Stochastic and deterministic models for age-structured populations with genetically variable traits

Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in continuous time of a population with (continuous) age and trait structures. The individuals reproduce asexually, age, interact and die. The 'trait' is an individual heritable property (d-dimensional vector) that may influence birth and death rates and interactions between individuals, and vary by mutation. In a large population limit, the random process converges to the solution of a Gurtin-McCamy type PDE. We show that the random model has a long time behavior that differs from its deterministic limit. However, the results on the limiting PDE and large deviation techniques \textit{\`a la} Freidlin-Wentzell provide estimates of the extinction time and a better understanding of the long time behavior of the stochastic process. This has applications to the theory of adaptive dynamics used in evolutionary biology. We present simulations for two biological problems involving life-history trait evolution when body size is plastic and individual growth is taken into account.Comment: This work is a proceeding of the CANUM 2008 conferenc

Spatial eco-evolutionary dynamics along environmental gradients: multi-stability and cluster dynamics

International audienceHow the interplay of local adaptation and dispersal determines species appearance, distribution and range dynamics is still incompletely understood. Here we combine individual-based simulations and mathematical analysis of large-population approximation models to advance the analysis of spatial spread and phenotypic diversification of a single-species population along a one-dimensional resource gradient. Local competition shapes selection on heritable variation in the individual ecological trait (niche position) and the evolutionary response feeds back on the local ecological state of the population (abundance). Key parameters of spatial spread and phenotypic diversification are the individual dispersal rate, the size of the spatial competition neighborhood, and the phenotype mutational variance. From a focal location the population spreads by forming clusters in space and/or trait, or by spreading along a continuous cline in both space and trait. The conditions for clustering are broader than previously known. The spacing of clusters is determined by the spatial scale of competition. When the space-trait domain is bounded, multi-stability occurs, whereby small initial differences can lead to alternative spatial and trait distributions. The transient dynamics involve adaptational lags which cause a slow-down in cluster formation and population range expansion

The evolution of dispersal under demographic stochasticity.

abstract: Temporal and spatial variations of the environment are important factors favoring the evolution of dispersal. With few exceptions, these variations have been considered to be exclusively fluctuations of habitat quality. However, since the presence of conspecifics forms part of an individual's environment, demographic stochasticity may be a component of this variability as well, in particular when local populations are small. To study this effect, we analyzed the evolution of juvenile dispersal in a metapopulation model in which habitat quality is constant in space and time but occupancy fluctuates because of demographic stochasticity. Our analysis extends previous studies in that it includes competition of resources and competition for space. Also, juvenile dispersal is not given by a fixed probability but is made conditional on the presence of free territories in a patch, whereas individuals born in full patches will always disperse. Using a combination of analytical and numerical approaches, we show that demographic stochasticity in itself may provide enough variability to favor dispersal even from patches that are not fully occupied. However, there is no simple relationship between the evolution of dispersal and various indicators of demographic stochasticity. Selected dispersal depends on all aspects of the life-history profile, including kin selection

Reproductive Flexibility: Genetic Variation, Genetic Costs and Long-Term Evolution in a Collembola

In a variable yet predictable world, organisms may use environmental cues to make adaptive adjustments to their phenotype. Such phenotypic flexibility is expected commonly to evolve in life history traits, which are closely tied to Darwinian fitness. Yet adaptive life history flexibility remains poorly documented. Here we introduce the collembolan Folsomia candida, a soil-dweller, parthenogenetic (all-female) microarthropod, as a model organism to study the phenotypic expression, genetic variation, fitness consequences and long-term evolution of life history flexibility. We demonstrate that collembola have a remarkable adaptive ability for adjusting their reproductive phenotype: when transferred from harsh to good conditions (in terms of food ration and crowding), a mother can fine-tune the number and the size of her eggs from one clutch to the next. The comparative analysis of eleven clonal populations of worldwide origins reveals (i) genetic variation in mean egg size under both good and bad conditions; (ii) no genetic variation in egg size flexibility, consistent with convergent evolution to a common physiological limit; (iii) genetic variation of both mean reproductive investment and reproductive investment flexibility, associated with a reversal of the genetic correlation between egg size and clutch size between environmental conditions ; (iv) a negative genetic correlation between reproductive investment flexibility and adult lifespan. Phylogenetic reconstruction shows that two life history strategies, called HIFLEX and LOFLEX, evolved early in evolutionary history. HIFLEX includes six of our 11 clones, and is characterized by large mean egg size and reproductive investment, high reproductive investment flexibility, and low adult survival. LOFLEX (the other five clones) has small mean egg size and low reproductive investment, low reproductive investment flexibility, and high adult survival. The divergence of HIFLEX and LOFLEX could represent different adaptations to environments differing in mean quality and variability, or indicate that a genetic polymorphism of reproductive investment reaction norms has evolved under a physiological tradeoff between reproductive investment flexibility and adult lifespan

Structure spatiale et viabilité des petites populations

Ferrière Régis. Structure spatiale et viabilité des petites populations . In: Revue d'Écologie. Supplément n°7, 2000. p. 135