Bayesian modeling of age-specific survival in nesting studies under Dirichlet priors

A hierarchical nest survival model integrating incomplete temporally varying covariates

Nest success is a critical determinant of the dynamics of avian populations, and nest survival modeling has played a key role in advancing avian ecology and management. Beginning with the development of daily nest survival models, and proceeding through subsequent extensions, the capacity for modeling the effects of hypothesized factors on nest survival has expanded greatly. We extend nest survival models further by introducing an approach to deal with incompletely observed, temporally varying covariates using a hierarchical model. Hierarchical modeling offers a way to separate process and observational components of demographic models to obtain estimates of the parameters of primary interest, and to evaluate structural effects of ecological and management interest. We built a hierarchical model for daily nest survival to analyze nest data from reintroduced whooping cranes (Grus americana) in the Eastern Migratory Population. This reintroduction effort has been beset by poor reproduction, apparently due primarily to nest abandonment by breeding birds. We used the model to assess support for the hypothesis that nest abandonment is caused by harassment from biting insects. We obtained indices of blood-feeding insect populations based on the spatially interpolated counts of insects captured in carbon dioxide traps. However, insect trapping was not conducted daily, and so we had incomplete information on a temporally variable covariate of interest. We therefore supplemented our nest survival model with a parallel model for estimating the values of the missing insect covariates. We used Bayesian model selection to identify the best predictors of daily nest survival. Our results suggest that the black fly Simulium annulus may be negatively affecting nest survival of reintroduced whooping cranes, with decreasing nest survival as abundance of S. annulus increases. The modeling framework we have developed will be applied in the future to a larger data set to evaluate the biting-insect hypothesis and other hypotheses for nesting failure in this reintroduced population; resulting inferences will support ongoing efforts to manage this population via an adaptive management approach. Wider application of our approach offers promise for modeling the effects of other temporally varying, but imperfectly observed covariates on nest survival, including the possibility of modeling temporally varying covariates collected from incubating adults.

Modeling age and nest-specific survival using a hierarchical Bayesian approach

Recent studies have shown that grassland birds are declining more rapidly than any other group of terrestrial birds. Current methods of estimating avian age-specific nest survival rates require knowing the ages of nests, assuming homogeneous nests in terms of nest survival rates, or treating the hazard function as a piecewise step function. In this article, we propose a Bayesian hierarchical model with nest-specific covariates to estimate age-specific daily survival probabilities without the above requirements. The model provides a smooth estimate of the nest survival curve and identifies the factors that are related to the nest survival. The model can handle irregular visiting schedules and it has the least restrictive assumptions compared to existing methods. Without assuming proportional hazards, we use a multinomial semiparametric logit model to specify a direct relation between age-specific nest failure probability and nest-specific covariates. An intrinsic autoregressive prior is employed for the nest age effect. This nonparametric prior provides a more flexible alternative to the parametric assumptions. The Bayesian computation is efficient because the full conditional posterior distributions either have closed forms or are log concave. We use the method to analyze a Missouri dickcissel dataset and find that (1) nest survival is not homogeneous during the nesting period, and it reaches its lowest at the transition from incubation to nestling; and (2) nest survival is related to grass cover and vegetation height in the study area.

Bias adjustment in Bayesian estimation of bird nest age-specific survival rates

The populations of many North American landbirds are showing signs of declining. Gathering information on breeding productivity allows early detection of unhealthy populations and helps develop good habitat-management practices. In this paper, we study the performance of the Bayesian model (He, 2003, Biometrics 59, 962-973) for age-specific nest survival rates with irregular visits. We find that the estimates are satisfactory except for the age-one survival rate. Usually the more days skipped between two visits, the more serious the underestimation of the age-one survival rate. We investigated the problem and developed three approaches to adjust for the underestimation bias. The simulation results show that the three approaches can significantly improve the estimation of the age-one survival rate.

Bayesian Modeling of Age‐Specific Survival in Bird Nesting Studies under Irregular Visits

In this article, a Bayesian model for age-specific nest survival rates is presented to handle the irregular visit case. Both informative priors and noninformative priors are investigated. The reference prior under this model is derived, and, therefore, the hyperparameter specification problem is solved to some extent. The Bayesian method provides a more accurate estimate of the total survival rate than the standard Mayfield method, if the age-specific hazard rates are not constant. The Bayesian method also lets the biologist look for high- and low-survival rates during the whole nesting period. In practice, it is common for data of several types to be collected in a single study. That is, some nests may be aged, others are not. Some nests are visited regularly; others are visited irregularly. The Bayesian method accommodates any mix of these sampling techniques by assuming that the aging and visiting activities have no effect on the survival rate. The methods are illustrated by an analysis of the Missouri northern bobwhite data set.