 Yes, one moment. Okay, do you see my first slide? Yes. Okay, let me just see this here. Okay, so okay, nice to be back with you. And yes, this will be more of a research talk relying on what I told you last time. But first, I wanted to acknowledge my main collaborators who did a lot of this work, my previous postdoc, Saipilozov, who now has a position back in Israel, and then Shishin He, who will soon be part of the faculty at Purdue University. So yes, today, I wanted to touch on assembly or the interaction of ecology and evolution, but in a system, as I said, with a lot of pieces. And I put here a second arrow coming back from the assemble system back to the diversity of the building blocks, which is a topic that I like to touch upon towards the end of the lecture. And you have seen this plot more times than you probably would like. I just wanted to remind you that for the purpose of the parasites, we will be talking about niche differences, differences in traits here that confer an advantage as a function of frequency, so an advantage to the rare disadvantage to the common. And in pathogens in general, we have the advantage, I think, relative to plant systems, because we do know which traits belong to these axes, in particular, that the traits that essentially relate to recognition by the immune system and the host gaining information, memory about the pathogen belong here, so that the distance or the overlap between pathogens in the traits in the molecules that are recognized by the immune system, the antigens or epitopes, that's what matters to this difference because of cross immunity and cross protection and access to host. Now, of course, I recognize that some of you, of course, are not so interested in pathogens. I like to ask you to make the effort to think that everything I say I think could be extrapolated. And of course, there are issues of level of organization, because I'm going to talk about variation within a species. But I like to remind people that the very interesting, and I think a very important hypothesis on diversity in rainforests, in coral reefs, the Johnson-Connell hypothesis is basically a mechanism that relies on frequency dependence, frequency dependent interactions with natural enemies. These are specialized interactions with natural enemies that act against your own offspring close to you. And I'm not going to describe this in detail just to point out that these are important mechanisms. There is a lot of recent literature on evidence for this kind of force. And I think it's a fascinating topic. Of course, we have the problem. And someone yesterday raised the issue of mutualism. This is a recent paper for these kinds of interactions in the rainforest, these Johnson-Connell mechanisms, but also bringing in mutualists. I remember someone asking about that yesterday. Of course, finding evidence of a particular mechanism doesn't mean that at the microscopic level of the whole community or the whole system, they are important in the patterns of diversity. So we also have a problem in these very diverse systems in asking, how should we determine whether those patterns matter? And of course, the purpose of neutral theory was to help in that respect. Now, I'm going to be talking about a system here, a parasite, the main parasite of malaria. And in particular, about this parasite in very high transmission regions. These are the endemic regions where there is very high prevalence. In fact, very high asymptomatic prevalence, because people gain protection against the parasite, but continue getting infected through life. So in some places in West Africa, with very high transmission, you find prevalences in, and I don't mean clinical prevalence. I mean, prevalence in the population that can be 40, 60, 70 percent of the population carrying the parasite. And of course, this is a very large reservoir for transmission. So in essence, we can think that the challenge of elimination and control in these regions is related to this very high strain diversity. So can we try, in this case, to understand diversity, not for the purposes of persistence, but for the purpose of elimination? And for those of you who do not come from within biology, most people know that malaria is a vector born transmitted. But importantly, it has a stage in the blood that's the asexual state and then a sexual state of the parasite in the mosquito. Now, this is what I like to do today. I like to show you that in this system, which is, I will show you, hyperdiverse from the perspective of antigenic variation, negative frequency dependent selection because of competition for hosts is really acting. This is based on some theory. This is computational theory based on stochastic agent-based models and network analysis of the structure of diversity that emerges from this assembly. I like to touch a little bit on consequences of this structure for resilience to perturbations, on consequences for the existence of a threshold in diversification that I think is important because below these threshold systems will possibly persist in a more fragile state. So just to start, we heard about multi-dimensional trait, trait spaces in terms of niche differences. Yesterday we also heard Daniel Fischer and we will hear more about essentially evolution in these very, very large spaces. Here is one and parasites and biology do it in a combinatorial way. For the very specific purposes here of our system, our parasite has 40 to 60 genes that encode for the same kind of protein. This is the major antigen seen by the immune system. So for our purposes, the female type of interest will be a combination of 40 or 60 genes. Now if you ask these genes that encode for this antigen, how many different genes