The observed range for temporal mean-variance scaling exponents can be explained by reproductive correlation

Abstract

The mean-variance scaling relationship known as Taylor's power law has been well documented empirically over the past four decades but a general theoretical explanation for the phenomenon does not exist. Here we provide an explanation that relates empirical patterns of temporal mean-variance scaling to individual level reproductive behavior. Initially, we review the scaling behavior of population growth models to establish theoretical limits for the scaling exponent b that is in agreement with the empirically observed range (1≤b≤2). We go on to show that the degree of reproductive covariance among individuals determines the scaling exponent b. Independent reproduction results in an exponent of one, while completely correlated reproduction results in the upper limit of two. Intermediate exponents, which are common empirically, can be generated through the decay of reproductive covariance with increasing population size. Finally, we describe how the link between reproductive correlation and the scaling exponent provides a way to infer properties of individual-level reproductive behavior, such as the relative influence of demographic stochasticity, from a macroecological pattern. © Oikos.