Reasoning in machine vision by learning fast and slow thinking.

In spatially structured populations, migration over generations shapes genetic variation and often leads to isolation-by-distance—a phenomenon in which geographically proximal individuals are more genetically similar than those farther apart. Although widespread across species and ecosystems, this phenomenon can be complex due to spatial heterogeneity in gene flow, which causes the relationship between genetic distance and geographic distance to vary across the landscape. Many methods have been developed to reveal spatial heterogeneity in isolation-by-distance. Of particular interest here are the methods EEMS and FEEMS, which model a population as a large network of connected demes at migration-drift equilibrium and infer symmetric migration rates between demes. These methods produce visual maps of regions of high/low effective migration rates, offering insights into spatial genetic variation. In modeling spatial heterogeneity in isolation-by-distance, as in other areas of population genetics, a coalescent-based perspective is incredibly helpful. In particular, expected pairwise coalescent times can be used to calculate the expected values of basic summaries, such as F, as well as to fit models of population structure, as in EEMS and related approaches. For a metapopulation composed of several subpopulations or ‘demes’, the structured coalescent provides a natural framework for the computation of expected pairwise coalescence times based on backward migration and coalescence rates.