Spatial and temporal scaling of population density and animal movement: A power law approach

Many ecological patterns are sensitive to spatial and temporal scale, but no general protocol has emerged for dealing with scale-dependence. We suggest that power laws, regularly used in the study of body size, can be applied to many such features. We used these techniques to describe two scale-sensitive aspects of caribou (Rangifer tarandus): population densities of North American herds when measured at varying spatial extents, and speeds of radiotracked individuals when observed at varying temporal resolutions. Log-log regression was applied, based on the power formula, Y= cX z. Non-isometric relationships existed for abundance versus area of the population range, but the pattern differed between groups. For sedentary caribou, animal numbers increased more slowly than spatial extent (z = 0.503). For migratory populations, this relationship was hyper-allometric (z > 1), and densities were generally lower for continental herds compared to insular Newfoundland herds living without wolves (Canis lupus). We surmise that defining population bounds may be more subjective for sedentary herds; migratory herd densities may increase with increasing population size. Distance moved versus the interval between radiolocations was also non-isometric (z = 0.551). We standardized these movements to eliminate the confounding effects of scale, enabling comparisons across seasons and populations. The power formula helps to clarify the debate over the use of ratios, where variables may change non-isometrically. Power laws may enable the synthesis of ecological patterns sensitive to scales of space and time.