Evolution and spread of multiadapted pathogens in a spatially heterogeneous environment.

Pathogen adaptation to multiple selective pressures challenges our ability to control their spread. Here we analyze the evolutionary dynamics of pathogens spreading in a heterogeneous host population where selection varies periodically in space. We study both the transient dynamics taking place at the front of the epidemic and the long-term evolution far behind the front.

Interactions between different predator-prey states: a method for the derivation of the functional and numerical response.

In this paper we introduce a formal method for the derivation of a predator's functional response from a system of fast state transitions of the prey or predator on a time scale during which the total prey and predator densities remain constant. Such derivation permits an explicit interpretation of the structure and parameters of the functional response in terms of individual behaviour. The same method is also used here to derive the corresponding numerical response of the predator as well as of the prey.

Asymptotic profile in selection-mutation equations: Gauss versus Cauchy distributions.

In this paper, we study the asymptotic (large time) behaviour of a selection-mutation-competition model for a population structured with respect to a phenotypic trait when the rate of mutation is very small. We assume that the reproduction is asexual, and that the mutations can be described by a linear integral operator. We are interested in the interplay between the time variable and the rate of mutations.

Pollen dispersal slows geographical range shift and accelerates ecological niche shift under climate change.

Species may survive climate change by migrating to track favorable climates and/or adapting to different climates. Several quantitative genetics models predict that species escaping extinction will change their geographical distribution while keeping the same ecological niche. We introduce pollen dispersal in these models, which affects gene flow but not directly colonization.

Virulence evolution at the front line of spreading epidemics.

Understanding and predicting the spatial spread of emerging pathogens is a major challenge for the public health management of infectious diseases. Theoretical epidemiology shows that the speed of an epidemic is governed by the life-history characteristics of the pathogen and its ability to disperse. Rapid evolution of these traits during the invasion may thus affect the speed of epidemics.

Dynamics of sexual populations structured by a space variable and a phenotypical trait.

We study sexual populations structured by a phenotypic trait and a space variable, in a non-homogeneous environment. Departing from an infinitesimal model, we perform an asymptotic limit to derive the system introduced in Kirkpatrick and Barton (1997). We then perform a further simplification to obtain a simple model.

On selection dynamics for competitive interactions.

In this paper, we are interested in an integro-differential model that describe the evolution of a population structured with respect to a continuous trait. Under some assumption, we are able to find an entropy for the system, and show that some steady solutions are globally stable. The stability conditions we find are coherent with those of Adaptive Dynamics.