask another Claire, you're saying the go extinct.
13:43:44 Okay, right so as as has been tell Hannah, even a hard time about yesterday there's absolutely crucial difference for evolution everything else revolution between 102 or two might as well be one, unless you sexual species, but the more than two is roughly
13:44:15 the same. OK, So, the chaos is is possible in that you have to think about, okay, now I'm going to go and change rotation. I'm now doing closely related strains, so I want to prioritize things in a different way.
13:44:26 The first thing I want to do is I want to say that the use of common resources keep the total population roughly constant, doesn't matter if the plan to grow and multiply to get back on so that I can see everything is now looking at different.
13:44:39 The one thing going to do is subtract off the average by or some reference strain on labels zero, subtract that off. So I've got the effective cell phones now are the our alpha minus our north and I left the other part, there's another crucial part which
13:44:53 is how they do in interaction with the average of all the other was an extra part in here which involves the double us which is my basic interaction, and then the interaction matrix really is a sums of differences of things.
13:45:05 And so to say that that starts off as being approximately random is a very reasonable assumption, more reasonable than having a very different.
13:45:14 And then I'm putting an extra pieces on a call the nation direction, this is the one that normally is the main one, and this is an afterthought. This I'm putting in as an afterthought because we want to look at its effect.
13:45:23 It's the average extra competition with the same.
13:45:27 And then we want to ask what phases of possible in a limit of a large number of budget.
13:45:33 So of course you know what model. So, the interactions with the same strain are not necessarily special, why is that well I've got a lot of close relatives, there's no particular reason that should compete substantially more with my siblings than with
13:45:46 my fourth customers.
13:45:49 Now if you've got small numbers of resources and you there is some tendency there but it's not a big enough tendency when the when the K gets some bark and the veal for some of these terms and differences are there approximately random and the crucial
13:46:00 part is that means zero, the crucial part is the correlations between how hype alfre effects like beta, and how beta tapes than alpha, and that can be either positive or negative to the cemetery.
13:46:12 Then I've got the selective difference isn't like the generalist differences between them. They need to be small enough will say how small the simplicity of keeping being zero, which people usually do, but that can be dangerous and we'll come back to
13:46:25 come back to the question, is it not necessarily special.
13:46:30 It seems like in this set of it. Why would it ever be special. The interaction with you if you're interacting if you're doing interacting via chemicals and environmental resources in the environment directly, then the essence what you eat, is correlated
13:46:43 by what your effect is on the environment. So the second order effects of that gives you a diagonal term in the lock in lockable terror, I just was puncog like that term, however, is only bigger than the orthogonal terms by and most of factors associated
13:46:56 with the number of the number resources. So if you have a lot very large number of title in there, so you're violating the you know the accounts with the number of resources, then, that that those terms are they bigger but they're not big enough to matter.
13:47:14 Okay, and so is it something about like when you secrete something is a creative right next to you and that space somehow matters or, like, like I said, you know, everything can be one mix know you're just a coral model if you've looked at do this.
13:47:27 Exactly. That's right, you're consuming something you've got a matrix of which mixture of resources you consume you've got a matrix of which resource another one consumes you got a matrix how they affect you.
13:47:37 People usually assume they those identical is proportional to the other words, even if your songs are correlated. That means that you have it you compete more with your perfect relatives than you do with, we want to someone on this because this is just
13:47:51 to that right but it's not but it's not a big enough effect, unless you have a very large number of resources, which matter a lot, right.
13:47:59 Alright.
13:48:02 So my so this is the so they've got generalist differences between them. Okay, there's generalist differences, but I say this is this crucial the crucially involved some of the interaction parts, because it's how you do against the average of the others.
13:48:14 Right, and so throwing this out is a really dangerous. a really dangerous thing.
13:48:19 People will do you normally would sort of thought, well, I will well evolved and so they're all sort of the same on average, and then the subtleties in how they differ from each other, which is a reasonable point but someone has to say is that what comes
13:48:31 out rather than assuming, and by the way for the for the junkies, I didn't do any scaling of anything with tape. Okay, I'm going to now come to my parameters, don't fk in and now the question is what, how does it depend on the three basic other symmetry
13:48:43 parameter, and this sort of Q term which is sort of the strength of the nice like effect is a normal thing is to assume that dominate and then go from there.
13:48:52 We're gonna, I'm gonna explain why.
13:48:54 Yeah, just to be clear so Q is some sort of measure of niche overlap between strange at the same speed right yeah so it's the extra interaction that you have with your with the ones that are famous.
13:49:05 Right. Okay, so it's it's the can be your niche overlap or something like that. Yep.
13:49:10 And the minus side is competitive.
13:49:14 Okay, so what is the phase diagram of this, of this model. Okay, so the phase I am is usually joined in three dimensions is only two dimensional that people make life more complicated.
13:49:25 So there's basically there's symmetry parameter here. And there's the strength of the nation directions, you notice I put a square root of k in here now, because what matters is how big this is relative to square root of k.
13:49:36 So the bit which is well.
13:49:39 Well, the bit which most of work is on is on this axis here. This is the access whether or not function, you have the perfect similar Cemetery in their things a very special.
13:49:48 And in fact, the more we understand it, the more specialized This is, I think, opportunities motivations from that will change the behavior qualitatively similarly to the opportunity small ecological feedback piece I was putting in in the evolution evolution
13:50:04 yq is the strength of the extra strength of the nation to recognize that yeah it's like how much more you interact with your with your siblings than you do without the average of it.
