Theoretical Population Biology最新文献

Social behavior is divided into four types: altruism, spite, mutualism, and selfishness. The former two are costly to the actor; therefore, from the perspective of natural selection, their existence can be regarded as mysterious. One potential setup which encourages the evolution of altruism and spite is repeated interaction. Players can behave conditionally based on their opponent's previous actions in the repeated interaction. On the one hand, the retaliatory strategy (who behaves altruistically when their opponent behaved altruistically and behaves non-altruistically when the opponent player behaved non-altruistically) is likely to evolve when players choose altruistic or selfish behavior in each round. On the other hand, the anti-retaliatory strategy (who is spiteful when the opponent was not spiteful and is not spiteful when the opponent player was spiteful) is likely to evolve when players opt for spiteful or mutualistic behavior in each round. These successful conditional behaviors can be favored by natural selection. Here, we notice that information on opponent players’ actions is not always available. When there is no such information, players cannot determine their behavior according to their opponent's action. By investigating the case of altruism, a previous study (Kurokawa, 2017, Mathematical Biosciences, 286, 94–103) found that persistent altruistic strategies, which choose the same action as the own previous action, are favored by natural selection. How, then, should a spiteful conditional strategy behave when the player does not know what their opponent did? By studying the repeated game, we find that persistent spiteful strategies, which choose the same action as the own previous action, are favored by natural selection. Altruism and spite differ concerning whether retaliatory or anti-retaliatory strategies are favored by natural selection; however, they are identical concerning whether persistent strategies are favored by natural selection.

New automated and high-throughput methods allow the manipulation and selection of numerous bacterial populations. In this manuscript we are interested in the neutral diversity patterns that emerge from such a setup in which many bacterial populations are grown in parallel serial transfers, in some cases with population-wide extinction and splitting events. We model bacterial growth by a birth–death process and use the theory of coalescent point processes. We show that there is a dilution factor that optimises the expected amount of neutral diversity for a given number of cycles, and study the power law behaviour of the mutation frequency spectrum for different experimental regimes. We also explore how neutral variation diverges between two recently split populations by establishing a new formula for the expected number of shared and private mutations. Finally, we show the interest of such a setup to select a phenotype of interest that requires multiple mutations.

Understanding the conditions that promote the evolution of migration is important in ecology and evolution. When environments are fixed and there is one most favorable site, migration to other sites lowers overall growth rate and is not favored. Here we ask, can environmental variability favor migration when there is one best site on average? Previous work suggests that the answer is yes, but a general and precise answer remained elusive. Here we establish new, rigorous inequalities to show (and use simulations to illustrate) how stochastic growth rate can increase with migration when fitness (dis)advantages fluctuate over time across sites. The effect of migration between sites on the overall stochastic growth rate depends on the difference in expected growth rates and the variance of the fluctuating difference in growth rates. When fluctuations (variance) are large, a population can benefit from bursts of higher growth in sites that are worse on average. Such bursts become more probable as the between-site variance increases. Our results apply to many ($\ge$ 2) sites, and reveal an interplay between the length of paths between sites, the average differences in site-specific growth rates, and the size of fluctuations. Our findings have implications for evolutionary biology as they provide conditions for departure from the reduction principle, and for ecological dynamics: even when there are superior sites in a sea of poor habitats, variability and habitat quality across space determine the importance of migration.

We study the response of a quantitative trait to exponential directional selection in a finite haploid population, both at the genetic and the phenotypic level. We assume an infinite sites model, in which the number of new mutations per generation in the population follows a Poisson distribution (with mean $\Theta$) and each mutation occurs at a new, previously monomorphic site. Mutation effects are beneficial and drawn from a distribution. Sites are unlinked and contribute additively to the trait. Assuming that selection is stronger than random genetic drift, we model the initial phase of the dynamics by a supercritical Galton–Watson process. This enables us to obtain time-dependent results. We show that the copy-number distribution of the mutant in generation $n$, conditioned on non-extinction until $n$, is described accurately by the deterministic increase from an initial distribution with mean 1. This distribution is related to the absolutely continuous part $W^{+}$ of the random variable, typically denoted $W$, that characterizes the stochasticity accumulating during the mutant’s sweep. A suitable transformation yields the approximate dynamics of the mutant frequency distribution in a Wright–Fisher population of size $N$. Our expression provides a very accurate approximation except when mutant frequencies are close to 1. On this basis, we derive explicitly the (approximate) time dependence of the expected mean and variance of the trait and of the expected number of segregating sites. Unexpectedly, we obtain highly accurate approximations for all times, even for the quasi-stationary phase when the expected per-generation response and the trait variance have equilibrated. The latter refine classical results. In addition, we find that $\Theta$ is the main determinant of the pattern of adaptation at the genetic level, i.e., whether the initial allele-frequency dynamics are best described by sweep-like patterns at few loci or small allele-frequency shifts at many. The number of segregating sites is an appropriate indicator for these patterns. The selection strength determines primarily the rate of adaptation. The accuracy of our results is tested by comprehensive simulations in a Wright–Fisher framework. We argue that our results apply to more complex forms of directional selection.

