Continuous response functions for quantifying the strength of edge effects

1. Ecological boundaries are a dominant feature of human-modified landscapes and have been the subject of numerous empirical studies. Robust statistical methods for determining the strength of edge effects are a vital requirement for the effective management of species that are negatively affected by habitat boundaries in heavily fragmented landscapes, but development of such methods has been slow. 2. We define edge effects as being composed of two complementary, and statistically definable, components: magnitude (the degree of difference in response values between patch and matrix interiors) and extent (the distance over which the difference in response values can be detected). 3. We present a statistical approach to rigorously delineate edge-effect magnitude and extent. Our approach adapts a form of the general logistic model to describe continuous response functions for any biotic or abiotic variable across ecological boundaries from the landscape matrix into focal patch habitats. The model describes sigmoid and unimodal response functions that have been both theoretically predicted and empirically demonstrated. We use the second derivatives of the functions as an objective means to calculate the magnitude and extent of edge effects, and present a bootstrap technique for calculating confidence intervals around these values. 4. Synthesis and applications. Our results show clearly that edge-effect magnitude and extent are not necessarily correlated, and therefore provide quantitatively different, and complementary, information about the strength of edge effects. Both effect magnitude and extent can be easily used for cross-study comparisons, either by directly comparing the absolute values of response variables in the patch and matrix, or by converting those values to a percentage change. Furthermore, this method provides a management tool for more accurately predicting the presence, spatial location and utilization of core habitat by species in fragmented landscapes.