13:50:16 Okay, so the phase which has been looked at a lot back to me I mean this nice phase here these unique large table community, it can have a community size be bigger than half the strain but you started with.
13:50:28 But you need to get this you need this extra sibling interaction to be bigger than all the square root of k, and the other. So if you start off by saying sort of things.
13:50:37 One is no big parameter there or you ask what happens when k increases.
13:50:42 So as soon as you increase you throw more in, you come across this line and this goes on state. So the whole question then is what happens in this regime when you no longer have a stable stable.
13:50:52 And people have done analysis on this line. We're going to be particularly interested in what happens along this line where there are no specific niches, or QE zero statistically, your interactions with your siblings are not bigger, and of course we can
13:51:04 increase go slightly away from it.
13:51:13 So we're going to be interested particularly along this line, and there's a special point along there which is this end, which is very special but it turns out, gives one lot of intuition, and may in some sense even be the right basis for what happens
13:51:17 in this whole region inside this triangle.
13:51:21 If you put selective differences on that are not very big, they have to be of order one of the square root of k, they only change things quantitative.
13:51:29 So what does that mean it means that if you start with a given sort of distributions like the differences and you add more and more types in, then you then yourself violating and it's not limited how many you can have right because generalists do well.
13:51:39 You can't just pack things in. If you, if when you've got generalist mutations, and one of the big problems by understanding that the diversity is you can find divide new niches all the way you want to keep dividing up, but something which is slightly
13:51:51 more general can come in and take over. And that's often what seen in models.
13:51:57 Okay.
13:51:58 Um, so how do you get the whole obviously the, the positive gamma, alpha is good for beta mean beta is good for alpha that's helping each other, have a battery beta beta bad for alpha is directly competing, so that's that's the common, how does one get
13:52:12 any symmetric correlations. Well the simplest, is that a one on one competition.
13:52:17 You're playing locally one on one fighting. Then you mix in, then you play local with someone else mixing console. So then you get this is the competition that automatically anti semitic ends with a lot of work on the much more interesting one, is when
13:52:29 you've got a host in a pathogen. So in that case I have a vector of the, of all my host strains and all my pathogen strains and my interaction matrix has this roughly anti symmetric minute if pathogen new is better against host j mu is worse that means
13:52:47 mu is worse for Jay, so it's positive for one of them negative for the others. But what does it tell you it tells you the deviations of this from the sort of average interaction between the age in the bacteria is strongly correlated with the deviation.
13:52:59 So is this one from average. So that gives you an anti correlation because I put the natural scientists.
13:53:04 Now you need to put in some stabilizing things here to stabilize the bacterial population, but you can just put it all minus ones there is a stabilized the bacterial population.
13:53:12 The bacteria are not going to be different from each other in, when I look at this more seriously accepted how they interact with pages.
13:53:19 I'm so sorry to go back to the last example of a beats BB lose day. Yeah, I'm presuming that doesn't work in the world where they're fit with their sort of like a rank one vector that orders everybody so can you.
13:53:31 Do we know how big the dimensionality sort of has to be for that to cross yeah you again you need you need to have a lot of insensitivity where the sensitivity of a b2b b2c but CBD, so it's it's the, in order to get these phases and most interest if you
13:53:46 need that. Amazingly, a lot of the literature, including by you know ecological people and Game Theorists and someone, they tend to have this anti symmetry structure that all kinds of things are completely special soon as you said the dawn and pieces
13:54:06 well you do against the others on average, that tends to be the dominant and the more things more variety you put in the more strains you put in the more that piece dominate. And so you really have to all of these say why doesn't why on the generalist of the coming, you can assume everything is perfectly balanced right so
13:54:13 can assume everything is perfectly balanced right so these have all of these perfect trade off models that I guess net didn't talk about but that is that is booked on and he was shown from the beginning, with some perfect title.
13:54:21 Right, but that's very vulnerable to small too small deviations.
13:54:30 So this I think is not is, I mean there's definitely models here and you can think about this in terms of resources and I think it's actually, this is a big important open question I'll come back to activity and so is it fair for me to remember this is
13:54:37 So is it fair for me to remember this is like one on one non transitive competition.
13:54:41 Yeah, really my head yeah if you really want to get the right order just pick right yeah yeah just just random thing but there's no ranking. Right.
13:54:49 Okay, so what this is you the basic dynamics when you Randy symmetric correlations to sort of kill the winner dynamics ecologically, are we focused on this blank stream.
13:55:02 Then, as this, if this say there's a whole bunch of blue strains, the blue strains that are good for the black strain, will make a buck on come up when it comes up then what does it do well it inhibits than the blue strange that the anti symmetric correlation
13:55:10 comes down, but it helps the red ones, the red ones will then come up, but the red ones will then push it back down again, you get this going up and down, general tendency of the ecological damage on a log scale on a log populations.
13:55:23 Those a special model, which is perfectly symmetric model where you can analyze a lot of things. I'm not going to go to this except for this line in the bottom.
13:55:31 You've got a whole bunch of strains here, the joint distribution, all of them is identical to the theory of neutral ecology, with with migration and and our top things going extinct.
13:55:47 This has nothing to do with that the dynamics is completely different.
13:55:51 Unfortunately, all the exact stuff which enables one to do equilibrium Cisco mechanics which it turns out this this this is after things are going extinct.
13:55:58 You cut that doesn't give you that max and the dynamics is what we're interested.
13:56:03 So do you have to go to dynamic field theory, you can't close the equations you have to do some politics on the stochastic equations themselves and it's somewhat somewhat tricky one can do simulations and actually you can very easily get to that once
13:56:15 effectively like the ID limit in them in simulations you don't be very large.
