A Bayesian mixed multistate open-robust design mark-recapture model to estimate heterogeneity in transition rates in an imperfectly detected system

Abstract

Multistate mark-recapture models have long been used to assess ecological and demographic parameters such as survival, phenology, and breeding rates by estimating transition rates among a series of latent or observable states. Here, we introduce a Bayesian mixed multistate open robust design mark recapture model (MSORD), with random intercepts and slopes to explore individual heterogeneity in transition rates and individual responses to covariates. We fit this model to simulated data sets to test whether the model could accurately and precisely estimate five parameters, set to known values a priori, under varying sampling schemes. To assess the behavior of the model integrated across replicate fits, we employed a two-stage hierarchical model fitting algorithm for each of the simulations. The majority of model fits showed no sign of inadequate convergence according to our metrics, with 81.25% of replicate posteriors for parameters of interest having general agreement among chains (r < 1.1). Estimates of posterior distributions for mean transition rates and standard deviation in random intercepts were generally well-defined. However, we found that models estimated the standard deviation in random slopes and the correlation among random effects relatively poorly, especially in simulations with low power to detect individuals (e.g. low detection rates, study duration, or secondary samples). We also apply this model to a dataset of 200 female grey seals breeding on Sable Island from 1985-2018 to estimate individual heterogeneity in reproductive rate and response to near-exponential population growth. The Bayesian MSORD estimated substantial variation among individuals in both mean transition rates and responses to population size. The correlation among effects trended positively, indicating that females with high reproductive performance (more positive intercept) were also more likely to respond better to population growth (more positive slope) and vice versa. Though our simulation results lend confidence to analyses using this method on well developed datasets on highly observable systems, we caution the use of this framework in sparse data situations.