Percolation theory suggests some general features in range margins across environmental gradients

TL;DR

This study applies percolation theory to model and analyze the structural features of species range margins across environmental gradients, revealing universal scaling laws and fractal properties relevant for understanding ecological responses to climate change.

Contribution

It introduces a gradient metapopulation model incorporating both broad and fine-scale heterogeneities, demonstrating universal scaling laws and fractal features at range margins.

Findings

The edge of the connected habitat region is a fractal with dimension 7/4.

Scaling laws describe how the width and length of the habitat edge change with environmental gradients.

Percolation theory effectively models range margin structures across diverse ecological scenarios.

Abstract

The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range margins is fragmentation, caused internally by population dynamics or externally by the limited availability of suitable habitat sites. We study both causes, and describe the transition from a connected to a fragmented state across space by means of a gradient metapopulation model. The main features of our approach are the following. 1) Inhomogeneities can occur at two spatial scales: there is a broad-scale gradient, which can be patterned by fine-scale heterogeneities. The latter is implemented by dispersing a variable number of small obstacles over the terrain, which can be penetrable or unpenetrable by the spreading species. 2) We study the occupancy of this terrain in a steady-state on two temporal scales: in snapshots and by long-term averages. The simulations reveal some general scaling laws that are applicable in various environments, independently of the mechanism of fragmentation. The edge of the connected region (the hull) is a fractal with dimension 7/4. Its width and length changes with the gradient according to universal scaling laws, that are characteristic for percolation transitions. The results suggest that percolation theory is a powerful tool for understanding the structure of range margins in a broad variety of real-life scenarios, including those in which the environmental gradient is combined with fine-scale heterogeneity. This provides a new method for comparing the range margins of different species in various geographic regions, and monitoring range shifts under climate change.