13:56:20 The crucial part is that some fraction of them will go extinct.
13:56:24 Water half will go extinct, all the ones that survive of the property that they occasionally blew up the high frequency.
13:56:30 The only way they can survive they blow the high street.
13:56:34 And those are those ladies and gentlemen later on we'll see why that's true going in a more interesting. They go all over the place on a log scale, there's this fractal stuff there and stuff and the crucial bit is just to there's nothing like an effective
13:56:46 stochastic birth and death. You might as well get an effective model with an effective population size is nothing like that the statistics of these some of these books.
13:56:57 Okay.
13:56:57 The problem is, as I said, it's a very special anti symmetric model. I should put a very or extremely or something in there as soon as we go away from this but sort of keep the rough structure of the anti symmetric correlations.
13:57:08 What happens then is you get wild room all the fluctuations is historically that chaos the drive, drive extinction, and you end up with a few of them, typically in a smaller mid cycle.
13:57:17 What you end up, end up with, and the rest of them. The could invade you can get ones that can invade that case you get a situation where things have gone extinct but they conveyed, but even if you if you really keep track of them all as they get smaller
13:57:31 and smaller, you can get in a state where you have a few left but basically it's divergent chaos and so you can't really make sense of the long time limit unless you put some distinctions like process.
13:57:43 Okay.
13:57:44 So the question is Can this chaotic phase be stabilized, well not surprising. One is that yes you can stabilize by migration, you can always save lives by migration if you put in the mainland, where you assume you have all the diversity that you want,
13:58:06 then that migrates into the island thing to go extinct here, but they they stay. But that's a cheat right we just replace the problem with understanding local diversity with the understanding of the mainland numbers.
13:58:07 Someone can do one can do you know the obvious thing to go beyond that is to do an island model, but here's a bunch of different people and there's their guts inside them and they're, they're moving around so the bacteria from one gut, was to someone
13:58:18 else's god, I'm, we've got a large number of them, number of them but you can select global extinction so the total number of total population size of the strain alpha, which is some of all the islands there that can still go extinct.
13:58:34 But the question is Will many types still survive wearing this regime when I sort of have this divergent candidate can I make some.
13:58:43 This I guess goes back to be the chest and being called spatial storage effect of how you can get stabilization of diversity migration.
13:58:48 And there's more work to be done with with with with addition and Michael Pierce and then also a field story and his thesis work with various collaborators and others like, because I was involved as well now on this I've done some similar things with,
13:59:08 in the anti symmetric actually in the independent case, and with some things are a reason, and the basic results are. I mean, they tend to they managed to push things through are so personal.
13:59:23 No cheaters No, no nothing like that No Game Theory.
13:59:35 And if you're if you're making me say I'm only allowing interact with the very least two types. I'll make you a slight generalization the model was something invades different.
13:59:37 Game Theory restricts enormously the name kind of interactions and things you have that are going on right there just interaction.
13:59:44 Okay. I didn't, I didn't intrinsically put in cycles here ab a b2b b2c. I just said these entities metric correlation. And, in fact, if you have.
13:59:53 Once you get back to a fade you can effectively have cycles of four but then we'll even cycles.
13:59:59 And that molecule and then you have to start looking at relative differences of how they attacked one one stage strain attacks one bacterial strains.
14:00:07 There's another way to do this without spatial structure.
14:00:10 And again, this is not been talked about various people but very few things worked out there's a lot of sort of words and statistical Carla's so on, which is he just said the spores, and the spores live a long time.
14:00:22 They don't live forever they die out so you can still go extinct, the spores occasionally vegetate, and the spores the replenished by the from the active population, but if you like the population is too small for too long the sport is just a diet and
14:00:35 you can't come back.
14:00:36 can't come back. So that's the other machine that one can ask about we still local in space so we've just got a time delay part of our differential equations if you'd like as well, which seems like a much more trivial trivial addition but the same basic effects are there.
14:00:49 effects are there. But then we've got a multiple Island lockable Tara model, or as a time delay equation, and it's exactly the same as before, each island is identical the interactions are identical each island, the Brahmins are the London, or the
14:01:05 Islamic labeling the islands and the Greek is labeling the strange, so you only interact with the ones on the same Island is you you migrate back and forth between them at a low rate, and you can migrate incrementally the other islands so it's a spatial
14:01:17 midfield. Everything is kept everything.
14:01:19 And you can analyze this again with spatial temporal feel theory in the ass and politics get more subtle and, but it's a fortunately, you can get to the with the theoretical framework there and capital simulations, you can get the regimes where you learn
14:01:35 where you learn something, if you just did the simulations blind, one would not, you would get the question quite likely some of the wrong conclusion.
14:01:44 So what ends up happening here is as a spatial temporal the chaotic phase, the islands desynchronized This is the crucial part. So the islands the synchronized because the smooth migration between them so chaos doesn't lock between them.
14:01:58 They desynchronized means what's going on this island is different from this one.
14:02:01 So you can have particularly that things are going extinct here one trains going extinct here but another one happens to be blooming times a good for there because which friends, it has, and that can sustain it that's the crucial crucial part.
14:02:14 I'm a order one faction actually typically very large fraction of the strains coexist and persist in definitely unlimited large number of islands, but some of them go globally extinct, the abundance is spread out on logarithmic scale, just like the single
14:02:27 Island one bouncing around a lot of the scale. The average gross weight of every strain is negative, almost all the strangers and negative, there are average always dying out.
