Integrated population models: Model assumptions and inference

Abstract

Integrated population models (IPMs) have become increasingly popular for the modelling of populations, as investigators seek to combine survey and demographic data to understand processes governing population dynamics. These models are particularly useful for identifying and exploring knowledge gaps within life histories, because they allow investigators to estimate biologically meaningful parameters, such as immigration or reproduction, that were previously unidentifiable without additional data. As IPMs have been developed relatively recently, there is much to learn about model behaviour. Behaviour of parameters, such as estimates near boundaries, and the consequences of varying degrees of dependency among datasets, has been explored. However, the reliability of parameter estimates remains underexamined, particularly when models include parameters that are not identifiable from one data source, but are indirectly identifiable from multiple datasets and a presumed model structure, such as the estimation of immigration using capture-recapture, fecundity and count data, combined with a life-history model. To examine the behaviour of model parameter estimates, we simulated stable populations closed to immigration and emigration. We simulated two scenarios that might induce error into survival estimates: marker induced bias in the capture–mark–recapture data and heterogeneity in the mortality process. We subsequently fit capture–mark–recapture, state-space and fecundity models, as well as IPMs that estimated additional parameters. Simulation results suggested that when model assumptions are violated, estimation of additional, previously unidentifiable, parameters using IPMs may be extremely sensitive to these violations of model assumption. For example, when annual marker loss was simulated, estimates of survival rates were low and estimates of immigration rate from an IPM were high. When heterogeneity in the mortality process was induced, there were substantial relative differences between the medians of posterior distributions and truth for juvenile survival and fecundity. Our results have important implications for biological inference when using IPMs, as well as future model development and implementation. Specifically, using multiple datasets to identify additional parameters resulted in the posterior distributions of additional parameters directly reflecting the effects of the violations of model assumptions in integrated modelling frameworks. We suggest that investigators interpret posterior distributions of these parameters as a combination of biological process and systematic error.