Related papers: Model of phenotypic evolution in hermaphroditic po…
Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…
Intraspecific trait variation has been increasingly recognized as an important factor in determining species interaction and diversity. Eco-evolutionary models have studied the distribution of trait values within a population that changes…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
A microscopic agent dynamical model for diploid age-structured populations is used to study evolution of polymorphism and sympatric speciation. The underlying ecology is represented by a unimodal distribution of resources of some width.…
How does the interplay between selection, mutation and horizontal gene transfer modify the phenotypic distribution of a bacterial or cell population? While horizontal gene transfer, which corresponds to the exchange of genetic material…
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…
Neutral speciation mechanisms based on isolation by distance and sexual selection, termed topopatric, have recently been shown to describe the observed patterns of abundance distributions and species-area relationships. Previous works have…
The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space where the measure determines the abundance of individual…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…
Building upon kinetic theory approaches for multi-agent systems and generalising them to scenarios where the total mass of the system is not conserved, we develop a modelling framework for phenotype-structured populations that makes it…
A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The…
We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…
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…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to…
We study the asymptotic behavior of stationary solutions to a quantitative genetics model with trait-dependent mortality and sexual reproduction. The infinitesimal model accounts for the mixing of parental phenotypes at birth.Our asymptotic…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary…