Recent range expansions have probably occurred in many species, as they often happen after speciation events, after ice ages, or after the introduction of invasive species. While it has been shown that range expansions lead to patterns of molecular diversity distinct from those of a pure demographic expansion, the fact that many species do live in heterogeneous environments has not been taken into account. We develop here a model of range expansion with a spatial heterogeneity of the environment, which is modeled as a gamma distribution of the carrying capacities of the demes. By allowing temporal variation of these carrying capacities, our model becomes a new metapopulation model linking ecological parameters to molecular diversity. We show by extensive simulations that environmental heterogeneity induces a loss of genetic diversity within demes and increases the degree of population differentiation. We find that metapopulations with low average densities are much more affected by environmental heterogeneity than metapopulations with high average densities, which are relatively insensitive to spatial and temporal variations of the environment. Spatial heterogeneity is shown to have a larger impact on genetic diversity than temporal heterogeneity. Overall, temporal heterogeneity and local extinctions are not found to leave any specific signature on molecular diversity that cannot be produced by spatial heterogeneity.
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