Related papers: Long time evolutionary dynamics of phenotypically …
The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
In this paper, we study the long-time behaviour of solutions of Cauchy problem for the parabolic $p$-Laplacian equation with variable coefficients. Under mild conditions on the coefficient of the principal part and without upper growth…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
We study the influence of stochastic effects due to finite population size in the evolutionary dynamics of populations interacting in the multi-person Prisoner's Dilemma game. This paper is an extension of the investigation presented in a…
Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank…
We consider an ecology model in which the population is structured by a spatial variable and a phenotypic trait. The model combines a parabolic operator on the spatial variable with a kinetic operator on the trait variable. We prove the…
Classical ecological models predict that large, diverse communities should be unstable, presenting a central challenge to explaining the stable biodiversity seen in nature. We revisit this long-standing problem by extending the generalized…
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…
In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Benam and Lobry established that randomly switching between two environments that are both favorable to the same species may lead to…
We examine to what extent the tempo and mode of environmental fluctuations matter for the growth of structured populations. The models are switching, linear ordinary differential equations $x'(t)=A(\sigma(\omega t))x(t)$ where…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which…
We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra equations, also when…
In recent years non-demographic variability has been shown to greatly affect dynamics of stochastic populations. For example, non-demographic noise in the form of a bursty reproduction process with an a-priori unknown burst size, or…
We study long time behavior of some nonlinear discrete velocity kinetic equations in the one and three dimensions with periodic boundary conditions. We prove the exponential time decay of solutions towards the global equilibrium in the…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
A fundamental problem in the fields of population genetics, evolution, and community ecology, is the fate of a single mutant, or invader, introduced in a finite population of wild types. For a fixed-size community of $N$ individuals, with…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…