Related papers: Critical population and error threshold on the sha…
We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of…
We construct a constant size population model allowing for general selective interactions and extreme reproductive events. It generalizes the idea of (Krone and Neuhauser 1997) who represented the selection by allowing individuals to sample…
Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way…
This paper is based on the complete classification of evolutionary scenarios for the Moran process with two strategies given by Taylor et al. (B. Math. Biol. 66(6): 1621--1644, 2004). Their classification is based on whether each strategy…
Random Fisher matrices arise naturally in multivariate statistical analysis and understanding the properties of its eigenvalues is of primary importance for many hypothesis testing problems like testing the equality between two multivariate…
We consider an interacting particle process on a graph which, from a macroscopic point of view, looks like $\Z^d$ and, at a microscopic level, is a complete graph of degree $N$ (called a patch). There are two birth rates: an inter-patch one…
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…
A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection…
The Waxman-Peck theory of the population genetics is discussed in regard of soil bacteria. Each bacterium is understood as a carrier of a phenotypic parameter p. The central aim is the calculation of the probability density with respect to…
We study general properties of the leading eigenvalue $\overline{w}(q)$ of Eigen's evolutionary matrices depending on the probability $q$ of faithful reproduction. This is a linear algebra problem that has various applications in…
We study a population model of fixed size undergoing strong selection where individuals accumulate beneficial mutations, namely the Moran model with selection. In a specific setting with strong selection, Schweinsberg showed that the…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
This is an introductory review of deterministic mutation-selection models for asexual populations (i.e., quasispecies theory) and related topics. First, the basic concepts of fitness, mutations, and sequence space are introduced. Different…
Threshold values in population dynamics can be formulated as spectral bounds of matrices, determining the dichotomy of population persistence and extinction. For a square matrix $\mu A + Q$, where $A$ is a quasi-positive matrix describing…
The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations…
Quasispecies theory provides the conceptual and theoretical bases for describing the dynamics of biological information of replicators subject to large mutation rates. This theory, initially conceived within the framework of prebiotic…
This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance).…
We show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold,…
We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse…
The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of…