Spatially explicit summary statistics for historical population genetic inference

1. The integration of population genetics with explicit spatial analyses is crucial to address a range of evolutionary and ecological questions under realistic scenarios. Ignoring space can lead to misleading inferences, yet incorporating spatial realism leads to using complex evolutionary models that necessitate distilling raw genetic data into summary statistics that capture information relevant to the models in question. However, summary statistics derived from traditional population genetic theory overlook the valuable spatial component of genetic variation that is innate in natural systems and can be informative about historical spatio-demographic processes. 2. To overcome this limitation, we introduce and evaluate a new set of spatially explicit summary statistics that can be calculated from a wide range of molecular markers and that take advantage of well-established spatial genetic algorithms to summarize the spatial distribution and autocorrelation of genetic variation. Using spatially explicit demographic simulations of SNP data, we characterize their behaviour under different realistic historical demographic scenarios and assess their relative contribution to accurate model selection and parameter estimation. 3. We demonstrate that under a wide range of parameter values, alternate demographic histories could be best differentiated by supplementing traditional summary statistics with these new spatial statistics. We identify different subset of statistics, including Euclidean distances in spatial-PCA space, Monmonier's identification of genetic breaks and spatial correlograms, that greatly improve discrimination of complex species histories and have sizeable potential to estimate associated parameters, although the added power is likely to be dependent on landscape models and sampling configurations. 4. These results highlight the potential benefits of condensing spatial genetic information into informative summary statistics to substantially improve testing alternative historical demographic models that reflect the complex spatio-temporal dynamics of species evolutionary histories. This study bridges phylogeography and landscape genetics by paving the way for phylogeographers wanting to incorporate spatial models and data as well as landscape geneticists wanting to incorporate history.