How Does Habitat Patch Size Affect Animal Movement? An Experiment With Darkling Beetles

Ecology, Oct, 1999 by Nancy E. McIntyre, John A. Wiens

The angles and distances between successive 5-s locations in the beetle movement pathways were surveyed electronically with a Pentax PTS-[II.sub.05] (Tokyo, Japan) surveying station. Angle and distance data were downloaded into a Corvallis Microtechnology CMT MC-II field microcomputer (Corvallis, Oregon, USA) and were translated into Cartesian coordinates with computer software designed by the Maptech Corporation (Loveland, Colorado, USA). Surveyed movement pathways were described by seven path metrics: (1) the habitat type (grass or sand) where a beetle was located for each 5-s time step, (2) the total number of time steps taken, (3) the number of stops (pauses in successive time intervals without spatial displacement), (4) net linear displacement to quantify the distance covered by a beetle, (5) displacement rate to quantify a beetle's velocity, (6) average movement distance (step length) per 5-s interval, and (7) fractal dimension to quantify path tortuosity (using the dividers protocol; Dicke and Burrough 1988). Fractal geometry was developed for the express purpose of measuring non-Euclidian objects (Mandelbrot 1983). Being neither perfectly straight lines nor completely random walks, movement pathways are non-Euclidian, and fractal geometry therefore provides a useful measure of path tortuosity (Wiens and Milne 1989, Milne 1991, Wiens et al. 1995). The fractal dimension of a movement pathway ranges from 1 to 2, with a value of 1 indicating a straight-line path and a value of 2 indicating a completely random path (Mandelbrot 1983). The fractal dimension was assumed to be independent of scale over the extent of our experimental design (Turchin 1996). In addition to comparing path tortuosity among our treatments, we also compared the fractal dimension of the movement pathways to the fractal dimension of the landscape treatment patterns, using the square perimeter-area formula of Gardner et al. (1987) as applied by Milne (1991), where D = log(area covered by grass patches)/log(perimeter of grass patches/four sides to a square patch). This value ranges between 1 (perfect square) and 2 (highly irregular shape) (Milne 1991). We also performed a regression of pathway [TABULAR DATA FOR TABLE 1 OMITTED] fractal dimension on average nearest neighbor grass-patch distance to determine if patch clustering affected beetle movements (either by attraction, which would be indicated by a positive association, or repulsion, indicated by a negative relationship). Nearest neighbor distances were calculated by measuring the straight-line distances between each grass patch and its five nearest grass-patch neighbors (two nearest neighbors for the 1 x 1 m treatment, as there were only three patches total). These distances were averaged across all grass patches within a treatment to give a single value for each treatment. A best fit regression line was used.

Because animal movement pathways are, by definition, collections of spatially autocorrelated points, we based our statistical analyses of pathway values on the replicate pathways within a treatment rather than on characteristics of individual pathways. A multivariate analysis of covariance (MANCOVA) was used to detect significant differences in movement path metrics with changes in habitat patch size over all treatments, with grass-patch size as a fixed main effect and soil surface temperature and grass-patch perimeter length as covariates. If significant overall effects were found, the model was reduced to a separate analysis of covariance (ANCOVA) for each of the seven pathway variables, with grass-patch size as a fixed main effect. If soil surface temperature and perimeter length were not significant covariates, models were further simplified as simple ANOVAs. Variables with significant ANCOVA or ANOVA models were then subjected to Fisher's protected least significant difference (LSD) comparisons among treatment means (Sokal and Rohlf 1981) to detect significant differences in path metrics among treatments.