SPATIAL SCALES IN THE STUDY OF REEF FISHES - A THEORETICAL PERSPECTIVE

Theoretical models imply that spatial scale derives its greatest impor tance through interactions between density-dependent processes and spa tial variation in population densities and environmental variables. Su ch interactions cause population dynamics on large spatial scales to d iffer in important ways from predictions based on measurements of popu lation dynamics at smaller scales, a phenomenon called the scale trans ition. These differences can account for large-scale population stabil ity and species coexistence. The interactions between density dependen ce and spatial variation that lead to the scale transition can be unde rstood by the process of non-linear averaging, which shows how varianc e originating on various spatial scales contributes to large-scale pop ulation dynamics. Variance originating below the scale of density depe ndence contributes less to the scale transition as the spatial scale o f the variation declines, while variation originating on or above the scale of density dependence contributes independently of the spatial s cale of the variation.