 Yeah, thank you for the introduction and I'm really glad to be able to participate in this workshop Currently, I'm a assistant professor at Purdue University and today I'm going to talk about some work that I've done during my postdoc at University of Chicago with Mercedes so in yesterday's previous talks that we heard yesterday and today we have seen a lot of study that focus on the the community that are composed of resources and consumer type of interactions. And today's talk I'm going to focus on the entity diversification that actually we can see kind of a very strong analogy between the community assembly at a level of species and at a level of strengths that becomes these different kinds of strengths. So we can think of like resources that different species are competing for for example carbon sources and different kind of nutrients. But then like we can also consider host immunity as a kind of resources and different kind of antigen variants are competing for these renewable host immunity resources so that once the hosts are immune to certain kind of variants then this resource is kind of consumed and then new hosts who are born to the system or hosts that who forget about the immune memory then they become renewed as a new kind of resources. And then we can also think of interactions between different species. For example, we study their coexistence or competitive exclusion and similarly for antigen compositions in the populations we can think of whether certain antigens can they can co-circulating in a population or whether one new antigens will competitively exclude the older ones. And now when we talk about abundance rank abundance of curves of different species in the community and their succession histories for antigens in the population we can also describe their diversity patterns and then think of the turnover and establishment of new genes as a kind of strain level assembly processes. And then when we think about species as generalists or specialists that are in terms of their resource usage, similarly for antigens they could elicit cross reactive immune memories for the host or whether they only elicit very specific memories. So these kind of analogies actually very importantly at the fitness level we can also borrow a similar coexistence theory that developed by Chesson to understand the fitness differences between different antigens. So for example, for antigens at the functional level, they need to bind to different kinds of receptors in the host. And then if there's any new mutations that change the shape of the original antigen so that their binding is not optimal anymore, there's differences in their functional fitness. So then we can, these kind of selection are these kind of selection we call them directional selection so that they influence the growth rate difference between different antigens, while our immune system they secrete antibodies to target these antigens. So then there's any conformational differences in the mutations so that change the shape of the proteins in the in the epitope sites that are targeted by antibodies, then here balancing selection, so called immune selection will be at work to select for new antigens that can actually escape this kind of host immunity check. So at this axis on the x axis, we are actually showing a kind of negative negative frequency dependent selection that is selecting for genes that differ in their niche space. So if we consider each variant of the antigen gene as a species, then we can actually directly borrow the framework from coexistence theory to study the long term evolution pattern of this antigen gene family as an ecological community dynamics in the two gene scenario as the cross immunity. So, so called niche divergence increases two genes, they can both exist in the population. Alternatively, if two genes, they have these functional gene functional level differences. So, so we call them absolute fitness differences, then one gene would take over. And if we draw a diagonal line, given the position of the two genes, along these two axes, we can actually decide whether they could coexist or one gene would actually take over. So this is only the scenario of two genes, but what about large gene families with constant innovation and different strategies to survive for the genes within the gene family. In this study, we would like to investigate coexistence of a large gene family that that is the major of from antigens of malaria. So, in malaria transmission there are actually very important three important epidemiological characteristics that are really observed in other kinds of diseases. One is that it hosts, they do not have a sterile immunity in even in an endemic regions, which means that even for adults here that we can see that a large proportion of the population, they constantly carry these parasites year round, not just in the west and also in the dry season, which means that they it forms a really large asymptomatic transmission reservoir, and then the symptomatic ones are only at the tip of an iceberg. And then these kind of transmissions are usually caused of a very large caused by a very large hyper diverse pool of parasites. And then the key driver for this really large reservoir is the antigenic variation. So, while under the micro scope when we see these infected red blood cells as the same type of parasites from the perspective of the immune system, actually, the parasites, in fact, in these individual red blood cells are wearing very different types during the asexual red blood transmission stage. And this is largely due to the extreme diversity displayed by our surface protein PF EMP one, which is encoded by the barging family. And this level of diversity is observed at different levels. So within the genome of a single parasite, each genome has about 60 different copies of these margins, which they encode the different variants of the same surface protein. And during the during the infection actually a parasites can change expression from one to the other. Thus, they can display different masks to our immune system, one at a time for for a very long period of infection duration. And then, at a, at a population level, we observe a really diverse pool of gene variants. So in very high endemic regions, there's this enormous pool of diversity that's shown here as a diversity accumulation curve, built from the sampling in Gabon children in the village from our collaborator, which reveals more than 6000 different kind of large in types as as you sample, and then the curve is very far from saturation, which means that if we actually sample a random combination of genes to to become different strains there's an astronomical possible combinations that we can get. And the driving force for this diversification is