Hierarchical Bayes estimation of hunting success rates

Although most post-season harvest surveys are conducted at the state level, the effective management of wildlife populations often requires estimates of hunting success rate, hunting pressure and harvest at the sub-area (such as management unit, regional, or county) level.Sample sizes for some sub-areas are often very small or even zero. Because of small sample sizes, estimates for small sub-areas often yield unacceptably large standard errors. In this article, a hierarchical Bayes model is used to estimate hunting success rates at the sub-area level from post-season harvest surveys. The computation is done by Gibbs sampling and adaptive rejection sampling techniques. The method is illustrated using data from the Missouri Turkey Hunting Survey 1994 Spring Season. The Bayesian estimates are close to the frequency estimates for the sub-areas with large sample sizes and more stable than the frequency estimates for those with small sample sizes. The Bayesian estimates will be more useful to wildlife biologists in estab-lishing hunting regulation on small sub-areas at no additional survey cost.     

Comparing model averaging with other model selection strategies for benchmark dose estimation

Model averaging (MA) has been proposed as a method of accommodating model uncertainty when estimating risk. Although the use of MA is inherently appealing, little is known about its performance using general modeling conditions. We investigate the use of MA for estimating excess risk using a Monte Carlo simulation. Dichotomous response data are simulated under various assumed underlying dose–response curves, and nine dose–response models (from the USEPA Benchmark dose model suite) are fit to obtain both model specific and MA risk estimates. The benchmark dose estimates (BMDs) from the MA method, as well as estimates from other commonly selected models, e.g., best fitting model or the model resulting in the smallest BMD, are compared to the true benchmark dose value to better understand both bias and coverage behavior in the estimation procedure. The MA method has a small bias when estimating the BMD that is similar to the bias of BMD estimates derived from the assumed model. Further, when a broader range of models are included in the family of models considered in the MA process, the lower bound estimate provided coverage close to the nominal level, which is superior to the other strategies considered. This approach provides an alternative method for risk managers to estimate risk while incorporating model uncertainty.

Estimating an homogeneous series of a population abundance indicator despite changes in data collection procedure: A hierarchical Bayesian modelling approach

Abundance indicators are required both to assess and to manage wild populations. As new techniques are developed and teams in charge of gathering the data change, data collection procedures (DCPs) can evolve in space and time. How to estimate an homogeneous series of abundance indicator despite changes in DCP? To tackle this question a hierarchical Bayesian modelling (HBM) approach is proposed. It integrates multiple DCPs in order to derive a single abundance indicator that can be compared over space and time irrespective of the DCP used. Compared to single DCP models, it takes further advantage for abundance estimation of the joint treatment of a larger set of spatio-temporal units. After presenting the general formulation of our HBM approach, it is applied to the juvenile Atlantic salmon (Salmo salar L.) population of the River Nivelle (France). Posterior model checking, using χ² discrepancy measure, do not reveal any inadequacy between the model and the data. Despite a change in the DCP used (successive removals to catch-per-unit of effort), a unique abundance indicator for the 425 spatio-temporal units (site × year) sampled over twenty-four years (1985-2008) is estimated. The HBM approach allows the assessment of precision of the abundance estimates and shows variation between DCPs: a reduction in precision is observed during the most recent years (2005-2008) when only the catch-per-unit of effort DCP was used. The merits and generality of our HBM approach are discussed. We contend it extends previous single DCP models or inter-calibration of two DCPs, and it could be applied to a wide range of specific situations (taxon and DCPs).     

On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

The Importance of Being Spatial (and Reserved): Assessing Northern Spotted Owl Habitat Relationships with Hierarchical Bayesian Models

Abstract:  Regional conservation planning increasingly draws on habitat suitability models to support decisions regarding land allocation and management. Nevertheless, statistical techniques commonly used for developing such models may give misleading results because they fail to account for 3 factors common in data sets of species distribution: spatial autocorrelation, the large number of sites where the species is absent (zero inflation), and uneven survey effort. We used spatial autoregressive models fit with Bayesian Markov Chain Monte Carlo techniques to assess the relationship between older coniferous forest and the abundance of Northern Spotted Owl nest and activity sites throughout the species' range. The spatial random-effect term incorporated in the autoregressive models successfully accounted for zero inflation and reduced the effect of survey bias on estimates of species–habitat associations. