Related papers: Finite populations with frequency-dependent select…
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
Kingman's model of selection and mutation studies the limit type value distribution in an asexual population of discrete generations and infinite size undergoing selection and mutation. This paper generalizes the model to analyse the…
For a family of models of evolving population under selection, which can be described by noisy traveling wave equations, the coalescence times along the genealogical tree scale like $\log^\alpha N$, where $N$ is the size of the population,…
Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently it has been introduced into evolutionary game theory. In evolutionary game dynamics, the…
We propose a general framework for the study of the genealogy of neutral discrete-time populations. We remove the standard assumption of exchangeability of offspring distributions appearing in Cannings' models, and replace it by a less…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
We consider a population of N individuals, whose dynamics through time is represented by a biparental Moran model with two types: an advantaged type and a disadvantaged type. The advantage is due to a mutation, transmitted in a Mendelian…
Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus on similar problems in the context of the standard…
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,…
We study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the…
To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…
The goal of this paper is to prove rigorous results for the behavior of genealogies in a one-dimensional long range biased voter model introduced by Hallatschek and Nelson [25]. The first step, which is easily accomplished using results of…
The increasing availability of population-level allele frequency data across one or more related populations necessitates the development of methods that can efficiently estimate population genetics parameters, such as the strength of…
The Moran process, as studied by [Lieberman, E., Hauert, C. and Nowak, M. Evolutionary dynamics on graphs. Nature 433, pp. 312-316 (2005)], is a stochastic process modeling the spread of genetic mutations in populations. In this process,…
The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
Longitudinal molecular data of rapidly evolving viruses and pathogens provide information about disease spread and complement traditional surveillance approaches based on case count data. The coalescent is used to model the genealogy that…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we…