Cody E. Deane

Correlations between annual recovery and survival probabilities estimated from tag‐recovery data have been used to quantify the demographic response of exploited populations to harvest. Deane et al. (2023) evaluated the bias and certainty of correlation parameters between recovery and survival probabilities estimated as random effects drawn from bivariate normal distributions relative to different prior distributions and sample size combinations. Riecke et al. (2024) observed that we incorrectly parameterized a precision matrix with Gamma priors and suggested using a Gamma(1,1) prior distribution for the standard deviations as an alternative. Riecke et al. (2024) provided results from tag‐recovery models that estimate mortality hazard rates after fitting these models to tag‐recovery datasets with large sample sizes. Here, we fit tag‐recovery models to the data we previously simulated (Deane et al. 2023) while using Gamma(1,1) as the prior distribution for standard deviations while parameterizing these models to estimate recovery and survival in discrete time or to estimate cause‐specific mortality as hazard rates. We compare our new results to previous results obtained while using Uniform(0,5) prior distribution for the standard deviations. When sample sizes were large, correlation estimates obtained with either prior distribution provided similarly reliable parameter recovery and inference, replicating results of Riecke et al. (2024). With smaller sample sizes similar to those available for most duck populations in North America, correlations estimated with either prior distribution were uncertain and ambiguous. With decreasing sample sizes, annual survival was estimated with increasing uncertainty when compared to annual recovery, likely contributing to the poor ability to estimate correlation. Consistent with the original interpretation of Deane et al. (2023) and previous literature, we found correlations were often estimated with high uncertainty such that the sign (+ or –) may be the only attribute of these parameters that can be reliably interpreted.

Access to high‐quality food is critical for long‐distance migrants to provide energy for migration and arrival at breeding grounds in good condition. We studied effects of changing abundance and availability of a marine food, common eelgrass (Zostera marina L.), on an arctic‐breeding, migratory goose, black brant (Brant bernicla nigricans Lawrence 1846), at a key non‐breeding site, Bahía San Quintín, Mexico. Eelgrass, the primary food of brant, is consumed when exposed by the tide or within reach from the water's surface. Using an individual‐based model, we predicted effects of observed changes (1991–2013) in parameters influencing food abundance and availability: eelgrass biomass (abundance), eelgrass shoot length (availability, as longer shoots more within reach), brant population size (availability, as competition greater with more birds), and sea level (availability, as less food within reach when sea level higher). The model predicted that the ability to gain enough energy to migrate was most strongly influenced by eelgrass biomass (threshold January biomass for migration = 60 g m⁻² dry mass). Conversely, annual variation in population size (except for 1998), was relatively low, and variation in eelgrass shoot length and sea level were not strongly related to ability to migrate. We used observed data on brant body mass at Bahía San Quintín and annual survival to test for effects of eelgrass biomass in the real system. The lowest observed values of body mass and survival were in years when biomass was below 60 g m⁻², although in some years of low biomass body mass and/or survival was higher. This suggests that the real birds may have some capacity to compensate to meet their energy demands when eelgrass biomass is low. We discuss consequences for brant population trends and conservation.

Recent empirical studies have quantified correlation between survival and recovery by estimating these parameters as correlated random effects with hierarchical Bayesian multivariate models fit to tag‐recovery data. In these applications, increasingly negative correlation between survival and recovery has been interpreted as evidence for increasingly additive harvest mortality. The power of these hierarchal models to detect nonzero correlations has rarely been evaluated, and these few studies have not focused on tag‐recovery data, which is a common data type. We assessed the power of multivariate hierarchical models to detect negative correlation between annual survival and recovery. Using three priors for multivariate normal distributions, we fit hierarchical effects models to a mallard (Anas platyrhychos) tag‐recovery data set and to simulated data with sample sizes corresponding to different levels of monitoring intensity. We also demonstrate more robust summary statistics for tag‐recovery data sets than total individuals tagged. Different priors led to substantially different estimates of correlation from the mallard data. Our power analysis of simulated data indicated most prior distribution and sample size combinations could not estimate strongly negative correlation with useful precision or accuracy. Many correlation estimates spanned the available parameter space (−1,1) and underestimated the magnitude of negative correlation. Only one prior combined with our most intensive monitoring scenario provided reliable results. Underestimating the magnitude of correlation coincided with overestimating the variability of annual survival, but not annual recovery. The inadequacy of prior distributions and sample size combinations previously assumed adequate for obtaining robust inference from tag‐recovery data represents a concern in the application of Bayesian hierarchical models to tag‐recovery data. Our analysis approach provides a means for examining prior influence and sample size on hierarchical models fit to capture–recapture data while emphasizing transferability of results between empirical and simulation studies.

