Related papers: Adaptive dynamics of nonlocal competition models w…

We study the long-time behaviour of phenotype-structured models describing the evolutionary dynamics of asexual species whose phenotypic fitness landscape is characterised by multiple peaks. First we consider the case where phenotypic…

This paper is devoted to the analysis of the long-time behavior of a phenotypic-structured model where phenotypic changes do not occur. We give a mathematical description of the process in which the best adapted trait is selected in a given…

We study the dynamics of phenotypically structured populations in environments with fluctuations. In particular, using novel arguments from the theories of Hamilton-Jacobi equations with constraints and homogenization, we obtain results…

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 introduce a stochastic individual model for the spatial behavior of an animal population of dispersive and competitive species, considering various kinds of biological effects, such as heterogeneity of environmental conditions, mutual…

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…

Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in…

In this work, we provide an asymptotic analysis of the solutions to an elliptic integro-differential equation. This equation describes the evolutionary equilibria of a phenotypically structured population, subject to selection, mutation,…

We analyze a nonlocal PDE model describing the dynamics of adaptation of a phenotypically structured population, under the effects of mutation and selection, in a changing environment. Previous studies have analyzed the large-time behavior…

We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…

We study macroevolutionary dynamics by extending microevolutionary competition models to long time scales. It has been shown that for a general class of competition models, gradual evolutionary change in continuous phenotypes (evolutionary…

Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…

We study the long time behavior of a parabolic Lotka-Volterra type equation considering a time-periodic growth rate with non-local competition. Such equation describes the dynamics of a phenotypically struc-tured population under the effect…

The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…

Evolutionary and ecosystem dynamics are often treated as different processes --operating at separate timescales-- even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field…

Competition for a limited resource is the hallmark of many complex systems, and often, that resource turns out to be the physical space itself. In this work, we study a novel model designed to elucidate the dynamics and emergence in complex…

Animals use various processes to inform themselves about their environment and make decisions about how to move and form their territory. In some cases, populations inform themselves of competing groups through observations at distances,…

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.…

This paper investigates a reaction-advection-diffusion system modeling interspecific competition between two species over bounded domains. The kinetic terms are assumed to satisfy the Beddington-DeAngelis functional responses. We consider…

We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which…