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

Abstract

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 (T exp ) and the effective size of the deme from which the expansion started (N anc ). 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 N anc . 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, T exp and N anc 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 N anc . When applied to pseudo-observed data sets, we could correctly recover both N and m (but not N anc ), 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.

Coalescent times, life history traits and conservation concerns: an example from four shark species from the Indo-Pacific

“…The resulting gene genealogies were poorly affected by the recent drop in connectivity, with both the normalized SFS and the inferredNe dynamic following the same trajectory of the corresponding scenario with the same long-term Nm and Tcol (Figures 7, 8, S5, S6, S7, S8, S9 and S10). We noticed the drop in N (Figure 8, S6, S9 and S10) had stronger influence than the drop in m(Figure 7, S5, S7 and S8), consistent with previous finding showing that the distribution of coalescent events depends not only by the Nmcompound parameter but also by their individuals values (Mona, 2017). These results imply that the simulated change in connectivity is too recent to significantly alter the pattern of coalescent events during the scattering phase and that a recent drop can be hardly detected on the basis of the SFS only.…”

“…This is the scattering phase described in the seminal works of (Wakeley, 1998(Wakeley, , 1999. Thescattering phase was considered instantaneous for mathematical tractability, with its outcome dependent on Nm only, but later works could disentangle the effect of N and m on the shape of the gene genealogy (Mona, 2017). The collecting phase starts when the lineages which did not coalesce have migrated to other demes of the array: they will then coalesce according to a Kingman process with a rate scaled by Nm and the number of demes of the array (Wakeley, 1999).…”

Coalescence times, life history traits and conservation concerns: an example from four coastal shark species from the Indo-Pacific

“…This is the scattering phase described in the seminal works of (Wakeley, 1998(Wakeley, , 1999. The scattering phase was considered instantaneous for mathematical tractability, with its outcome dependent on Nm only, but later works could disentangle the effect of N DEME and m on the shape of the gene genealogy (Mona, 2017). The collecting phase starts when the lineages which did not coalesce have migrated to other demes of the array: they will then coalesce according to a Kingman process with a rate scaled by Nm and the number of demes d of the array (Wakeley, 1999) (Figure 7).…”

Demographic inferences after a range expansion can be biased: the test case of the blacktip reef shark (Carcharhinus melanopterus)

“…Range expansions (REs) have likely occurred several times throughout the evolutionary history of many species, both as a consequence of environmental changes and as instances of invasion processes. While there is a growing interest in the genetic consequences of REs (Excoffier et al 2009;Mona 2017;Mona et al 2014), few empirical studies have explored REs quantitatively (but see Barbujani et al 1995;Francois et al 2008;Gaggiotti et al 2009;Hamilton et al 2005;Neuenschwander et al 2008;Potter et al 2016;Ray et al 2005;Schneider et al 2010). Rather, empirical population geneticists frequently employ simplistic population models, without concern that they may yield misleading inferences.…”

“…While considerable effort has been devoted to developing methods to identify the origin of a RE (He et al 2017;Peter and Slatkin 2013;Ramachandran et al 2005), estimating demographic parameters in the constituent demes remains challenging due to a lack of available analytical procedures. Comprehensive simulations coupled with approximate Bayesian computation can offer solutions (Mona 2017;Neuenschwander et al 2008), but they still require detailed knowledge of the ecology and the distribution of the target species, which is usually unknown.…”