14:02:37 But when you think of what the effects of migration that doesn't average. The ghost rates growth rates affect the logarithm the population size. What, what that is averages the numbers, which is the exponential of the logarithm that's doing this random
14:02:50 walk. And so you expect that you will get an order something to persist IQ and I'm a negative, negative growth.
14:02:57 But all ones that persist in spite of the negative growth rate, they have blooms up to large, large number, and this is absolutely crucial.
14:03:06 And the dynamics on each island is roughly like the anti symmetric model, but the sort of floor that stops extinctions coming from coming from migration, but that migration for of course depends self consistently on how many of the individuals that strain
14:03:20 there are on other end.
14:03:24 So, one thing that can happen even an infinite and and this can happen to infer number of items as well but this simulation just with Tim does look at one strain or logarithmic scale this down here is the migration floor.
14:03:37 If you get below a an abundant the factional abundance of one over n where any local population on the island, and you go extinct. And here you see one that's fluctuating to extinction across all the time.
14:03:48 So that that's some fraction of the strange that here's one that comes in on one island happens to come into the time when the conditions are good for it comes up, it then comes back down again and would go extinct exceptions, it went up high, it can
14:04:00 see the other islands it's needed a bunch of other islands. Most of them are successful, but some of them go up, and eventually then this comes in. so this is an invasion of a of that.
14:04:09 And sorry I should have put a teacher's name on here, he is trying to understand this.
14:04:15 This process turned out to be very subtle.
14:04:19 In the middle somewhere.
14:04:21 With this total population size constraint is the smell of the entire meta popular no no this is one digital teams, this is one straight.
14:04:29 I'm only looking at one strain and this is across the across the islands Yeah, thank you. Yeah, but this is invasion from one out of a single string. Yeah, if I look at the well the picture of the many strains and when I was not very can't see very much,
14:04:40 but the you, and you can constrain the total population on the island or you can have some interaction because you can ask a question so you must have thought about this.
14:04:49 So this was always compelling even when I read the pre print, but it seems like if you had these repeated bottlenecks, which is the way you maintain these in like the motivation you had at the beginning in the bottlenecks are pretty easy to see in genomics,
14:05:02 right, usually. That's my understanding.
14:05:14 If you can sustain from repeated bottleneck. You have to go through is a bottlenecks is like going from one person's got to another. If we assume that usually when that happens either zero strain survival one five, then you have to all those signatures,
14:05:20 a mostly in the genetic diversity that gets formed in the new gut.
14:05:25 So you have to have a separation enough of timescales to be able to pull things out any sweep is also sort of like a bottleneck right because you in some part of the genome if it's sexual, you can tweak things up, and that you can mention to be able to
14:05:36 able to see it in the trees because basically, if you look at the trees we know what bottlenecks look like in trees, and I just feel like have you have you tried to do the maximum likelihood or any, any kind of thing because the tree, the tree bottlenecks
14:05:50 right on the model under what model you can do maximum likelihood neutral, we find out over me
14:05:57 rephrase punk I just question slightly, maybe it's getting at the same thing. Yeah, so, yeah, it seems like in this process, you're surviving because you're constantly re colonizing new islands.
14:06:07 Right. And so if we think about, I don't want to use this word but an effective effective number of islands in which you're president for that itself sort of forms a bottleneck right you can write more than that number of strains and right can you come
14:06:20 to that and explain the effect of that. Yeah. Is that roughly what you were. Yeah, it just. Okay.
14:06:27 No, I think so, if you start asking about you know you put labels and he's asking about genealogies and so when I think it gang becomes an interesting question as to what sort of, what will it look like in which quantities, will you have to do, no truly
14:06:38 be some quantities for what you can find in fact population size.
14:06:46 What you can manufacture populations, there may be completely different than these ones. and then you have to start asking, which quantities, do I have with really distinct distinguishing between scenario.
14:06:49 There will be some other quantities.
14:06:51 So for example, when I first showed the blood distribution abundances on log scale.
14:06:56 I could have policies which gives me effective noise.
14:07:00 The, which is my population is spread around spread around a bit and I've got it and so on to the bigger population more columns and have an effective process which is not birth that's the cast the generally but it's more like the bottlenecks, which will
14:07:12 which will give you some effective parameters. But the nice thing is you then have predictions about the connection between the dynamics and the and the snapshots, and here the dynamics is what distinguishes distinguishes, sorry, one more quick question.
14:07:24 So, in this model can you calculate the number of islands on whichever given strain is.
14:07:30 Yeah I tell you the number yet. Why is that I can tell you the relevant thing I mean you can you can count with anything it's all just how it scales Yeah, yeah, yeah, yeah.
14:07:38 Okay, so this is this is just an example. So here's actually where it goes locally extinct one of them and then get three gets pre populated populated there.
14:07:48 The initial snapshot of the abundance distributions at roughly this spread out on the log looks OK, so the crucial thing is that this phase is pretty robust.
14:07:59 In fact, in some ways, I would say it's very, very robust.
14:08:02 If you take a finite population for Ireland, the real local extinctions you still get them with a case IV, however, and this is relevant. You need to have your migration rate sort of total migration in and out, being big enough that you're getting a flux
14:08:14 of things coming in all the time. So if you really low migration rate, then you will get many more global extinction and we don't really know what happens there.
14:08:22 I think you can still sustain things but we don't understand that. Sorry, case number of strength. Very kk number strains Yeah, yeah, yeah. So most of most of it, the number that survive as you lower the migration right the number goes goes down, and
14:08:36 quite whether it goes to zero or quite how as you as you decrease that is not there's not some is not clear. Because that's that's a, that's an important question of course, what's your specialty mix like chocolate Cockers, there's not discrete islands
14:08:50 is a continuum, and then there isn't this big such a big distinction in zero and one.
