Estimating correlations among demographic parameters in population models

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.