Ascribing ecological meaning to habitat shape by means of a piecewise regression approach to fractal domains

A fractal dimension (FD) indicates the ability of a set of structures to fill the Euclidean space where it is embedded. For habitat boundaries, FD is bound to a plane, thus 1 <= FD <= 2. FD is low for simple shapes and increases as patches become more irregular. Some authors have found that FD metric delineating area-perimeter relation (APR) is best fitted through piecewise linear curves, where the slope of each line segment is one-half the FD over the corresponding scaling region. The detection of shifts in boundary FD of landscape habitats is a significant issue in ecology, since discontinuities could be an index of a substantial modification of the processes and dynamics that generate and maintain habitats. This work makes use of fractal analysis to examine the relationship between anthropogenic processes and habitat spatial patterns. It proposes two goals (1) suggesting Multivariate Adaptive Regression Splines (MARS(R)) as a fast and effective approach to discover shifts in APR of landscape patches; (2) explaining the substantial existence of such shifts using a set of human-related predictor variables. MARS methodology has been applied to 6 types of habitats within the Baganza stream watershed (Parma, Italy) and the discovered patterns have been correlated with anthropogenic variables that could influence APR. A standardized linear discriminant analysis (DA) has been used to predict FDs from the set of the employed predictors. DA corroborated the existence of breakpoints in APR and explained the contribute of predictor variables in determining the discovered shifts.