Scaling in the growth of geographically subdivided populations: invariant patterns from a continent-wide biological survey

Abstract

We consider statistical patterns of variation in growth rates for over 400 species of breeding birds across North America surveyed from 1966 to 1998. We report two results. First, the standard deviation of population growth rates decays as a power-law function of total population size with an exponent $β= 0.36\pm0.02$. Second, the number of subpopulations, measured as the number of survey locations with non-zero counts, scales to the 3/4-power of total number of birds counted in a given species. We show how these patterns may be related, and discuss a simple stochastic growth model for a geographically subdivided population that formalizes the relationship. We also examine reasons that may explain why some species deviate from these scaling-laws.