Metapopulations in multifractal landscapes: on the role of spatial aggregation

Abstract

The use of fractals in ecology is currently pervasive over many areas. However, very few studies have linked fractal properties of landscapes to generating ecological mechanisms and dynamics. In this study I show that lacunarity (a measure of the landscape texture) is a well suited ecologically scaled landscape index that can be explicitly incorporated in metapopulation models such as the classical Levins equation. I show that the average lacunarity of an aggregated landscape is linearly correlated to the habitat that a species with local spatial processed information may perceive. Lacunarity is a computationally feasible index to measure, and is related to the metapopulation capacity of landscapes. A general approach to multifractal landscapes has been conceived, and some analytical results for self-similar landscapes are outlined, including the specific effect of landscape heterogeneity, decoupled from that of contagion by dispersal. Spatially explicit simulations show agreement with the semi-implicit method presented.