Home range: A fractal approach

Abstract

Most current methods for describing animal home range assume that it may be represented as a Euclidean type shape such as a bell shaped curve or a closed polygon. Landscape ecology has increasingly shown that ecological objects are more often highly fragmented and irregular. A fractal approach to description of animal home range was thus developed. For each point where the animal was observed, a circle centered on this point was first laid down to represent the area searched for prey by the animal during a short time interval. In this way the behavior of the animal and differences between species can be represented. Next, a fine grid is laid over the map and the height of each grid square computed by the number of circles that overlap that square. Then, the fractal dimension of the resultant 3-D surface is calculated at several scales. From an analysis of data from a hawk, the existence of perching behavior can be inferred, as well as the observation that at coarse scales the hawk behavior is self-similar and resembles a random walk. The home range thus analyzed in no way resembles a closed figure such as a polygon because it is highly fragmented. Further analysis showed that the fractal measures are relatively insensitive to sample size and to measurement error. Code is included for performing the analyses.

Cross‐Scale Morphology, Geometry, and Dynamics of Ecosystems

“…Mandelbrot ( 1982) has formalized the description of such textural attributes using fractal geometry, and the concept has begun to be applied in ecology (Burrough 1981, Kent and Wong 1982, Bradbury et al 1984, Frontier 1986, Krummel eta!. 1987, Milne 1988, 1991, Wiens and Milne 1989, Loehle 1990). One of Mandelbrot's more intuitively revealing examples considers the length of a coastline as measured by animals with various step lengths.…”

Movements of Marine Fish and Decapod Crustaceans: Process, Theory and Application

“…In contrast to most statistical models, fractal analysis is relatively insensitive to sample size, measurement error and to measurement scale (Loehle, 1990). The fractal dimension (D) has increasingly been applied to studies of movement including home range movements (e.g.…”

“…Dicke and Burrough, 1988;Wiens and Milne, 1989;Crist et al, 1992). Loehle (1990) calculated D for both the path taken by an animal (measure of tortuosity) and for the pattern of the patches used by the animal. The technique involved building a 3-D surface of spatial activity over a mapped area and calculating the fractal dimension of the surface at multiple scales.…”

Range structure, microhabitat use, and activity patterns of the saxicolous lizard Tropidurus torquatus (Tropiduridae) on a rock outcrop in Minas Gerais, Brazil

“…In a broader ecological context, home range, which is the space that individuals use to carry out their life cycles (Rose 1982), can reveal information about the spatial ecology, resource holding power, and social mating systems operating in a group (Brown & Orians 1970, Loehle 1990. Indeed, animals are non-randomly distributed in space (Hodder et al 1998), and some studies have shown that they respond to diversity in microhabitat resources by adopting selection strategies to increase their survivorship and opportunities for successful mating (Davies 1991, Lott 1991.…”