Algebraic theorem of selection by spatial sorting

Abstract

The study of population expansions has produced a new class of directional and non-directional models of evolution that represent spatial sorting and gene surfing, respectively. These expansion models differ from their classical analogs, selection and genetic drift, in one key aspect. Unlike classical models that measure evolutionary change in a closed population, expansion models measure evolution in a moving frame of reference. This raises several fundamental questions, such as what drives evolution in a moving frame of reference, and whether spatial sorting and gene surfing are truly spatial analogs of selection and genetic drift. To answer these questions, we propose an identity, the sorting theorem, that is analogous to Prices theorem and is a general descriptor of evolution in a moving frame of reference. The sorting theorem reveals that evolutionary change in expansion models is driven by heritable variation in parental phenotypes and differential sorting fitness--the number of offspring a parent leaves in a newly colonized patch. Interestingly, this finding implies that spatial sorting, as currently defined, is not a spatial analog of selection. Our work shows that the sorting theorem can play a valuable role in organizing evolutionary thinking and building a unified theory of evolution during population expansion.