we find in a local population in these high transmission regions of the order of tens of thousands? So you can do the combinatorics, of course, it's astronomical. And so what the immune system sees and gains information on is this very heterogeneous population of strains. Of course, this molecule, I just will say a little bit about it, it's this molecule PFEMP1. It's basically exported to the surface of the red blood cell because it has a function. It makes the red blood cell sticky. It helps the parasite in the stick to the walls of the capillaries, etc. I will not worry about function. I will just say that because it is so exposed, it needs to, it's very involved in immune evasion. And so this is what the parasite does. Once it infects a red blood cell, it expresses one of these genes, then it expresses another, then it expresses another. And believe it or not, there is a certain synchrony of the whole population inside your infection. So they are showing their cards to the host in a sequential fashion. What this achieves is a longer infection than if we were showing everything at once in about the phenotype. So our fitness here will be affected by duration of infection. Now, because if a host has gained memory, the parasite does not express it. So you have a shorter infection, shorter growth rate of the parasite, etc. So that's fitness. But if you, as I said, you could think of any other way in which the fitness is affected, doesn't matter. Here it is duration. And on top of that, the parasite plays a game of incredible diversification because different phenotypes, different repertoires can shuffle their genes during the sexual phase in the mosquito. And during the asexual one, they can produce true innovation because different genes can produce new genes. So all these variations and there is very high, of course, if there is high transmission, there is high recombination. And so you can say, well, there cannot be structured to this mess. There is this huge number of genes, new genes recombination of the combinations is their structure. So this is work in collaboration with my colleague Karen Day, who is a molecular epidemiologist, a phenomenal one working on malaria. And she basically sequenced the marker of these genes in every child in these populations from Gabon. And what you see in this matrix here in blue is basically all the genes isolated from each child in each row against the same isolates. And then you ask with this per-wise type sharing, how much overlap there is between these. All you have to see is that there is a light color. So essentially, each infection is almost unique. I mean by that each combination of these antigens that the hosts are seeing with an infection are almost unique. You can tell me, well, that's not surprising. If it were a random system, there is so much variation. We expect this. But if you randomize appropriately, keeping the frequencies here on the right on top, you see that the degree of overlap here in red, the mean overlap is lower than the one that you expect at random. So there is a force pulling these things apart. So we will ask whether this is frequency-dependent competition. And if so, how can we tell? I mean, how should I look at this data to be able to tell? Now, from my previous lecture, and a bit of art, you may expect that we should look for clusters, that the emergent niches from these kinds of interactions should be clusters of similar parasites. This is not exactly what we have. So what should we expect to see? So existing strain theory, as I showed you last time, will not encompass this very, very large empirical diversity. It also does not necessarily in some forms allow for, at least in the versions for malaria, for true innovation. What I mean by that is a system whose pool is open to new variation. And mostly, there is no explicit comparison to neutral models. By that I mean models that retain the demography of transmission, all the birth death processes, the extinction, but have no specific interaction. So we built, we extended, in fact, an individual-based formulation we had from the past in which we basically have a pool of margins from which we get immigration into the system. Sorry, we start assembling the system. We have transmission between hosts, and each gene is composed of two variants. This is needed here because we need to be able to have recombination generating new genes, but you could do it in a different way. So what we have is a system in which each host remembers all the, I'm calling, oh, sorry, this is advancing by itself. Each host remembers the types, the genes it has been seen before. I will use the word genes, but I mean their product here, really. And if they have seen something, then the parasite cannot express it. So they have shorter infections and essentially that parasite will transmit less. So we basically have the mitotic recombination, the meiotic recombination. We can do that in the computer. And we can also build neutral models. We build two models here on the right. We basically have a model in which transmission occurs, but there is no, essentially no specific memory. There is just complete neutrality of parasites coming in and infecting the host. The one in the middle is more interesting epidemiologically and it's what models typically do. They say, well, your degree of protection is not a function of whom infecting you, but how many times you have been infected. So this has a protection, but again, it's a generalized protection. And we parameterize these neutral models to match the duration of infection with age so that we are not comparing apples and oranges. What I wanted to tell you is we basically look at which properties will give away that there is a structure