Using genetic data to estimate diffusion rates in heterogeneous landscapes

Lionel Roques (1) , E. Walker (1) , Pierre Franck (2) , Samuel Soubeyrand (1) , Etienne Klein (1)

1 BioSP - Biostatistique et Processus Spatiaux
2 PSH - Unité de recherche Plantes et Systèmes de Culture Horticoles

Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to increase the survival of endangered species. In this paper, we propose a mechanistic-statistical method to estimate space-dependent diffusion parameters of spatially-explicit models based on stochastic differential equations, using genetic data. Dividing the total population into subpopulations corresponding to different habitat patches with known allele frequencies, the expected proportions of individuals from each subpopulation at each position is computed by solving a system of reaction-diffusion equations. Modelling the capture and genotyping of the individuals with a statistical approach, we derive a numerically tractable formula for the likelihood function associated with the diffusion parameters. In a simulated environment made of three types of regions, each associated with a different diffusion coefficient, we successfully estimate the diffusion parameters with a maximum-likelihood approach. Although higher genetic differentiation among subpopulations leads to more accurate estimations, once a certain level of differentiation has been reached, the finite size of the genotyped population becomes the limiting factor for accurate estimation.

Mots clés: reaction-diffusion; stochastic differential equation; inference; mechanistic-statistical mode; allele frequencies; genotype measurements; Agroecology; statistical model

Mots clés: Agroécologie; donnée génétique; coefficient de diffusion; modèle statistique

Domaines: Sciences de la Terre

Lionel Roques, E. Walker, Pierre Franck, Samuel Soubeyrand, Etienne Klein. Using genetic data to estimate diffusion rates in heterogeneous landscapes. Journal of Mathematical Biology, 2016, 73 (2), pp.397-422. ⟨10.1007/s00285-015-0954-4⟩. ⟨hal-01512092⟩