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 distribtion. 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
(σ2) 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 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.