14:08:55 I mean this distinction between regions of ocean which are empty of that, that your your strain on ones that aren't which which bars is going to figure out how to, how to understand thoughtfully left at just the right time so I'll tell them the assignment
14:09:09 afterwards. The. Okay, so another bit and this is comes back to the question which Ben was asking and I think maybe punk rock is getting it. We have a finite number of islands, then you can just by chance, all of them happened to be at the wrong time
14:09:21 on the islands, same time, and so we will globally extinct and then you had the. And it turns out that's you also get that even if your population size infinitely.
14:09:32 It doesn't matter but the but the crucial bit. And this is where the robustness is that if you look at a given strain and you look at its dependence on Island.
14:09:45 At the time it'll survive for is exponentially longer number of islands, the coefficient depends on the strains are the ones that are sort of close to borderline will be won't be able to last.
14:09:50 So essentially this is like the, this is like the ratio of the islands of the number of islands of which you, which you need to be a big enough population any given time to sustain, but no more or less so its extensive with the number of islands.
14:10:05 Seems like no no no it didn't it's it's it's intensive for any given strain is a given number, which if the islands are many more islands in that that's sufficient.
14:10:17 Right, so this is independent number five, this is just it just depends on the strain.
14:10:20 So I should I interpreted d times one over be one over be is a number of islands, a strain alpha if you have more than one over the other islands, then you will be likely to last for a long time.
14:10:33 And it goes grows exponentially number one, it's sort of a new creation process basically to go extinct invasion also has aspects which are like new creation and I said that but some things that you just try crucially be as independent by Right.
14:10:46 Yeah, because it's exponential long in the number of hours, and in practice, you know you do 10 or 20 Islands, you get a very large fraction that the coaches, um, you know I've started with you hundred.
14:10:57 Okay, real spatial structure, again, is what we're trying to start doing when you get local mixing maybe occasional long distance transport certainly important almost probably almost all all microbes, what happens there.
14:11:10 Okay so that we, you know, qualitative IDs I think this phase will survive, but we don't really know.
14:11:19 Okay, so now we come to the crucial part, which is Kansas a high diversity phase evolve, or maybe a simple one if I start with a high diversity phase which is assembled.
14:11:29 Can it does it does it persist. By now allow it to evolve or allow more things to innovate. So the hardest situation is where the evolutions much slower than the ecology evolution is really fast because I was getting the first anyway from the, from the
14:11:42 evidence.
14:11:42 So if I just do a invading problem of adding new strains so I let things go extinct but I keep adding new ones with some anti symmetric correlations there, then what happens if you start with a number which is you know bigger than what a 50 or so, you
14:11:55 will start going and off to someone at a time you will basically deterministic the co op, your number of strains will just increase roughly linearly in time, you tend not to get much extinct.
14:12:05 If you have small numbers it tends to crash and the new creation process is hard, we don't understand where this number of orders 50 comes from. It's hard to nuclear age did you start with a small number, you have to bring ones together that involved
14:12:27 you like. And then it's stable. Is this with or without islands. What was no this is this is this this is this say this with islands or spores. Okay. Yeah, either one, sorry.
14:12:29 Yeah, so this is asking.
14:12:31 Yeah, it's this spatial temporal the chaotic phase, can be okay the other way which is the most interesting one is I can mutate the existing strange and have some correlation with the parent, and then depending on the correlation, it'll drums or how fast
14:12:46 it goes up, down here it sort of mainly replacement when it's very small effect.
14:12:52 Mutations on but again you get this behavior that it seems to go up, go up.
14:12:56 So this is saying that in the sense of being able to find it in a pretty robust and basic model that continual evolution and diversification is is not so maybe not too surprising can say absolutely not an explanation, but it's it's a, you know, sort of
14:13:09 know, sort of qualitative scenario which may be walking again there's there's two phases basically there's a there's eigenvalue like problem, which is always positive, you increase the diversity eigenvalues negative diversity goes down.
14:13:22 If big numbers you can get more that's literally then crashes.
14:13:26 You don't necessarily in this phase, but any given model, I don't like most things with thanks additions, I can't tell you a pri which phase something is in if it didn't the phase then certain things apply, I guess I was confused about what sets the differences
14:13:39 the number, you said the number of innovations if you go to the last slide for a second.
14:13:43 So there's several things which I'm not there yet, number of strains.
14:13:49 So here, these ones are just starting with different initial strains. Okay, but I can also do it. This is now looking at different correlations the parent, but I can also start changing parameters I didn't show one for that I can change the how, how it
14:14:02 correlated the anti correlated the interactions are, and that'll change whether I tend to go up or go down, just so I understand you start with something that's in this phase, then you add that number of new strains, or you start the whole start with,
14:14:15 you start with some number strain some immediately go extinct right here you see they immediately go to thing, then you start adding new ones randomly.
14:14:22 I see new ones be not allowing re invasions of the extinct. Okay, so you keep adding new ones randomly, and the, it will keep growing and the level of understanding it keeps on going.
14:14:31 So what's different between those strings is just so I understand is you start with 400, you let it go extinct, and then just starting with this one is just starting with different numbers.
14:14:39 Okay, good. Yeah, this one is doing different, different correlations with the parents, and there's another one which is different. I should have put the one which has a different values of the symmetry parameter, which, as a function of that you need
14:14:51 to be going up or going down. And as often migration similar similar thing.