and that there is a structure in which this competition for host is playing a role. So for this, we decided to look at networks because with the recombination in the system, we cannot look at trees. And I think these networks are appropriate also in the microbial world. We follow the sort of movement of genes, but anyhow, here we get this network where the nodes are the repertoires. And then we have weighted links that tell us how much two repertoires overlap. And we have these bi-directional links just because we may have some repeated genes that does not matter so much. What I wanted to say is that of course, if we start with a medium gene pool in this assembly process, we will see that we get some clusters in these networks. By the way, we take the network and we threshold, I should say, because otherwise everything is connected to everything. We only keep the links of the strongest above a certain threshold to sort of have the interactions that are still the strongest. So the most similar was the structure of the most similar parasites. You can see in red, a typical just here example chosen from a model where you see some degree of clustering. And then on the blue and yellows, the corresponding neutral moles. Now, a degree distribution or anything would distinguish these networks. But when you get to systems with a very large pool of variation, then the difference between the networks is not so evident. I'm just illustrating here with the degree distribution where of course, you cannot distinguish it. If you look hard enough, you may say there are differences in this network. Can we tell them apart? So we built a network classifier based on an ensemble of network properties. For example, we can give them, we can consider three way motives in the networks and other properties. And I will not go into details. If you look here at the bottom, sorry, in the right, just to mention that we use a number of network features, not just on motifs, but distance reciprocity, transitivity, a bunch of, as I said, a bunch of features. And here on the left, you can see for high diversity, the scale going from light blue to purple shows you how many times we properly classify a simulation. If we give it blindly to the system, can we basically classify it to the right model for different parameters? And you should just see that we do and that how much the network features contribute to the classification is here on the bottom right. You see that the motifs are important, another, but also some other distance related properties. So we said, okay, we have this classifier. What happens if we apply it to real data? And this is work of course in collaboration with current day, we have a long longitudinal study now in its seven years. So that's nice here in northern Ghana in the Bongo district. So we built this classifier and then to be able to classify the empirical system, we used a method called discriminant analysis on principal components. That's what we use for the classification. And I gave the reference here at the bottom. This method is a very nice method to find groups in genetic data. It was specifically developed for this and it combines the two multivariate methods, discriminant analysis and principal components. I will not get into details. I would be glad to discuss it. But you can see here in the colors, the two principal axes that are from many, many simulations. The points are different simulations in yellow and blue, the two neutral moles. In red, all the simulations in a certain feasible parameter regime for our system, where you see the difference. And the black dot is the empirical data, which classifies with very, very high probability to this immune selection regime. So this is telling us the networks in the network we observe of this similarity between repertoires seems closer to what we expect under those conditions. Now, as I mentioned, there were no clear clusters. It's not a simple cluster structure. And the way to see it is that we are looking at limiting similarity, but in this limit of a very high dimensional space. And it looks, it doesn't look cleanly like clusters. So we did look at the structure. That was the structure in a given season, in a given time. We can look at the structure over time, where each network is built for, let's say, a different season. And we can connect them. We can connect them also to similarity, the same similarity, the same threshold as we did before. And what I'm going to do to show you very quickly in this paper is if we look as a function of time and we look at modularity of these networks with a network approach that basically relies on a random walk, basically we identify clusters and we can, well, modules. So groups of repertoires that are more similar to each other than to members of other groups. And then we track them in time. So these are modules in time with a multilayer network. And I wanted to show you that although we don't have clear clusters, if we look at the modules, there is a large number of modules on top here of the left. When we have immune selection, we see these modules persist for a while. At some point, they go extinct and others are arising in this assembly process. To the right, in B on top, you see these much less persistent cluster, well, modules in the neutral model. So there is a certain, in this very sparse, I would say, in this system where everything is so different from each other, there are, there is something you can call strengths. But it's perhaps not what we have been used to think about. So anyhow, let me just pause here and just say that of course, we don't have the simple clusters, but we have some limiting similarity structure that is affected by this cross immunity. And we