Robustly estimating the demographic contribution of immigration: Simulation, sensitivity analysis and seals.

Identifying important demographic drivers of population dynamics is fundamental for understanding life-history evolution and implementing effective conservation measures. Integrated population models (IPMs) coupled with transient life table response experiments (tLTREs) allow ecologists to quantify the contributions of demographic parameters to observed population change. While IPMs can estimate parameters that are not estimable using any data source alone, for example, immigration, the estimated contribution of such parameters to population change is prone to bias. Currently, it is unclear when robust conclusions can be drawn from them. We sought to understand the drivers of a rebounding southern elephant seal population on Marion Island using the IPM-tLTRE framework, applied to count and mark-recapture data on 9500 female seals over nearly 40 years. Given the uncertainty around IPM-tLTRE estimates of immigration, we also aimed to investigate the utility of simulation and sensitivity analyses as general tools for evaluating the robustness of conclusions obtained in this framework. Using a Bayesian IPM and tLTRE analysis, we quantified the contributions of survival, immigration and population structure to population growth. We assessed the sensitivity of our estimates to choice of multivariate priors on immigration and other vital rates. To do so we make a novel application of Gaussian process priors, in comparison with commonly used shrinkage priors. Using simulation, we assessed our model's ability to estimate the demographic contribution of immigration under different levels of temporal variance in immigration. The tLTRE analysis suggested that adult survival and immigration were the most important drivers of recent population growth. While the contribution of immigration was sensitive to prior choices, the estimate was consistently large. Furthermore, our simulation study validated the importance of immigration by showing that our estimate of its demographic contribution is unlikely to result as a biased overestimate. Our results highlight the connectivity between distant populations of southern elephant seals, illustrating that female dispersal can be important in regulating the abundance of local populations even when natal site fidelity is high. More generally, we demonstrate how robust ecological conclusions may be obtained about immigration from the IPM-tLTRE framework, by combining sensitivity analysis and simulation.