14:14:57 Okay, so we have to now come back and be honest about generalists. So what happens if we allow generalist mutations. So instead of just allowing the visa change.
14:15:08 I now allow the essence, which are generalists right if your essence higher than your parents and everything else equivalent you can't coexist because you beat your up to repair.
14:15:17 So then it turns out the behavior depends on the tail of the distribution of the SS.
14:15:22 The is what happens is you would might imagine you push higher higher the tail of the distribution of yeses and at least you know with nice distributions that sort of gets narrower and narrower to disabuse of SS.
14:15:32 Okay. And it's sort of harder and harder to go there so maybe you expect it to slow down, and in fact this is now showing what happens as you as you go you see that it comes out quickly initially the number of streams, and then it gradually slows down
14:15:45 the essays are going up, as this is happening. The problem is again for number of invasion to the successful. To be successful you know you'll need to have a higher risk than the others, like it's harder, harder but again that in terms of those units
14:15:56 units that basically comes up again roughly, roughly.
14:16:04 The, but it continues to diversify, it improves on average in the sense that the average so the population, just gradually pizza.
14:16:10 So this is gets you to a state which is like it said at the beginning it's reasonable to assume that all the essays are similar, otherwise evolution would have destroyed most of them long, long ago.
14:16:20 And so you can say this is a justification for saying that it's not unreasonable for an assembled community to start with a narrow distribution best.
14:16:28 And then the number of strains you can get to, to coexist goes is one over the square of the, one of the variants of Yes, yes, this depends a lot on the distribution right if you have an exponential goes to a fixed value or something.
14:16:58 And so what happens then is you just gradually keep marching outwards, you get federal federal average but you get to a steady state. The only thing is not steady state is the essence which would gradually increase.
14:17:00 So there's a little side note down in the, in the bottom that's even exponential distribution, then what happens is there's only one characteristic scale of the SS associated with that there's one characteristic scale of the diversity in symbol models.
14:17:08 Now of course at some point you start putting out a generalist mutations and so you should say there's a sort of a dropping, dropping off of it but if you if you have a sub exponential one, then you don't get, if it's super exponential we have a long
14:17:29 then the diversity crashes, you go up and you find more and more distribution of dental list but the other one will be them, and the diversity crash. And so the thinking about these things is, is, is important specially if one is treating it as being
14:17:39 interactions and s, which is a real cheap. Right, so we talk about Tara models What does one doing when you put in a lot of things in, you're saying the phenotype of the organism is defined by how it interacts everyone else live in the future in the past,
14:17:52 don't want right we want to carry around some phenotype, and interact via those, and of course that's the nice thing with any of the resource models interacting via chemicals, is that you have some phenotype and how you interact with another one is determined
14:18:02 by your phenotype genotype phenotype. And so we really want to go and look at the question about the phenotype of the organ.
14:18:13 So this takes me to the last thing, which is how much I'm coming back to the question this context, how much complexity, do I need, in the sense of the phenotypic complexity of the organisms or, or the environment.
14:18:25 So I'm now going to say that I have interactions v are some may be modest dimensional phenotypic properties of the organism, such as vectors of how you consume resources and how you how they affect you and how they affect you and then you can ask okay
14:18:37 can hi diversity exists, simple resource models and they give you water D more general interactions via chemicals give you all to do with a small coefficient can work out in sort of bend the model and so on.
14:18:49 I would like is if it's much much bigger than di for example if I took the number of carbon resource number of nitrogen number of number of phosphate number of other things it's like a multiply those numbers together.
14:18:59 And I think that's the diversity I expect that we we said less a puzzle. When you have to add up the number of chemicals which you interact with. It's much, it's much harder.
14:19:08 And sure enough, if you do, you know you do in here interactions with the chemicals. These are low rank matrix effectively, and the maximum size they become a misdeed, and you don't get this chaos at least if you go in the, in the resource.
14:19:20 Now you can when you asked on having too many things in and tracking and resource then it goes chaotic and I won the big question is really understanding what happens, what happens.
14:19:32 Now, let's come to the back to your fate. So what do I mean by the dimension there. I've got one species of this of each. They're identical, except for the reception of the bacteria and the tail of the page.
14:19:43 And those are characterized by some possibly low dimensional vector right so the type j bacteria has a vector their excellence from one D, and this page of the of the tail, and I'm just going to make a simple model, where I just take the doc product between
14:19:57 them. That's the fringes the binding. And then I just say that, depending on the phrase that binding it's all the determines the chances that the bacteria dies, and the distribution of offspring number of the, of the thing, but have some deterministic
14:20:09 functions, one for the for the bacteria, and one for the month of the thing.
14:20:15 And both of these functions you know increasing, increasing functions.
14:20:19 Um, there's somewhat different from each other, of course, but that's that actually.
14:20:26 Okay.
14:20:26 To make sure I'm understanding you.
14:20:28 So here d might be much smaller than the sequence length of the receptor, because these receptor, like you know I would say that I mean that the first guest is sequence like there was, if I if I have a one dimensional you know if I just effectively charge
14:20:43 or something to prioritize each amino acid it's that that ballpark. Yeah, but again I mean these are these are character models is not to be taken seriously.
14:20:55 No Just wondering in low dimensional in what sense because you said these low dimensional and possibly automatic so I mean I'm yeah, I'm here to let us when we can say, compared to what I'm trying to explain.