is quite different from normal speciation process. The diversification for this antigenic gene for this gene family in malaria is through recombination processes, and there are two types of recombination in the system that both promote diversification policies. One is the myotic recombination, which creates new strains, and this happens in the sexual reproduction stage within the mosquito. So then different combinations of genomes, they can shuffle their components with each other during this sexual recombination stage. And more importantly, during the asexual cycles within the host, there's another type of recombination called ectopic recombination. And this occur this occurs between two different genes from the same gene family in the genome. And it can happen at any stage of the reproduction cycles so that some of the fragments from the two genes they can recombine and become a new gene within the within the genomes, therefore creating potentially new antigenic variance. And we have, we have talked about how this enormous diversity can be observed both at the gene level. So then we have a super large pool of the local genetic diversity of this gene, and also at the level of combination of the genes. So if we, if we, we then connect how this how we can think about this antigens as a community of species, we can, we can consider these different gene variants as different phenotypic traits. And then the gene pool is basically the possible trade, trade space, and then each strain is a combination is a combination of these strains to become individual competitors between each other. And here we want to focus on the, the, the generation of these different gene variants that is basically the gene pool and the trade space. And we want to know if there is any kinds of threshold for this antigenic different diversification processes. So that is it possible that at a certain regime, at a certain regime below this threshold, the gene pool is kind of constant but then above this threshold, the diversification process is really fast. And this would be very important, very important for us to understand malaria transmission. So basically we know that if we reduce the transmission intensities in the, in the system, we will of course decrease the antigenic diversity in the population. But what we don't know is how this decrease occurs and in particular whether it involves a threshold transition. So this is try to complement the traditional are not concepts of describing whether an epidemic will occur. Here we focus on like investigating this different epidemiological measure that can define a threshold, basically describing this diversification processes of antigens, and whether we can separate these two kinds of regimes. The reason why we think it exists, such a threshold exists is because each gene when they, when they come into the system, they need to pass through several kinds of drift processes. And because they first need to dominate in the parasite population within the host and then get transmitted to at least one person before the end of the infection, and also they need to be propagated in a population to compete with other kinds of existing antigens. So therefore, we are, we would imagine there's such kind of threshold for one scenario below this diversification threshold, a new gene just come and then sometimes goes, and then these kind of new genes they don't really overlap with each other. So then they don't really accumulate in the population. While above this diversification threshold, we would observe a lot of overlapping lifespan of new genes, and then some of them would be lasting in the population. So basically, we are imagined that the establishment of such genes would be possible when the average death rate of these genes would be lower than their generation rate. Is there any questions so far? I don't see questions in the chat or in the participant list, but if anyone wants to ask something, otherwise I think you can move on. Okay, great. So basically, how we are going to propose this new epidemiological threshold is first that we consider the rate of generation of these new mutations, and this basically is determined by the population size of the parasites, and then the generation rate of new mutations. And here mutations I refer to both the real mutations and also recombination processes in this system. And then we consider for these new mutations, we need to calculate their invasion probability, because if they create something that antigenically different, then they have an advantage to replace the existing ones because they have a higher potential host immunity resources to still be depleted, that haven't been depleted. And then also we need to consider the functional level fitness of these new genes because they might not be functional in binding anymore, so then these genes will also be selected out. So this P invasion probability here, we are considering both their functional level fitness and also their niche divergence compared to other existing antigens. And then we then compare it to the death rate of these genes, basically we call it T new, one over T new is the death rate and T new is the overall lifespan of these genes. And then, so then we call this epidemiological threshold as RD, and it's the product between G new and T new basically is N times mu times P inversion and then P invasion and then T new. So, in the, to confirm this, the existence of this threshold, we model a realistic diversity, a realistic stochastic individual based stochastic model to incorporate recombination mutation and migration policies that create a population that is open to constant innovation. And also in the paper that is going to be impressed. We, we list the analytical approximation of how we calculate this P invasion, and also approximation from solving diffusion equations for T new to actually have an approximation for this quantity. So if you're interested, you can refer to that paper for specific equations, if you're interested. Is there any question so far. Well, I had a question that I actually wrote in the chat and, but I think it's a good discussion. Okay, yeah, so I think we can move on. Okay, yeah. So, so our numerical simulation actually confirmed that there is a sharp transition between these two regimes. So here, what I'm showing on the x axis is the log value of our teeth that we calculate from the simulations, and then the y axis is shows the percentage of new genes that we calculate at the end of each simulation. And then each point here represents a simulation with different combinations of parameters. For example, within host dynamic different within host dynamics rules, strength of trade off and transmission rates and seasonalities. And then. So, so therefore this, we see this