Abstract
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.
Highlights
Capture–mark–recapture–resight and capture–mark–recovery data can be used to estimate demographic parameters such as true and apparent survival, site fidelity, movement and harvest rates, breeding propensity, demographic heterogeneity, and relationships among these parameters and environmental covariates (Brownie & Pollock, 1985; Cam, Link, Cooch, Monnat, & Danchin, 2002; Gimenez, Cam, & Gaillard, 2018; Kendall et al, 2013; Kendall, Nichols, & Hines, 1997)
Estimating relationships between demographic parameters can lead to more effective conservation actions (Arnold, Afton, Anteau, Koons, & Nicolai, 2016; Servanty et al, 2010, 2011), where biologists might direct conservation actions toward demographic components which are intrinsically linked, such as pre-and postfledging survival (Nicolai & Sedinger, 2012) or adjust anthropogenic harvest rates to affect population growth rates of wild organisms (Nichols, Runge, Johnson, & Williams, 2007; Péron, 2013; Runge et al, 2002; Williams & Johnson, 1995)
Work on the effects of harvest on survival has focused on understanding process correlations (ρ) between survival and harvest rates (Arnold et al, 2016; Bartzen & Dufour, 2017; Sedinger, White, Espinosa, Partee, & Braun, 2010), where a strong negative correlation suggests additive relationships between survival and harvest, and minimal or no correlation may be indicative of compensation or partial compensation, these relationships are complex (Arnold et al, 2016; Péron, 2013)
Summary
Capture–mark–recapture–resight and capture–mark–recovery data can be used to estimate demographic parameters such as true and apparent survival, site fidelity, movement and harvest rates, breeding propensity, demographic heterogeneity, and relationships among these parameters and environmental covariates (Brownie & Pollock, 1985; Cam, Link, Cooch, Monnat, & Danchin, 2002; Gimenez, Cam, & Gaillard, 2018; Kendall et al, 2013; Kendall, Nichols, & Hines, 1997). Given the structure of covariance matrices, where the covariance is equal to the product of the square roots of the applicable variances, and a process correlation between the applicable parameters (σiσjρi,j), the use of the Wishart, scaled inverse Wishart (O'Malley & Zaslavsky, 2008), or hierarchical half-t (Huang & Wand, 2013) priors for a precision matrix often leads to the underestimation of ρ. This has important implications for the interpretation of process correlations, affecting biological inference and management decisions. Normal distributions to estimate process correlations among demographic parameters of wild organisms, as well as research in other fields where inverse Wishart distributions are used as prior for covariance matrices for multivariate data (e.g., Multivariate spatial models, Gelfand, Diggle, Guttorp, & Fuentes, 2010; Bayesian structural equation models)
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