The introduction of the spatial Lambda-Fleming–Viot model ($\Lambda$V) in population genetics was mainly driven by the pioneering work of Alison Etheridge, in collaboration with Nick Barton and Amandine Véber about ten years ago (Barton et al., 2010; Barton et al., 2013). The $\Lambda$V model provides a sound mathematical framework for describing the evolution of a population of related individuals along a spatial continuum. It alleviates the “pain in the torus” issue with Wright and Malécot’s isolation by distance model and is sampling consistent, making it a tool of choice for statistical inference. Yet, little is known about the potential connections between the $\Lambda$V and other stochastic processes generating trees and the spatial coordinates along the corresponding lineages. This work focuses on a version of the $\Lambda$V whereby lineages move rapidly over small distances. Using simulations, we show that the induced $\Lambda$V tree-generating process is well approximated by a birth–death model. Our results also indicate that Brownian motions modelling the movements of lines of descent along birth–death trees do not generally provide a good approximation of the $\Lambda$V due to habitat boundaries effects that play an increasingly important role in the long run. Accounting for habitat boundaries through reflected Brownian motions considerably increases the similarity to the $\Lambda$V model however. Finally, we describe efficient algorithms for fast simulation of the backward and forward in time versions of the $\Lambda$V model.

We consider the Moran model of population genetics with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the distant past, far beyond the most recent common ancestor of the population (thus connecting population genetics to phylogeny), and analyse the mutation process along this line.

To this end, we use the pruned lookdown ancestral selection graph (Lenz et al., 2015), which consists of a set of potential ancestors of the sampled individual at any given time. Relative to the neutral case (that is, without selection), we obtain a general bias towards the beneficial type, an increase in the beneficial mutation rate, and a decrease in the deleterious mutation rate. This sheds new light on previous analytical results. We discuss our findings in the light of a well-known observation at the interface of phylogeny and population genetics, namely, the difference in the mutation rates (or, more precisely, mutation fluxes) estimated via phylogenetic methods relative to those observed in pedigree studies.

The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary – but fixed – spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings $C={\left(C_t\right)}_{t=0}^{\infty }$ from a finite set $G$ to itself. The set $G$ represents the “sites” (in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, $C_t:G\to G$, maps each site $g\in G$ to the site containing $g$’s ancestor, $t$ time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio $r$, we find that measures of genetic dissimilarity, among any set of sites, are scaled by $4r(1-r)$ relative to the even sex ratio case.

In Athreya et al. (2021), models from population genetics were used to define stochastic dynamics in the space of graphons arising as continuum limits of dense graphs. In the present paper we exhibit an example of a simple neutral population genetics model for which this dynamics is a Markovian diffusion that can be characterized as the solution of a martingale problem. In particular, we consider a Markov chain in the space of finite graphs that resembles a Moran model with resampling and mutation. We encode the finite graphs as graphemes, which can be represented as a triple consisting of a vertex set (or more generally, a topological space), an adjacency matrix, and a sampling (Borel) measure. We equip the space of graphons with convergence of sample subgraph densities and show that the grapheme-valued Markov chain converges to a grapheme-valued diffusion as the number of vertices goes to infinity. We show that the grapheme-valued diffusion has a stationary distribution that is linked to the Griffiths–Engen–McCloskey (GEM) distribution. In a companion paper (Greven et al. 2023), we build up a general theory for obtaining grapheme-valued diffusions via genealogies of models in population genetics.

Sexual selection plays a crucial role in modern evolutionary theory, offering valuable insight into evolutionary patterns and species diversity. Recently, a comprehensive definition of sexual selection has been proposed, defining it as any selection that arises from fitness differences associated with nonrandom success in the competition for access to gametes for fertilization. Previous research on discrete traits demonstrated that non-random mating can be effectively quantified using Jeffreys (or symmetrized Kullback-Leibler) divergence, capturing information acquired through mating influenced by mutual mating propensities instead of random occurrences. This novel theoretical framework allows for detecting and assessing the strength of sexual selection and assortative mating.

In this study, we aim to achieve two primary objectives. Firstly, we demonstrate the seamless alignment of the previous theoretical development, rooted in information theory and mutual mating propensity, with the aforementioned definition of sexual selection. Secondly, we extend the theory to encompass quantitative traits. Our findings reveal that sexual selection and assortative mating can be quantified effectively for quantitative traits by measuring the information gain relative to the random mating pattern. The connection of the information indices of sexual selection with the classical measures of sexual selection is established.

Additionally, if mating traits are normally distributed, the measure capturing the underlying information of assortative mating is a function of the square of the correlation coefficient, taking values within the non-negative real number set [0, +∞).

It is worth noting that the same divergence measure captures information acquired through mating for both discrete and quantitative traits. This is interesting as it provides a common context and can help simplify the study of sexual selection patterns.