threshold that is robust to different assumptions and parameter combinations. So, so here that we see that above the threshold of our deep larger than one, which is log already larger than zero there's a fast accumulation of new genes but below this threshold there's hardly any accumulation of the genes. And then, on the right I'm showing that actually the transmission intensities which is measured in malaria system as the etymological inoculation rate. They increases monotonically with our deep. But why do we still need to go to use our deep value instead of the direct direct calculation of this entomological inoculation rate is because we know that with reduction of this inoculation rate, antigenic diversity reduces, but we don't really know where this transition that will allow us to predict that the system would be having a more constant pool of antigens, instead of fast accumulation of new antigens. And I also want to note here that all of these are endemic transmissions, which means that they are, they're well above the traditional are not threshold that epidemics, whether the epidemics can be a sustained. So all of these conditions they have constant transmission. Okay, so. And then here I'm showing you how actually below and above the threshold how the accumulation of different new genes are different. So, on the X axis are different years and then on Y axis are the frequencies of these new genes. So great color here indicates very low frequency of new genes and then the other colors and coloring the ones that are relatively more abundant when they were generated. And then we can see that below the threshold new genes are generated but then their lifespan are usually really short. And then, so then they come and go and they don't really stay in the system. So, at this regime they are more governed by stochastic processes, rather than their fitness compared to other new genes. While above this threshold if we look at how the generation of new genes, it's a sharp, it's a really sharp difference from the previous graph that we see new genes they would be generated and they don't really easily got lost in the system. Rather, they, they kind of persist at low frequency but they persist for a really long time in the, in the population and then the general, the accumulation of new genes is really fast. So, how does the, how will this threshold actually help us understand the effectiveness of interventions in these transmissions, or whether we can actually quantify our effort in the effectiveness of interventions in the system. So, so here we look at how antigenic diversification, whether they recover or not if we reduce the transmission intensity below this RD threshold. And then what we found is that if, if the transmission rate was reduced but then not below the threshold, then after the intervention. The new genes will still accumulate and then dominant in the system together with the other genes that were generated before this intervention. So, so here the dotted line indicates when the intervention intervention started. And then, if they were reduced below this threshold of ID, then the accumulation of new genes are very slow compared to the other existing genes. Are there any questions so far. I don't see any questions in the chat. So, and then, so then like we would like to know whether measuring this quantity would also give us advice that about the, how will the system respond in terms of epidemiological quantities, compared to other existing measures. And then here. So we reduce we reduce we quantify our leaf. Based on different percentage of reduction in the biting rate, colored as different colors here, and then we we measure how the system respond to this, all these different levels of interventions. And then we found that prevalence rate in the host would risk would recover really fast. If the reduction of the biting rate doesn't push the system below our deep equals one, but then if when the system was pushed below this threshold, then the prevalence rate, and then the multiplicity of infection. And then they stay low and then they don't rebound as other other scenarios, which means that if we measure this are the value in the field, it has practical guidance in terms of predicting how the effectiveness of the intervention or how fast the system will be respond in the in the empirical settings. So here I'm just showing you one result from the analytical approximation of our deep. As I mentioned that we developed an approximation for team you using and diffusion equation based on the frequency dependent selection. And here we don't really have time to develop how I achieved it, but then I would like to just show you the relationship between between team you and then the proportion of susceptible population, the proportion of susceptible post in the population. So basically, we see that the lifespan of a new gene is most strongly correlated with the percentage of susceptible host. Basically, we can think of them as still usable close memory immunity resource. And then, once the, once the, once the population has a has a large amount of still available. Open niches, then there, then the new genes will not really have much advantage to invade the system. But then if this resource is already deep depleted, which means that as is very low, then there is a really high advantage, a really large advantage for new genes to be able to invade the system and then stay in the system for a long time. So, and then dotted line is basically time to fixation for offer a neutral variant. So once the system still has very less open space for the host immunity, then a new gene would be very have a huge advantage much higher have a much higher lifespan than a normal neutral variant in the population. So, just to conclude from what I have told you so far, we observe a sharp transition in the accumulation of antigenic variation that is related to transmission intensity. And then this RD measure provides a very useful value to to evaluating the effectiveness of intervention in controlling this antigenic diversification processes. And then once this threshold is across is cross the epidemiological system should be more susceptible to further interventions because the pool of the genes are relatively closed. And then so the next step for our work is to actually have empirical estimation of RD, which will require a lot of fitting of the epidemiological and molecular data. So, in general, this concept should be able to apply to other infectious diseases, not just with and also mostly for the multi gene families. Or gene families that have multi locus, these kind of antigenic variation. And it also we could also speculate that for community assembly processes are similar. There could be potentially a similar threshold for