14:21:09 how many strains are good. That's the question Can I have more strains on the dimension, can I have more than the dimensions squared. More exponential the dimension,
14:21:13 just a very simple question So Jen you represent multiple types of bacteria or so j stages I've multiple types of faith. Okay, multiple types of bacteria, the age of generalists, they can track all of them, they attack them but they attack them slightly
14:21:26 different from each other. Okay, alright so just a killing probability is berries over some small range compared to that effect. So it really generalist, but if you if you try to do a detailed analysis, you would tell they're all equivalent if you measure
14:21:38 it more carefully, you would realize okay geez this one produces on average, 103 phase and this one produces 94, and so on. So, So basically you simplified it essentially to like almost like a collision parameter like essentially like the likelihood of
14:21:52 a particular page interacting the strength which it interacts with a toast, what was that planktonic that that's a good approximation right then it is pairwise interactions is the right thing yeah i agree with that.
14:22:01 But then I'm saying that the only depends on the binding energy and both of the countries that are non binding energy and I'm assuming the simplest possible things I'm sort of monotonic.
14:22:10 Right. And just the one other question is is there a reason both have not the same dimensional vector I guess that the No, no, absolutely not. I mean I can get one of them can be more complicated thing binding the other but, yeah.
14:22:23 Um, but yeah, the thing is is going to be, you know, is this the larger small and the door do I needed.
14:22:28 And what are the functions.
14:22:29 So if the if the functions. If the functions are linear roughly linear.
14:22:36 Obviously they're close to each other, I'd say it's roughly linear and the maximum coexisting diversity is odd, it's sort of like interacting with your resources you don't give.
14:22:43 However, if you start taking these functions to be more tense like model functions.
14:22:59 Then, it appears that at least if you're lucky in what choices you made of the F and G, which my first choice, lucky you can get seemingly opportunity how diversity for the dimension bigger than somewhere around four albums of the high I don't, it's hard
14:23:05 to push things numerically I don't understand it enough analytically, to know whether it really keeps going. They don't specialize.
14:23:13 They get to be generalists, I haven't put in a special generalist mutation, but the phases can quite easily become generalists do better as a general it's just by increasing the magnitude of all there and directions, the way the model.
14:23:25 The model with these with these functions and the end they do they will do that. And then that sort of fluctuate around how good they are in that sort of general way and then the, you know, the bacteria chasing the pages of chasing the bacteria and the
14:23:37 bacteria running away and you get to know complicated felonies and things which isn't starting to starting to look.
14:23:51 Um, but it looks as if you can certainly have a phase worth continuing diversification. Now if you choose if you're unlucky and you choose different functions here that are actually futures ones that are more biologically motivated in some ways, then
14:23:57 you tend to find the diversity goes down on the other side of the question.
14:24:09 But nevertheless the fall as a matter of principle, it appears that we've done low dimensional phenotype, that you can get diversity which is at least exponential in that and maybe that, you know, in some senses arbitrarily is arbitrary high.
14:24:19 I got nieces right if you need finer and finer, but niches if you're going to do it by by dividing up phenotype space Indonesia's, and you need to make finer and finer divisions here they all stay.
14:24:30 They all stay generals King. King, can you give me some intuition, is it the non linearity of f and g which allows this exponential retention of diversity.
14:24:39 So here's a here's an interesting, an interesting question. Supposing I take a random low rank matrix, like I got by indirect integrating out the, the, the environment or I get it by here, or if I look at this I say if I just had this is a matrix that
14:24:56 I've got a non low rank matrix with the chunks of JMU okay and then I take a nonlinear function that matrix.
14:25:03 And then I look at properties that makes resulting matrix, can I tell what the dimension.
14:25:08 Right. Well, turns out if you take a if you take a low rank.
14:25:12 Turns out if you take a if you take a low rank. You know symmetric one, you can as eigenvalues in a pop out.
14:25:16 If you take a completely non symmetric matrix you take these functions being uncorrelated with each other, then you.
14:25:23 As far as I know, there's no simple way to even estimate what the rank is of the matrix got so you can get very high rank, hearing things from taking a nonlinear function of a low rank maker.
14:25:35 So you can try it try just take a, you know, low rank, a matrix of, you know, d by Nyn is large, and these small multiply that by another random matrix of an ID, multiply those two together.
14:25:49 So you've now got an n by n matrix rank de. Look at the, then take a nonlinear function of it, just take these sign sGn plus make it plus minus one, and the look at it I cannot expect.
14:26:00 Okay, I mean doesn't look like a nice semicircle until till he gets large, but then you look at it and then you start looking at the actual eigenvalues the original matrix and try to make sense of it.
14:26:10 So if anyone wants to explore this and is interested in doing it I'm happy happy to talk about it because we're playing around and not much things we know it's relevant for for learning things because machine learning things you have stuff where you've
14:26:21 got these very high dimensional on the more modest dimensional, and you've got nonlinear functions. So the related questions.
14:26:36 Scale RNA in certain ways I can certainly do it and show that it only depends on the first derivative, and the center thing of f. So I think the scaling of RNA are really important, or what what here so I'm I'm my crucial one here is that my dimension
14:26:47 is staying order one and my tell you is getting really hard. Okay, if I take a low rank matrix. Well, if I take a matrix with lots of zeros in it. And I all I need is login nonzero elements per row and the statistics of like a normal random independent
14:27:02 ID random matrix. The if you these low rank things is more subtle as to what it is you need to get sick, but it certainly is not it's not true that if you.
14:27:13 There's a, you can, you can work out some things when the DNNDNK I mean the strings here both are the same order, and you've got a ratio between, between those but the low rank folks the nonlinear function parts of it, do change things.
14:27:27 They definitely changed. In the interest of time, I'll stop asking questions and let you finish, because I only have I only have I think that two more slides.