1. Recent empirical studies have quantified correlation between survival and recovery by estimating these parameters as correlated random effects with Bayesian multivariate mixed effects models fit to tag-recovery data. In these applications, increasingly negative correlation between survival and recovery indicates increasingly additive harvest mortality. The power of mixed effects models to detect non-zero correlations has rarely been evaluated and these few studies have not focused on a common data type in the form of tag recoveries. 2. We assessed the power of multivariate mixed effects models to estimate negative correlation between annual survival and recovery. Using three priors for multivariate normal distributions, we fit mixed effects models to a mallard (Anas platyrhychos) tag-recovery dataset and to simulated data with sample sizes corresponding to different levels of monitoring intensity. We also demonstrate a method of calculating effective sample size for capture-recapture data. 3) Different priors lead to different inference about additive harvest when we fit our models to the mallard data. Our power analysis of simulated data indicated most prior distribution and sample size combinations resulted in correlation estimates with substantial bias and imprecision. Many correlation estimates spanned the available parameter space (–1,1) and were biased towards zero. Only one prior combined with our most intensive monitoring scenario allowed our models to consistently recover negative correlation without bias. Underestimating the magnitude of correlation coincided with overestimating the variability of annual survival, but not annual recovery. 4) The inadequacy of prior distributions and sample size combinations typically assumed adequate for robust inference represents a concern in the application of Bayesian mixed effects models for the purpose of informing harvest management. Our analysis approach provides a means for examining prior influence and sample size on mixed-effects models fit to capture-recapture data while emphasizing transferability of results between empirical and simulation studies.

Informing conservation and management decisions for habitats frequented by species of high management interest often face the challenge of limited resources for conducting wildlife surveys. When surveys are focused on local areas or sparsely distributed species, it may also be difficult to obtain counts sufficient for implementing abundance models that account for imperfect detection. With replicated aerial surveys collected within a 70.25‐km²portion of the Eastern Alaska Range, Alaska, USA, during the summers of 2013–2015, we estimated daily abundance of Dall’s sheep using two different estimation methods: BayesianN‐mixture models and Poisson regression models. We then compared estimates of relative abundance from both model types while paying special attention to the assumption of closure within individual survey units. With abundance estimates obtained from individual survey days, we then estimated the average number of Dall’s sheep within the survey area for the period 1 July–1 October. Daily ewe abundance followed a quadratic pattern, with 10–20 ewes being within our survey area in early July and late September, and approximately 90 ewes within the survey area in mid‐August. Lamb‐to‐ewe ratios averaged 0.2 from July–September, while ram‐to‐ewe ratios averaged 0.4 from July until mid‐August before increasing to about 1.0 by the end of September. These results indicate that our survey area is an important habitat to local Dall’s sheep populations when lambs are vulnerable to predators. Accordingly, human recreation and military training within the survey area should be minimized 1.5–3.0 months after parturition to minimize disturbance. We also found thatN‐mixture models displayed a pattern of abundance estimates that increased in magnitude as model complexity increased. We thus recommend an a priori approach toN‐mixture model construction that balances the risk of overfitting models to modest data against the risk of fitting models that do not explain heterogeneity in abundance and detection probability. Lastly, we suggest simple improvements to replicated, aerial surveys for species like Dall’s sheep focused on reducing violations of the closure assumption within individual survey units, which can reduce bias of density estimates obtained withN‐mixture models.