seem to have it in nature. So I said this structure is both non-random and non-neutral. We have some sort of clusters that would constitute, it's the best you can find that you could call strengths, and it's very dynamic. So okay, you can say, does this matter at all? And this is largely, now I'm going to move to unpublish work. What we, I like to show you one example that this matters to a response to perturbation. So the kind of perturbation we have here is one that reduces transmission. So if you look here to the right, you see transmission is seasonal in our model and in the real system. And we parameterize this from the real system, including during an intervention that can last a certain number of years, from two to five years. We use this intervention that reduces, it's known as IRS for indoor residual spraying. We are essentially decreasing the number of vectors, the transmission rate for a while, and then we release it again. I like to show you that in the model, if we compare the response of the system, one of the neutral models, the one, the generalized immunity model where there is no specific interaction, just a generalized interaction, then what we find is some increased persistence under this negative frequency dependent selection. So increased persistence during the intervention. So if I reduce transmission, which is equivalent here to reducing the growth rate of the parasite, right? For two, five or 10 years in the plots, and I vary, for example, the initial pool size of the system, you can see that the extinction probability in blue for the generalized immunity tends to be higher than for when you have this kind of frequency dependent selection. So there is this longer persistent, this higher persistence of the parasite through the intervention. And it's not due to abundance because the prevalence as you see at the bottom is very similar between the two systems. So this, you can ask, well, why is this? And I did, oh, sorry, perhaps I did, let's see. Well, this is, sorry, I should have added here the reference, this is a paper now in reviewing frontiers in ecology. So you, sorry, I will add that. But what I wanted to show you is that if we look at this quantity I showed you before, which is a measure of overlap, the distribution of overlap. If you look under selection here at the bottom, the distribution of overlap before intervention is in yellow during intervention in purple and then after intervention. And you see that there is, there are in the population parasites with very, very little overlap because of this competition. And that is quite robust during the intervention. Of course, it changes afterwards because of the transience, but also because you have lost a lot of diversity during intervention. But this reduced overlap gives you longer duration and therefore higher fitness, which allows you to make it through the intervention. And this is not the case for generalized immunity. You cannot maintain this fraction of the population that is extremely different from each other. So in some way, this structure would, this limiting similarity would enable persistence. Now, I like to show you, and this is the part that I'm most interested in showing you at the moment. We discussed this at the end of Daniel Fisher's lecture yesterday. What about the diversification, the accumulation of innovation in this system? And this is the connection between a force, this frequency dependent selection is acting at the level of the individuals that are our phenotypes of interest. But it's also acting at the level of the genes, right, that are part of the pool of variation. So I'm going to kind of try to show you that these things are connected. And I'm going to speculate even farther and say that a system that is hyperdiverse in nature will always be built from many, many pieces, a lot of genetic variation and phenotypic variation at the lower level, what Daniel yesterday called the nano phenotype. Because the same force, you cannot have one without the other. And here is the idea. There will be a threshold. I will show you that there is a threshold. This is in a paper now in review by Shishin and I, and you see that this idea of a threshold in the diversification of the genes, right? So below the threshold, a new gene comes in, but it goes extinct. So these invading genes come in but cannot stick around a lot. Above the threshold, by the time a new gene goes out, others have come in. So you can accumulate novelty in the system. We wrote this by analogy to perhaps not a complete analogy to with R0. We wrote it as something we call Rd. And this is the sort of a reproductive number or an innovation number for new genes. They have, you have two components, genu and the new rate of gene accumulation and continue the time, the average time that one of these new genes stays around. In this paper, we derived an expression for genu. I don't have time here to show the details, but it relates on the basis of population genetics on the size of the population, size of the parasite, the rate of change, a mutation rate in the broad sense here, a recombination rate, and then this P invasion, which is the probability that something new invades. And that depends a lot on how many susceptibles you have. So that will be influenced by, again, this kind of selection. And then genu, the expression for genu, we got an approximation from some very nonlinear PDE in the supplement, but we don't have a closed form solution for genu. So computationally, I like to show you that there is a threshold, that threshold. So when this number is smaller than one, you cannot accumulate diversity. So here it is in the log, the log of our deep. So the threshold is at zero. And then what I'm plotting