14:27:35 So conclusions and less.
14:27:37 So firstly, you know, the most crucial thing which in some ways that we all know, but I think tend to forget that high dimensional bullet biology more is different, a lot of intuition about low dimensional things is misleading.
14:27:48 Another one, which we should know more I certainly didn't realize how true it was until I started working with this is that systems are having the optimal function and energy and optimization principle.
14:28:01 A very unstable and higher dimensions is a dangerous assumption you always have to ask what if I allow small deviations.
14:28:05 Okay and then the question is what's not some not so surprising in the sense of it appears that simple models. So the continual evolution with without diversity I thought initially that if you have a small feedback with a fully theological feedback, even
14:28:18 when the environment is simple, that's enough to drive evolution for forever without slowing down is extensive fine scale diversity stabilized in a specialty temporary ecologically chaotic chaotic phase, the continual diversification by revolution I showed,
14:28:35 and that you don't need much, but ok so just last side on the question of. Okay, so my provocative one is to ask where the prediction is essential for diversity.
14:28:48 If we only had interaction veered competing for different resources, even with space and time dependence of those resources and so on. Can you in your sort of relatively simple ways about special pleading stabilizers arbitrary large amounts of diverse.
14:29:01 A now I'm not gonna lie spatial gradients excellent ratings of course the organisms can establish gradients. The.
14:29:08 But I think if you do it in this sort of you know, sort of, well mixed like thing of where you've got the hosts running around. And so you you've got a lot of independent ones without real spatial structure that's maybe one is a harder taste the actual
14:29:20 face all the great.
14:29:22 So one particular one is if you then you know consumer resource like models on a you know homogeneous space as to what what happens. So that one can ask you know what other possible phases might that be one of them.
14:29:36 Which again, along we're starting think about is if you have multiple distinct stable communities.
14:29:41 But invariably each one of them had the same as 100 species species 10 species, they all there, but the different strains of those, and each one of these communities, there's some strain that can invade it.
14:29:53 But the strangers displaced from here, except for the unlucky ones can find someone else to invade in principle, you need to have some kind of nonsense activity here, in order to get them to get this, but you don't have to put that in by hand.
14:30:07 It's something that at least in these in these systems can come out so this is certainly a potential one I think that question is very relevant for things like the guts.
14:30:18 Another one is you could say, well, really things are effectively neutral enough because of bottlenecks and the selection is not really happening that fast.
14:30:27 That with, you know, sort of, not evolution, and the new the ecology getting to be close to neutral. The that fast enough to sustain the evidence for these, you know, partial sweeps that you see in the in the genomes, is a my think is is saying that that
14:30:45 can't be right by itself, but of course the interplay is important. I mean any of these models you know things eventually go extinct and you have to replenish the diversity by evolution, but you can have the evolution at least two models being much slower
14:30:56 than the ecology. Now of course with microbes the time scales are usually not not separate as my number I like to give them enough to give a sense of the big numbers in evolution that pro core Caicos every day, finds all possible triple mutation.
14:31:15 That's the thing saying it's got a barrier, you know, can't get there because there's has to do some deleterious immediate can do all possible triples every day.
14:31:35 Okay, so here's something which I'm just learned about the other day from Jq. And, of course, Jeff course group about some experiments that they doing that will motivate but this is a couple of collaborate was with Diane Boonen who's involved in the things
14:31:43 also mentioned before, and they start putting more species in, but they have a model where they've got a bunch of different islands a bunch of different than a test shoot.
14:31:51 And then there if you put too many in you find some good things and you keep adding more and it gets chaotic and things go up and down, driving more extinctions, then they start putting migration, and they find that that can stabilize this chaos, at least
14:32:03 least on the timescales of things they've, they've looked at, and if you put too much migration, you lose it if you put too little migration, you lose it, but this an intermediate regime.
14:32:12 Right, so, so this is something which is, I would say is qualitatively similar to what comes out in the simple models. I certainly would not claim this as an explanation.
14:32:20 In particular, this is a. There's no particular reason. These are, at least as far as they know there aren't failures involved. And these are not trying to kill each others as far as knowing this not.
14:32:34 They're not optimized. And so it's not clear that has much to do with it. However, the prelim indications are that these kind of this kind of template card phase can exist even over towards the more symmetric interaction part of the phase diagram which
14:32:47 is what you get from creating for a resource, so it's it's a, you know, it's suggestive I think it's fun that they, they saw something but I would be the master claim that this show the theory.
14:33:01 Right. and,
14:33:02 of course, I can say very little about this last, last one, but what the hope is that if one starts having a bunch of different concrete scenarios, or something like this, or this kind of the spatial temporal the chaotic one, you know, when should we
14:33:24 to make a much predictions at least it'll suggest what kind of data one would like, in particular for populations whereas some idea of the spatial mixing processes. And if you don't have any idea about that it's sort of hard to get a sense to get a sense of sense of things like the hot spring, we don't really have a design that we
14:33:31 the hot spring, we don't really have ideas and that we can sort of put downs, but we don't really have a sense of how, how much mixing there is within a spring springs.
14:33:42 Between Yellowstone and other parts of the world. So it's very hard to the uncertainties are so big on those parts that even if you knew the sort of relevant things to the ecology and evolution locally on wouldn't really know where to go.
14:33:53 I think the ones where you have some sense of the transport around like you know human.
14:34:00 The human ones. The or things where the things in the in the ocean one maybe has a better chance at sort of pointing directions to look right because I've done.
14:34:23 think we can go for cookies unless somebody has another question.
14:34:28 Great, thank you.