Using gridCoal to assess whether standard population genetic theory holds in the presence of spatio-temporal heterogeneity in population size

Spatially explicit population genetic models have long been developed, yet have rarely been used to test hypotheses about the spatial distribution of genetic diversity or the genetic divergence between populations. Here, we use spatially explicit coalescence simulations to explore the properties of the island and the two-dimensional stepping stone models under a wide range of scenarios with spatio-temporal variation in deme size. We avoid the simulation of genetic data, using the fact that under the studied models, summary statistics of genetic diversity and divergence can be approximated from coalescence times. We perform the simulations using gridCoal, a flexible spatial wrapper for the software msprime (Kelleher et al., 2016, Theoretical Population Biology, 95, 13) developed herein. In gridCoal, deme sizes can change arbitrarily across space and time, as well as migration rates between individual demes. We identify different factors that can cause a deviation from theoretical expectations, such as the simulation time in comparison to the effective deme size and the spatio-temporal autocorrelation across the grid. Our results highlight that FST, a measure of the strength of population structure, principally depends on recent demography, which makes it robust to temporal variation in deme size. In contrast, the amount of genetic diversity is dependent on the distant past when Ne is large, therefore longer run times are needed to estimate Ne than FST. Finally, we illustrate the use of gridCoal on a real-world example, the range expansion of silver fir (Abies alba Mill.) since the last glacial maximum, using different degrees of spatio-temporal variation in deme size.