from my simulations in the y-axis is the percentage of new genes during a window of time. So choose a window of time and then count how many new genes have accumulated by the end of this simulation. And I should say that the points here are different simulations with very different both parameters and assumptions. And we see that below this number, there are no new genes accumulating below zero and above they do. And what is interesting is that on the right, I have plotted something similar in the y-axis, but for a quantity that measures the intensity of transmission. This is the number of infected bytes per unit of time in malaria. And this is interesting because this tells us that as we reduce transmission, we are going to push the system below this threshold. This threshold is well above our zero of one. So this is a system where transmission occurs, but you have lost the ability to accumulate essentially the building blocks of diversity. And this is illustrated here in the simulations. Each color is a new gene coming into the system and plotting the frequency. And this is over time in a simulation over the transients of the system. The gray color, we are accumulating all the genes that are very, very at very low frequency. The colors are those that have higher frequency. And you can see below threshold things are coming in, but they are not sticking to the right. This system is very happily accumulating diversity. So you can ask, does this matter for population dynamics, for what I'm going to call epidemiology? Well, we only have some preliminary results on this. And what you see on top is just over time, a system now with an intervention where at this time zero here, we are going to reduce transmission in a way that, for example, doesn't cross this threshold in the left or crosses this threshold. So we see before the genes that were there, the frequency of the genes that were there before intervention and those that now are there building up after intervention. And again, when we cross the threshold here on top in the right, you see that you cannot accumulate new genes. We did here in different colors, you see in the plot with the bars, how much we have reduced this quantity in these four different simulations. Only in the green one we have crossed this threshold. And I will focus now on the center plot here at the bottom to look at what has happened to prevalence after that intervention. And you see that in all the simulations that have not crossed, we get a reduced prevalence and then the system rebounds. Very characteristic of all the efforts to intervene in these very high transmission regions. You release intervention, the system comes back. Interestingly, in this, when we in the green simulation, that does not happen. So in practice, there is nothing in the system at the population level that is easy to measure that will tell you you have crossed this threshold. But it appears to make a difference and a difference we need to investigate further to how the system responds to these kinds of interventions. And in particular, how fast the system rebounds or whether it rebounds. So let me note here, of course, that for a while here, these systems, because we I should have said this is not a simulation where we let the system rebound. I'm sorry, we have just reduced transmission to a lower level. And this is why you see that the prevalence basically reaches a different sort of steady state after intervention. We have sort of decreased diversity. And therefore, and we have decreased transmission. So we get to lower levels. So let me sort of try to extrapolate some thoughts here that I think apply to the system, but may apply to others. These hyper diverse systems may well occur at the opposite end of neutrality. Work coexistence is a sample under interactions that are specific and frequency dependent. So interactions that will lead to this negative frequency dependent selection, which is a form of balancing selection and therefore should enable diversity. It is in these evolutionary systems along the lines of the stabilizing competition, for example, of Chesson. I think more importantly, large phenotypic diversity in this system is built from a large pool of diversity at the lower level of organization. And this is not by chance. This is not by chance because I just showed you that the ability of the system to accumulate diversity with this kind of critical threshold is going to also be influenced by these same interactions and selection. So this would set the stage for the existence of an unappreciated threshold that concerns the accumulation of genetic variation on which high biodiversity is built. So that when we lose diversity of species, for example, we may be losing much more because we may be losing the diversity of the traits that allows the system to have that coexistence in the first place. And the question that is worrisome is how do we know that we have crossed this threshold and transition to increase fragility of the system? I think that's important. There is a question in the chat by Aditya. So how do you parametrize mutations? Are mutants related to the parents at all or are they totally new types? Yes. Thank you very much. That's a very good question. I know they are related to the parents because remember, and of course, the two that each type has two elements, so this is very hierarchical, allow us to do recombination. And so there will be some similarity. And in fact, we have, we use an empirical sort of result from recombination on that, that for example, if the, I'm trying to remember the details, but not all the recombinants are viable, right? Like something very far from the parents is not going to be very viable. So we are kind