Analyzing Taylor’s Scaling Law: qualitative differences of social and territorial behavior on colonization/extinction dynamics

The power law relation between the mean population count and its variance (Taylor’s Power Law, TPL) is among the few general patterns in population ecology. While the TPL has been described to be pervasive across taxa, the causes of variation of the exponent describing this relation is not well understood. We compare the TPL exponents for two species with different social systems and behavior: Piñon jays (Gymnorhinus cyanocephalus) and Western scrub-jays (Aphelocoma californica). We analyze the underlying processes that generate the expected values of population size and its variance. Using a probabilistic model, we identify and estimate important processes involved in the generation of the TPL exponents. While both species show a scaling relationship between their mean and abundance, share a common negative relation between mean abundance and colonization–extinction rates, they differ greatly in the statistical distributions of colonization, extinction, the mean number of colonists, the probability of zero abundance and population sizes. We show how different aspects of the processes that generate abundance affect the TPL exponent, thereby providing empirical guidelines to interpret differences in the scaling relation between mean and variance of population size.