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 the margins due to global change pressures, such as invasions and range shifts, we lack a mathematical theory of spatial sorting to understand these evolutionary patterns. To this end, I present an algebraic theorem of evolution, which we call the sorting theorem, to elucidate the general mechanism of selection at margins. The sorting theorem suggests that at population margins, evolution can ensue by any biological mechanism that yields a statistical association between the number of offspring that individual leaves at the margin and the mean phenotype of those offspring. Thus, the sorting theorem can facilitate axiomatic development and criticism of spatial sorting theory. Its role in guiding research in this context is analogous to that of Price’s theorem in natural selection theory.