of, it's not a completely new type. And then you can decide, you can sort of measure similarity at that level of the epitopes. We have some evidence that in this part of the gene, there are two epitopes, so two parts of the molecule that the system recognized. There may be more, but we recombine them and then we have some similarity to the parents as a function of that. We also have mutations, but they are not so important in this system. These, the details of that mole are described in the paper by He and collaborators in nature communications 2018. So if you like to see more details of this, that's the place to look. Aditya say thanks. Thank you. Thank you for the question. I forgot, I'm trying to give here the big picture, but and yeah, I obviously, I think some of these results will not be dependent on these specific assumptions, but I think we have to consider them in particular when trying to parametrize the system and so on. So this question of the increased fragility, of course, here at the moment, we have only preliminary results on this. I have shown you some preliminary results. We know in malaria that when we intervene, we move the system towards lower diversity of the parasite when we reduce transmission, and we know that the low transmission systems that are so, for example, the low transmission systems in continents where, for example, transmission is lower like South America or geographic locations of low transmission are systems that respond more easily to intervention than these very high transmission systems. So there's an interesting question of could we determine, how could we determine that we have crossed this kind of threshold so that then we could say the system is at a stage where we should hit it with further intervention because it is in a susceptible place. Of course, for conservation, we would like the opposite. Let me now mention that I like to end with some references to other hyperdiverse systems with this kind of selection or interaction, other eco-evolutionary systems like this for some of you who may be interested. This appeared very, very recently. In this work, we look at the strain diversification of a microbe and a virus through the CRISPR-induced immune memory of the microbes. So we know microbes can acquire memory of who infects them, of the viruses, and this is also a very piecewise system, a very combinatorial system where the microbe basically takes parts of the genomes into its genome and that constitutes memory. So we work here with bipartite because for microbes and viruses, we can look both at the host and at the viruses. We can look at bipartite networks. And if you are interested in this connection between the eco-evolutionary dynamics and how you see the network structure that arises, we looked at this here. It's a much more dynamic system with different dynamical regimes that alternate until the viruses go extinct. And that may be because this is much more of a predator system, a predator-prey system than the disease systems I was showing you before, just to end. This is another paper. It's not of mine, but it's a phenomenal paper by the group in Harvard, Mark Lipset, and colleagues. On another pathogen that is incredibly diverse, Streptococcus pneumonia, they have been looking a lot at how these systems respond to vaccination. You vaccinate with specific strains. How does the system respond? Why is this paper fascinating? And I think it is because it gets to this very important question of these niche differences or these frequency dependence. How high dimensional are these spaces? They look at the genes of these microbes that are non-core genes. So they are believed non-essential. They are not present in all the genomes. They looked at, I forget if it's 3,000 or 4,000. At that point, it doesn't matter. And they wrote a system of equations based on the replication equations, which on the basis of frequencies will predict which strains would come out from this vaccination in the empirical system in the real world. And they managed to do so. So this means that some very effective frequency dependence is being played by genes that we don't even think are so important. It must be through myriad interactions, maybe with viruses. Who knows? I can't begin to kind of think how this is happening. Very, very interesting paper, and I recommend that you look at it. So I like to end here and just recon, I don't know if I went too fast or too slow, but maybe there is time for questions. This is, I like to acknowledge, as I mentioned, Karen Day and her group for all the very interesting conceptual and empirical work. Thank you for listening. Thank you very much. So it's open for questions. So maybe I can start. I think you showed this data from Congo and where there was this very high diversity, which you could quantify. And could one use data of this type to quantify this, at least maybe not the treasure, but relative, I mean, how populations tend relative to each other. Yes, that is the case. By the way, I didn't put the slide here. I thought I had put the slide here. If you compare population, of course, if you compare systems, parasite populations in different geographical regions, right, it has been done. I showed you, I wanted to show you where we got this information on the number of genes in different places. So what Karen does is she sequences the genes, looks at counts as different genes, those that differ at a certain level of of sequence divergence. And then she counts them and she does the typical cumulative curves that we do for species, but we do, we can do them here for genes. So I wanted to show you those curves, but I didn't put them here. So they are typical cumulative curves, and you can do some extrapolation