Heritable variation in traits that enhance dispersal rates can accumulate at population margins by spatial sorting. This mechanism of selection differs from natural selection as evolutionary change can ensue even in the absence of differential lifetime reproductive success. Although evidence suggests that populations are rapidly evolving at margins due to global change pressures, such as invasions and range shifts, we lack a mathematical theory of spatial sorting to understand these

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... patterns. To this end, we present an algebraic theorem, or the sorting theorem, to elucidate the nature of selection at margins, which can, in turn, facilitate axiomatic development of spatial sorting theory. The role of the sorting theorem in guiding research in this context is analogous to that of Price's theorem in natural selection theory.