On the role played by the carrying capacity and the ancestral population size during a range expansion.

Most species are structured and various population genetics models have been proposed to investigate their history. For mathematical tractability, most of these models make the simplifying assumption of equilibrium. Here we focus on the properties of a nonequilibrium spatial explicit model, range expansions (REs). Despite their abundance, many details of their genetic consequences need yet to be fully investigated. The model we studied is characterized by four main parameters: the effective population size of each deme (N), the migration rate per generation per deme (m), the time of the expansion (Texp ) and the effective size of the deme from which the expansion started (Nanc ). By means of extensive coalescent simulations, we focused on two aspects of range expansions for fixed Nm: (1) the separate influence of N and m and (2) the role of Nanc . We compared our results with an equilibrium stepping stone model and found two main features typical of REs: an excess of rare variants for larger N and a complex interaction between N, Texp and Nanc in shaping the degree of population differentiation (which depends only on Nm in the stepping stone model). Finally, we developed an approximate Bayesian computation approach to jointly estimate N and m and to infer Nanc . When applied to pseudo-observed data sets, we could correctly recover both N and m (but not Nanc ), provided a large number of demes were sampled. These findings highlight how it will be possible to estimate the dispersal rate in nonequilibrium metapopulations by using population genetics approaches.