KPP transition fronts in a one-dimensional two-patch habitat.

This paper is concerned with the existence of transition fronts for a one-dimensional two patch model with KPP reaction terms. Density and flux conditions are imposed at the interface between the two patches. We first construct a pair of suitable super- and sub solutions by making full use of information of the leading edges of two KPP fronts and gluing them through the interface conditions.

Adaptation in a heterogeneous environment II: to be three or not to be.

We propose a model to describe the adaptation of a phenotypically structured population in a H-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous mathematical analysis of this model. We show that the large-time behaviour of the solution (persistence or extinction) depends on the sign of a principal eigenvalue, [Formula: see text], and we study the dependency of [Formula: see text] with respect to H. This analysis sheds new light on the effect of increasing the number of patches on the persistence of a population, which has implications in agroecology and for understanding zoonoses; in such cases we consider a pathogenic population and the patches correspond to different host species.

Allee effect promotes diversity in traveling waves of colonization.

Most mathematical studies on expanding populations have focused on the rate of range expansion of a population. However, the genetic consequences of population expansion remain an understudied body of theory. Describing an expanding population as a traveling wave solution derived from a classical reaction-diffusion model, we analyze the spatio-temporal evolution of its genetic structure.

Success rate of a biological invasion in terms of the spatial distribution of the founding population.

We analyze the role of the spatial distribution of the initial condition in reaction-diffusion models of biological invasion. Our study shows that, in the presence of an Allee effect, the precise shape of the initial (or founding) population is of critical importance for successful invasion. Results are provided for one-dimensional and two-dimensional models.

Mathematical analysis of the optimal habitat configurations for species persistence.

We study a reaction-diffusion model in a binary environment made of habitat and non-habitat regions. Environmental heterogeneity is expressed through the species intrinsic growth rate coefficient. It was known that, for a fixed habitat abundance, species survival depends on habitat arrangements.

Analysis of the periodically fragmented environment model: I--species persistence.

This paper is concerned with the study of the stationary solutions of the equation [Equation: see text] where the diffusion matrix A and the reaction term f are periodic in x. We prove existence and uniqueness results for the stationary equation and we then analyze the behaviour of the solutions of the evolution equation for large times. These results are expressed by a condition on the sign of the first eigenvalue of the associated linearized problem with periodicity condition.