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. We identify five types of epidemic profiles arising for different levels of spatial heterogeneity and different costs of adaptation. In particular, we identify the conditions where a generalist pathogen carrying multiple adaptations can outrace a coalition of specialist pathogens. We also show that finite host populations promote the spread of generalist pathogens because demographic stochasticity enhances the extinction of locally maladapted pathogens. But higher mutation rates between genotypes can rescue the coalition of specialists and speed up the spread of epidemics for intermediate levels of spatial heterogeneity. Our work provides a comprehensive analysis of the interplay between migration, local selection, mutation, and genetic drift on the spread and on the evolution of pathogens in heterogeneous environments. This work extends our fundamental understanding of the outcome of the competition between two specialists and a generalist strategy (single- vs. multiadapted pathogens). These results have practical implications for the design of more durable control strategies against multiadapted pathogens in agriculture and in public health.

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.

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. We show that plant populations may escape extinction because of both spatial range and ecological niche shifts. Exact analytical formulas predict that increasing pollen dispersal distance slows the expected spatial range shift and accelerates the ecological niche shift. There is an optimal distance of pollen dispersal, which maximizes the sustainable rate of climate change. These conclusions hold in simulations relaxing several strong assumptions of our analytical model. Our results imply that, for plants with long distance of pollen dispersal, models assuming niche conservatism may not accurately predict their future distribution under climate change.

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 t and the rate ε of mutations. We show that depending on α > 0 , the limit ε → 0 with t = ε - α can lead to population number densities which are either Gaussian-like (when α is small) or Cauchy-like (when α is large).

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. Here we study the influence of virulence evolution on the spatial spread of an epidemic. At the edge of the invasion front, we show that more virulent and transmissible genotypes are expected to win the competition with other pathogens. Behind the front line, however, more prudent exploitation strategies outcompete virulent pathogens. Crucially, even when the presence of the virulent mutant is limited to the edge of the front, the invasion speed can be dramatically altered by pathogen evolution. We support our analysis with individual-based simulations and we discuss the additional effects of demographic stochasticity taking place at the front line on virulence evolution. We confirm that an increase of virulence can occur at the front, but only if the carrying capacity of the invading pathogen is large enough. These results are discussed in the light of recent empirical studies examining virulence evolution at the edge of spreading 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. Thanks to this simpler equation, we can describe rigorously the dynamics of the population. In particular, we provide an explicit estimate of the invasion speed, or extinction speed of the species. Numerical computations show that this simple model provides a good approximation of the original infinitesimal model, and in particular describes quite well the evolution of the species' range.

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.