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.

Since the initial development of the robust design, this capture‐recapture model structure has been modified to estimate temporary emigration and expanded to include auxiliary information such as band recovery and live resight data using maximum likelihood approaches. These developments have allowed investigators to separately assess individual and group effects on true survival, site fidelity, and temporary emigration. Additionally, recent advances in the BUGS language have allowed researchers to develop increasingly complex, user‐specified models in Bayesian frameworks. The robust design has rarely been implemented in the BUGS language, and previous attempts to parameterize the robust design in BUGS exhibited strong bias in estimates of temporary emigration rates. Given the limitations of current parameterizations of the robust design in Bayesian frameworks, and our research objectives, we have developed a parameterization of the robust design in the BUGS language that produces unbiased estimates of all model parameters. We use this novel model structure to examine lifetime carry‐over effects of environmental conditions during early life on annual breeding probabilities of Pacific black brent Branta bernicla nigricans breeding on the Yukon–Kuskokwim River Delta in Western Alaska. We found that individuals that were more structurally developed as goslings bred at increased rates as adults (β = 0.14, f = 0.94), with no effect on adult survival (β = 0.01, f = 0.62). Additionally, we provide evidence for long‐term declines in apparent survival of breeding adult females at the population level (β = −0.01, f = 0.90). This novel model structure can be easily expanded (Gibson et al., in press) and has important implications for population modelling at broad scales, where we apply it to a declining population of Pacific black brent. Given long‐term declines in gosling growth on the Yukon–Kuskokwim Delta, we predict future declines in population trajectories as a result of lifetime carry‐over effects of environmental conditions during growth on adult fecundity and long‐term declines in adult survival.

Estimating correlations among demographic parameters is critical to understanding population dynamics and life‐history evolution, where correlations among parameters can inform our understanding of life‐history trade‐offs, result in effective applied conservation actions, and shed light on evolutionary ecology. The most common approaches rely on the multivariate normal distribution, and its conjugate inverse Wishart prior distribution. However, the inverse Wishart prior for the covariance matrix of multivariate normal distributions has a strong influence on posterior distributions. As an alternative to the inverse Wishart distribution, we individually parameterize the covariance matrix of a multivariate normal distribution to accurately estimate variances (σ 2) of, and process correlations (ρ) between, demographic parameters. We evaluate this approach using simulated capture–mark–recapture data. We then use this method to examine process correlations between adult and juvenile survival of black brent geese marked on the Yukon–Kuskokwim River Delta, Alaska (1988–2014). Our parameterization consistently outperformed the conjugate inverse Wishart prior for simulated data, where the means of posterior distributions estimated using an inverse Wishart prior were substantially different from the values used to simulate the data. Brent adult and juvenile annual apparent survival rates were strongly positively correlated (ρ = 0.563, 95% CRI 0.181–0.823), suggesting that habitat conditions have significant effects on both adult and juvenile survival. We provide robust simulation tools, and our methods can readily be expanded for use in other capture–recapture or capture‐recovery frameworks. Further, our work reveals limits on the utility of these approaches when study duration or sample sizes are small.