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

Significance We show that the variation of plant and animal populations through time can provide basic insights into how populations interact with their environment, even when environmental covariates are unobserved. We contrasted the effects of two types of temporal variation on population dynamics showing that fluctuations in the strength of competition among individuals can change a well-known scaling relation between the population variance and population abundances. The scaling of the population variance is explored using a large database of time series, as well as two well-studied ungulate populations. Our results suggest that higher-order variance scaling may be present in many animal populations, both reducing the long-run population variance relative to the standard model and providing important information on how populations are regulated by their environment. 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.