on how at what level they should saturate. If you go to South America or New Guinea, those curves saturate at much lower levels than for West Africa. Very, very clear difference. So yeah, by your geographically, we know that now, of course, we are saying that this transition is not just a continuous transition, that there is this threshold that should apply, right? So can you apply that in time to a system in a transient state where you intervene? And now the problem is you could monitor, of course, you can monitor as we are trying to do the changes in the gene diversity, but in terms of the accumulation of new genes that are coming in, right, you need to do that over a certain amount of time. So it's not a very practical way to find out whether you have crossed this threshold. There must be other ways, yeah, to determine this, but certainly the point we are trying to make is that we should be monitoring this diversity, which is not typically done because this is such a complex system that it's typically not even considered in epidemiological models of malaria, right? I mean, we, at best, deal with generalized immunity. Yeah, yeah. Sorry for a long one. Question from the chat. The question is from Pavel Lyomi. When we are below the threshold limit, is it possible for the generic system to go to extinction? Yes, of course it is. And the thing that is interesting, maybe she meant the ones with, when you say generic, perhaps you meant, maybe I'm going to answer that in two ways, for the system. No, sorry, for the genetic system. Okay, thank you. So it is possible, but this is what is interesting, right? And I think this touches on some open questions at the moment, is that that threshold, so that when you mention extinction, you are talking about demographic extinction, right? And to some degree, at least from the, from some perspectives, R0 or R would be more important there, right? So that's a demographic number. And of course, you can view, you can look at extinction in a stochastic way and so on. That's purely a demographic phenomenon, right? Here, this system, as I said, you can cross this threshold at levels where you are transmitting still very well, right? But you are doing so with much less diversity. So it is somehow of a hidden threshold from the population dynamics, but we are saying that there are, that it should be important that we have begun to look at that. It's very early work when I showed you that the system that has crossed it essentially stays at the lower level, right? And has a different response to the perturbation. So, presumably we know, I'm going to speculate here, the biogeographic regions that that steady state have very different levels of diversity, have over very long evolutionary times, and large regions in some sort of metapopulation, right? Have assembled much less diversity. So they live in, some of those may exist below this threshold, right? And we believe the ones that in West Africa that are still transmitting at very high level are on the right. I like to mention that some of the pieces of these genes that we find in humans, of the var genes, can be found in parasites of primates, so that the phylogeny of these var genes can also have very, very deep branches, because this kind of balancing selection will promote persistence, not just of the parasites, of the parasites that coexist, but once you have become part of the established genes, you can exist for a long time. And so that's why also you can accumulate diversity. And I think that, yeah, these are all open questions. Sorry, I took long enough. Are there other questions? Thanks. So there are no other other questions. So you should, you can either raise your hand and open up your microphone or write in the chat. So looks like there is no other questions. So so I have a curiosity, Mercedes, if I may. So you spoke about this, like synchronization phenomenon that occurs inside the body where this parasite expresses different epitopes at different times. So how does this, how is this synchronization achieved? Yeah, that's a fascinating question. By the way, there is a body of theory, but I cannot, I don't think there is a full answer. I mean, there isn't an understanding of that, right? There is a literature on that, there are different hypotheses. And the question, of course, one critical question is on which the different moles differ is whether the immune system is involved, right? So is it something just from the parasite or is it that falls to the immune system? Right. And so, of course, it's not completely perfect, but there are waves of parasitemia within the host that are dominated by some of these types, right? So we have, I must say, of course, you know this. No, it looks like this, I mean, this synchronization inside the host and the diversity, they are a key factor, right? Yes, yes, of course, the synchronization is very important because if you showed your 50, I'm going to say 50, if you showed your 50 faces at once, right? Then the immune system could react, you know, could protect here and could shorten the infection much, much faster, right? And in fact, I should say, but of course, this sequential, for the theory, of course, here, because the fitness is related to duration of infection, but I showed you models in which the other day in which the memory affected the risk of infection given contact. So the transmissibility and not the duration, it doesn't matter because the fitness of the parasite is the product of the two. So I strongly believe that the results I just showed you would extrapolate to other systems with different assumptions as long as you had this competition that depends on overlap and distance. Okay, thank you very much. So I think we can