Related papers: On selection dynamics for a nonlocal phenotype-str…
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…
The well-posedness of a non-local advection-selection-mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such…
We study the singular limit problem for nonlocal conservation laws in which the sign of the initial datum is unrestricted and the velocity of the conservation law depends on a nonlocal approximation of the absolute value of the density. We…
The rates at which individuals memorize and forget environmental information strongly influence their movement paths and long-term space use. To understand how these cognitive time scales shape population-level patterns, we propose and…
We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and…
Phenotypic evolution implies sequential fixations of new genomic sequences. The speed at which these mutations fixate depends, in part, on the relative fitness (selection coefficient) of the mutant vs. the ancestor. Using a simple…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
In this paper, we study an integro-differential equation which describes the evolutionary dynamics of a population structured by a phenotypic trait. This population undergoes asexual reproduction, competition, selection, and mutation. We…
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact…
We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents : we assume that each individual…
We study the evolution of asexual microorganisms with small mutation rate in fluctuating environments, and develop techniques that allow us to expand the formal solution of the evolution equations to first order in the mutation rate. Our…
Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To understand better this impact, we propose a mathematical model…
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…
This paper is concerned with an analysis of the dynamics of a non-autonomous, single population age based growth model with harvesting formulation. First, we derive sufficient conditions for permanence and positive invariance. Then, by…
The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic,…
We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to…
We study an equation structured by age and a phenotypic trait describing the growth process of a population subject to aging, competition between individuals, and mutations. This leads to a renewal equation which occurs in many evolutionary…
We consider a periodic extension of the classical Kingman non-linear model (Kingman, 1978) for the balance between selection and mutation in a large population. In the original model, the fitness distribution of the population is modeled by…
We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation…
In this paper we study a nonlinear size-structured population model with distributed delay in the recruitment. The delayed problem is reduced into an abstract initial value problem of an ordinary differential equation in the Banach space by…