Related papers: Mutation, selection, and ancestry in branching mod…
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is…
For a continuous state branching process with two types of individuals which are subject to selection and density dependent competition, we characterize the joint evolution of population size, type configurations and genealogies as the…
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 an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability $\mu$ of…
Motivated by present activities in (statistical) physics directed towards biological evolution, we review the interplay of three evolutionary forces: mutation, selection, and genetic drift. The review addresses itself to physicists and…
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
McNamara and Dall (2011) identified novel relationships between the abundance of a species in different environments, the temporal properties of environmental change, and selection for or against dispersal. Here, the mathematics underlying…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
We study the response of a quantitative trait to exponential directional selection in a finite haploid population at the genetic and the phenotypic level. We assume an infinite sites model, in which the number of new mutations per…
Which factors govern the evolution of mutation rates and emergence of species? Here, we address this question using a first principles model of life where population dynamics of asexual organisms is coupled to molecular properties and…
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and…
We consider the mutation--selection differential equation with pairwise interaction (or, equivalently, the diploid mutation--selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the…
In this paper we consider two continuous-mass population models as analogues of logistic branching random walks, one is supported on a finite trait space and the other one is supported on an infinite trait space. For the first model with…
We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak…
A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage…
Surnames and nonrecombining alleles are inherited from a single parent in a highly similar way. A simple birth-death model with mutations can accurately describe this process. Exponentially growing and constant populations are investigated,…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite…