Mise en place d'une structure génétique spatiale au cours d'une colonisation: modèles mathématiques et cas d'études chez deux espèces forestières (cèdre et hêtre) – ColonSGS

Colonisation and spatial expansion of a plant species is a major phenomenon in ecology, evolutionary biology, population genetics, and biogeography. This phenomenon must also be taken into consideration in management strategies related to spatial expansion of invasive species, species displacement in conjunction with climate change or fragmentation of natural habitats. Extensive empirical and theoretical knowledge is available on the dynamics of colonisation, especially on the persistence of a spreading species, the speed and shape of its colonization front. Reaction-diffusion (R-D) models were largely used to investigate these questions in homogeneous, heterogeneous or fragmented environments as well as in the presence of an Allee effect. Theoretical studies have then extended R-D models to take into consideration the presence of long-distance dispersal (LDD). They proved that LDD had a major impact on the colonisation pattern and made it possible to properly describe the most influential characteristics of the dispersal kernel. In contrast, fewer theoretical studies were devoted to the spatial dynamics of genetic diversity along a colonisation process, despite its importance for population genetics and evolutionary biology. In particular, the consequences of long-distance dispersal and spatial heterogeneity on the spatial pattern of diversity were essentially studied using simulation approaches and less comprehensively than what was done for population dynamic purposes. For example, the effect of the exact shape of the dispersal kernel was not fully investigated: studies on spatial genetic structure during expansion mostly focused on thin-tailed dispersal functions (mixture of two Gaussian, exponential). Further, and although weakly investigated, the spatial structure of diversity is expected to be strongly affected by (i) the fragmentation of the environments into favourable and unfavourable habitats and (ii) the variations of the dispersal function depending on the positions of the individuals relative to the wave front. The originality of the project presented here is to associate 1) a mathematical approach derived from the reaction-diffusion formalism, 2) a pragmatic simulation approach fed by physical models for wind-dispersed seeds and 3) the thorough description of the dynamics and genetics of two colonisation events occurring on Mont-Ventoux since 150 years. The first question tackled will be that of the origin of long-distance dispersers and how mixing of different origins occurs at long distance. First, this question will be considered from the mathematical point of view, using R-D models and integro-difference models. We will focus on the effects of (i) presence/absence of LDD, (ii) heterogeneity/fragmentation of the environment, and (iii) presence/absence of Allee effect. Second we will develop an Eulerian-Lagrangian approach to model wind-dispersed seeds in a heterogeneous environment. We will use this model to evaluate how air flow in the canopy of an expanding tree population generates spatial variations of the dispersal kernel that may affect the mixing of seeds origins at long-distance. Third, we will conduct aerial photograph analyses and experiments using microsatellite markers on a study site on Mont-Ventoux where a cedar colonisation over few kilometres is ongoing since 1860. This will allow quantifying empirically how mixing of origins really occurs at this site and if it affects the spatial pattern of the population. The second question tackled will concern the set-up of the spatial genetic structure (SGS) during the successive dispersal events that generate the colonisation. First, mathematical models (R-D and integro-differences) will be used to focus on the simplified question of the fate of a mutant appearing on a colonisation wave front. Here again, we will theoretically investigate the effects of LDD and heterogeneity of the environment on the possible futures for the mutant. Second, a simulation approach on a grid will be used to investigate this same question in the presence of demographic stochasticity and results will be compared with the deterministic approach. More realistic simulations including the characteristic of tree life-cycles will also be used to investigate more precisely the set-up of a SGS such as those measured from microsatellite data. Third, a landscape genetics approach will be used to study the re-colonisation of beech on the north-face of Mont-Ventoux. We will genotype, position and measure ages of ~1000 adult beech trees in order to retrieve the refugia and colonisation routes explaining the spatial structure of genetic diversity observed today. Finally, we will estimate the SGS for cedar and beech at different distances relative to the colonisation front and for the different cohorts of individuals to understand how SGS evolved with time and space during these two colonisations.