Theoretical Population Biology最新文献

The infinitesimal model of quantitative genetics relies on the Central Limit Theorem to stipulate that under additive models of quantitative traits determined by many loci having similar effect size, the difference between an offspring’s genetic trait component and the average of their two parents’ genetic trait components is Normally distributed and independent of the parents’ values. Here, we investigate how the assumption of similar effect sizes affects the model: if, alternatively, the tail of the effect size distribution is polynomial with exponent $\alpha <2$, then a different Central Limit Theorem implies that sums of effects should be well-approximated by a “stable distribution”, for which single large effects are often still important. Empirically, we first find tail exponents between 1 and 2 in effect sizes estimated by genome-wide association studies of many human disease-related traits. We then show that the independence of offspring trait deviations from parental averages in many cases implies the Gaussian aspect of the infinitesimal model, suggesting that non-Gaussian models of trait evolution must explicitly track the underlying genetics, at least for loci of large effect. We also characterize possible limiting trait distributions of the infinitesimal model with infinitely divisible noise distributions, and compare our results to simulations.

Individuals delay natal dispersal for many reasons. There may be no place to disperse to; immediate dispersal or reproduction may be too costly; immediate dispersal may mean that the individual and their relatives miss the benefits of group living. Understanding the factors that lead to the evolution of delayed dispersal is important because delayed dispersal sets the stage for complex social groups and social behavior. Here, we study the evolution of delayed dispersal when the quality of the local environment is improved by greater numbers of individuals ($e.g.$, safety in numbers). We assume that individuals who delay natal dispersal also expect to delay personal reproduction. In addition, we assume that improved environmental quality benefits manifest as changes to fecundity and survival. We are interested in how do the changes in these life-history features affect delayed dispersal. We use a model that ties evolution to population dynamics. We also aim to understand the relationship between levels of delayed dispersal and the probability of establishing as an independent breeder (a population-level feature) in response to changes in life-history details. Our model emphasizes kin selection and considers a sexual organism, which allows us to study parent–offspring conflict over delayed dispersal. At evolutionary equilibrium, fecundity and survival benefits of group size or quality promote higher levels of delayed dispersal over a larger set of life histories with one exception. The exception is for benefits of increased group size or quality reaped by the individuals who delay dispersal. There, the increased benefit does not change the life histories supporting delay dispersal. Next, in contrast to previous predictions, we find that a low probability of establishing in a new location is not always associated with a higher incidence of delayed dispersal. Finally, we find that increased personal benefits of delayed dispersal exacerbate the conflict between parents and their offspring. We discuss our findings in relation to previous theoretical and empirical work, especially work related to cooperative breeding.

Altruism and spite are costly to the actor, making their evolution unlikely without specific mechanisms. Nonetheless, both altruistic and spiteful behaviors are present in individuals, which suggests the existence of an underlying mechanism that drives their evolution. If altruistic individuals are more likely to be recipients of altruism than non-altruistic individuals, then altruism can be favored by natural selection. Similarly, if spiteful individuals are less likely to be recipients of spite than non-spiteful individuals, then spite can be favored by natural selection. Spite is altruism's evil twin, ugly sister of altruism, or a shady relative of altruism. In some mechanisms, such as repeated interactions, if altruism is favored by natural selection, then spite is also favored by natural selection. However, there has been limited investigation into whether both behaviors evolve to the same extent. In this study, we focus on the mechanism by which individuals choose to keep or stop the interaction according to the opponent's behavior. Using the evolutionary game theory, we investigate the evolution of altruism and spite under this mechanism. Our model revealed that the evolution of spite is less likely than the evolution of altruism.

A multi-type neutral Cannings population model with migration and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a multi-type coalescent sharing the exchangeability and consistency property. The proof gains from coalescent theory for single-type Cannings models and from decompositions of transition probabilities into parts concerning reproduction and migration respectively. The following section deals with a different but closely related multi-type Cannings model with mutation and fixed total population size but stochastically varying subpopulation sizes. The latter model is analyzed forward and backward in time with an emphasis on its behavior as the total population size tends to infinity. Forward in time, multi-type limiting branching processes arise for large population size. Its backward structure and related open problems are briefly discussed.

Given a labeled tree topology $t$, consider a population $P$ of $k$ leaves chosen among those of $t$. The clade of $P$ is the minimal subtree of $t$ containing $P$ and its size is given by the number of leaves in the clade. When $t$ is selected under the Yule or uniform distribution among the labeled topologies of size $n$, we study the “clade size” random variable determining closed formulas for its probability mass function, its mean, and its variance. Our calculations show that for large $n$ the clade size tends to be smaller under the uniform model than under the Yule model, with a larger variability in the first scenario for values of $k\ge 5$. We apply our probability formulas to investigate set-theoretic relationships between the clades of two populations in a random tree, determining how likely one clade is contained in or it is equal to the other. Our study relates to earlier calculations for the probability that under the Yule model the clade size of $P$ equals the size of $P$ – that is, the population $P$ forms a monophyletic group – and extends known results for the probability that the minimal (non-trivial) clade containing a random taxon has a given size.

Modern molecular technologies have revolutionized our understanding of bacterial epidemiology, but reported data across studies and different geographic endemic settings remain under-integrated in common theoretical frameworks. Pneumococcus serotype co-colonization, caused by the polymorphic bacteria Streptococcus pneumoniae, has been increasingly investigated and reported in recent years. While the global genomic diversity and serotype distribution of S. pneumoniae have been well-characterized, there is limited information on how co-colonization patterns vary globally, critical for understanding the evolution and transmission dynamics of the bacteria. Gathering a rich dataset of cross-sectional pneumococcal colonization studies in the literature, we quantified patterns of transmission intensity and co-colonization prevalence variation in children populations across 17 geographic locations. Linking these data to an SIS model with cocolonization under the assumption of quasi-neutrality among multiple interacting strains, our analysis reveals strong patterns of negative co-variation between transmission intensity ($R_0$) and susceptibility to co-colonization ($k$). In line with expectations from the stress-gradient-hypothesis in ecology (SGH), pneumococcus serotypes appear to compete more in co-colonization in high-transmission settings and compete less in low-transmission settings, a trade-off which ultimately leads to a conserved ratio of single to co-colonization $\mu =1/(R_0-1)k$. From the mathematical model’s behavior, such conservation suggests preservation of ‘stability-diversity-complexity’ regimes in coexistence of similar co-colonizing strains. We find no major differences in serotype compositions across studies, pointing to adaptation of the same set of serotypes across variable environments as an explanation for their differential interaction in different transmission settings. Our work highlights that the understanding of transmission patterns of Streptococcus pneumoniae from global scale epidemiological data can benefit from simple analytical approaches that account for quasi-neutrality among strains, co-colonization, as well as variable environmental adaptation.

In this paper, we investigate the consequences of dormancy in the ‘rare mutation’ and ‘large population’ regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second ‘small mutations’ limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011).

The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the ‘speed of adaptation’ of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.

Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.

Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright–Fisher diffusion and the Kingman coalescent, where the former describes the stochastic evolution of neutral allele frequencies in a large population forwards in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backwards in time. As well as providing a richer description than either model in isolation, duality often yields equations satisfied by quantities of interest. We employ the so-called Bernoulli factory – a celebrated tool in simulation-based computing – to derive duality relations for broad classes of genetics models. As concrete examples, we present Wright–Fisher diffusions with general drift functions, and Allen–Cahn equations with general, nonlinear forcing terms. The drift and forcing functions can be interpreted as the action of frequency-dependent selection. To our knowledge, this work is the first time a connection has been drawn between Bernoulli factories and duality in models of population genetics.