Stochastic models for the growth rate of animal populations: Variance scaling and decomposition

All animal populations fluctuate through time. These fluctuations are due both to the intrinsic properties of populations such as the random nature of births and deaths, and to extrinsic, environmental factors driving birth, survival, and migration dynamics. This dissertation is concerned with building models to describe these fluctuations using simple but general models describing how populations interact with their environment. The results are not just interesting for their own sake, but also have important implications for wildlife conservation and management efforts. Chapter 2 looks at how autocorrelated environments drive fluctuations in natural populations. Our results provide an interesting new perspective on when environmental autocorrelation will be important to account for, and how ecological processes can disrupt the autocorrelation present in environmental factors. The models developed in Chapter 3 include a derivation of demographic and environmental stochasticity, and a single-species stochastic model that accounts for interspecific interactions. We tested this model with an experimental time series that tracked the extinction of populations in microcosms, finding that we could greatly improve predictions about the time to extinction when accounting for fluctuations induced by interspecific interactions. Finally, in Chapter 4 we looked at the influence of stochastic environments on the strength of density dependence. This is a perspective that has long been ignoredbut turns out to have interesting implications for population stability. We show that variation in the strength of density dependence will often yield more stable dynamics than the standard model of environmental variation but that there are cases where it can also destabilize dynamics, leading to periods of exponential growth followed by population crashes. Taken together this work further justifies the application of single-species time series methods to complex ecological systems. This has important implications for management and conservation applications where information is limited and single-species approaches are used, often without understanding whether the assumptions behind the single-species approach are valid.