Evidence and implications of higher-order scaling in the environmental variation of animal population growth

Environmental stochasticity is an important concept in population dynamics, providing a quantitative model of the extrinsic fluctuations driving population abundances. It is typically formulated as a stochastic perturbation to the maximum reproductive rate, leading to a population variance that scales quadratically with abundance. However, environmental fluctuations may also drive changes in the strength of density dependence. Very few studies have examined the consequences of this alternative model formulation while even fewer have tested which model better describes fluctuations in animal populations. Here we use data from the Global Population Dynamics Database to determine the statistical support for this alternative environmental variance model in 165 animal populations and test whether these models can capture known population-environment interactions in two well-studied ungulates. Our results suggest that variation in the density dependence is common and leads to a higher-order scaling of the population variance. This scaling will often stabilize populations although dynamics may also be destabilized under certain conditions. We conclude that higher-order environmental variation is a potentially ubiquitous and consequential property of animal populations. Our results suggest that extinction risk estimates may often be overestimated when not properly taking into account how environmental fluctuations affect population parameters.