Complex edge effect fields as additive processes in patches of ecological systems

The edge effect is one of the main phenomena studied by landscape ecology, since it plays a decisive role in determining the structure and dynamics of ecological patches. Most conservation issues involving spatial considerations (design of reserves, land use planning, etc.) require—implicitly or explicitly—an analysis of the edge effects under operation and of their consequences. These are classically analyzed through empirical measurements of linear gradients referenced to the patch border, which yield models of edge effects that: (i) wrongly assume a simple spatial relationship to a single point of the border (the nearest one), (ii) provide flawed predictions on the effect fields generated in ecological patches. Malcolm (1994) has recently addressed these problems by considering an alternative approach that formally integrates the edge effect of every point along a patch border (‘point edge effect’), to generate edge effect fields. In this paper, we deepen the analysis of this concept of addition of multiple point edge effects to generate total effect fields, revealing some important restrictions of Malcolmʹs method. These restrictions are: (i) linear point edge effects, and (ii) homogeneity of the point edge effect along the patch border. Here we carry out an extended application of this method to patch borders (homogeneous or heterogeneous in their point edge effects) of any geometry and to point edge effects of any kind, no matter how irregular or complex these might be. We provide a general numerical solution for the calculation of edge effect fields by means of a topological parameterization, which has been implemented in a program that can be easily run in MATHEMATICA software. We further show how patch shape and size can interfere with the point edge effect, giving rise to complex effect fields within the patches, which cannot be explained by edge effect penetration alone.