diversification. Due to the how these traits how whether these traits can be evolved fast fast enough or not. And then, as Mercedes mentioned from the last talk. We, we could also speculate that in these kind of really hyper diverse systems, hyper diverse ecosystems, there must be some kind of balancing selection. These frequencies dependent competition in work that ensures or promote really high diversity and then co existing coexistence of many different species. For example, the Jensen column hypothesis. And then if you're interested, you can, you can see the, you can download the paper from bio archive, and then it should be out in plus computational biology soon. Thank you. And I would like to acknowledge my collaborators. And a lot of help for discussion from everyone from Pascal's lab and they slept at university and Melbourne, and then my colleague, shy, also from our system professor, and then Catherine Shazia and Karen from university at the University of Melbourne. Thank you. So, is there any question. I have one but I want to give the priority to what. Well, I can ask the question that I, that I. So, when you calculate the, the. So this, this position point, it seems to me the sort of argument you have, it seems to me sort of related to the transition between being in a periodic selection of the gym where you have a strain that between with a beneficial mutation that go to fixation and then there is no interference between a strain spreading beneficial mutations. So the transition between this period selection regime and current interference and where instead you have multiple strains with the beneficial mutations that interfere with each other. So, if the connection. There is actually a connection between our view and the transition between the period selection and the current interference, or is just completely different things. You may interference. Do you mean interference as just a pure competition between different strengths or. Well, I mean, yeah, I mean that they, I mean I mean interference in the sense that you have multiple beneficial mutations that sort of slow down the dynamics of fixation and therefore you have coexistence of multiple beneficial mutations, because they sort of slow down the time scale of having the competitors going out of competitive exclusion. Right because you have time scales right the time scale so their eyes of a new mutation and the time scale of extinction. And somehow there is a transition where mutations are fast enough that you have these mutants and the fact that they slow down. The time scale of extinction so I was wondering if there is a connection there. There is a there there is. If so so when you have multiple. Yes, so when you have multiple new mutations, they would. Usually they don't occur in the same. Usually they don't occur simultaneously in the same post. But they, when they're at low frequencies they kind of do not really interfere with each other, but when they reach certain kind of frequencies at a population level. Every gene in the population they will have to be at a lower frequency so it's kind of when you don't have a lot of diversity than each new gene would be really beneficial and then sweep into the population. And then once you have you accumulate a large diversity then each of them would suffer to to a lower frequency at equilibrium just because you have you have a lot more composition. I don't know if that if that's what you're asking or it's different. I, she's seen just the problem. The problem is that clonal interference at least in microbial communities, or microbial evolution I think is is very different than what we have here in the typical months, because generally, it is really mutations in the, what you call the functional access so that affect the fitness and then there is competition for some resources. So I don't think clonal interference refers to this negative frequency dependence competition that is specific competition and forms niches. I don't think it does I think not in the traditional way it is model. So I think if you want to actually promote diversity. specific and it's not. I think it with it's not necessarily treated as a, you know, this this access that that that has to do with niche formation and niche formation under under interactions it's really affecting traits that influence the fitness of the microbes and how much access to the resources that they have so it's the orthogonal access to the one that really forms a structure of dissimilarity and the interaction of ecology and evolution that we are talking about here. It's it's difficult because it is the way competition is thought about and you have to relate. I guess to the specific assumptions of competition when people talk loosely about clonal interference. And this is another question by aditia was asking when you are past the diversification pressure. What sets the timescale of the turnover of biodiversity. Does each strain stick around indefinitely, or do they turn over at some rate. Yeah, this is a very good question. So the timescale of turnover is set by many different conditions of the transmission. So as I mentioned, when the, as I mentioned when the trend. So basically, when the transmission rate is high enough in the system which means that the competition. The population size is large and then the competition for hosts is strong. Then the, the, the, the new genes, so the new genes will be more preferred and then these, these kind of genes will stick around in the in the population for very long. If the pop, if the, if the transmission of when the transmission rate is very low, and then the, their new genes cannot be ensured to have to be promoted into and then propagated in the population. A lot of them would be very short lived, but the ones that actually pass through these kind of drift barriers, they can still persist really long in the, in the population so it's very interesting that basically we can partition these new genes into short lived ones and then the very long lived ones that basically could indefinitely be incorporated in the system such as a lot of other immune related genes or these kind of large. These kind of like immune related genes, because they are under balancing selection they could be maintained in the population, much longer than sometimes than the species, the, the, the, the, sometimes even longer than the species themselves. So, would you, would you say that the majority of the diversity is coming from the fact that new genes are entering at a high rate or is it coming from the fact that the successful genes are sticking around for a long time. Yeah, so for the long term evolution, it is because the balancing selection that these genes persist in the system for a long time, but they could be really old.