Demographic inference under a spatially continuous coalescent model

In contrast with the classical population genetics theory that models population structure as discrete panmictic units connected by migration, many populations exhibit heterogeneous spatial gradients in population connectivity across semi-continuous habitats. The historical dynamics of such spatially structured populations can be captured by a spatially explicit coalescent model recently proposed by Etheridge (2008) and Barton et al. (2010a, 2010b) and whereby allelic lineages are distributed in a two-dimensional spatial continuum and move within this continuum based on extinction and coalescent events. Though theoretically rigorous, this model, which we here refer to as the continuum model, has not yet been implemented for demographic inference. To this end, here we introduce and demonstrate a statistical pipeline that couples the coalescent simulator of Kelleher et al. (2014) that simulates genealogies under the continuum model, with an approximate Bayesian computation (ABC) framework for parameter estimation of neighborhood size (that is, the number of locally breeding individuals) and dispersal ability (that is, the distance an offspring can travel within a generation). Using empirically informed simulations and simulation-based ABC cross-validation, we first show that neighborhood size can be accurately estimated. We then apply our pipeline to the South African endemic shrub species Berkheya cuneata to use the resulting estimates of dispersal ability and neighborhood size to infer the average population density of the species. More generally, we show that spatially explicit coalescent models can be successfully integrated into model-based demographic inference.