Scaling Laws in the Fine-Scale Structure of Range Margins

Abstract

Margins of the geographic distributions of species are important regions in terms of ecological and evolutionary processes, including the species’ response to climate change. This paper reviews some spatially explicit metapopulation models of range margins across environmental gradients (e.g., across latitudes or altitudes). These models share some robust results, which allow for generalizations within a broad variety of species and environments: (1) sharp edges can emerge even across relatively smooth environmental gradients; (2) intraspecific competition combined with dispersal limitation is a sufficient condition for the sharpening; (3) at the margin, the “mainland” of continuous occurrence splits into “islands”. Computer simulations pointed out some characteristic scaling laws in the size distribution of the islands, and in the structure of the hull of the mainland. The hull is a fractal with a dimension 7/4. Its width and length scale with the gradient according to characteristic scaling laws (with exponents 3/7 and 4/7, respectively). These general features follow from a second-order phase transition from a connected to a fragmented state. The results contribute to understanding the origin of vegetation zones and the spatial pattern of ecotones.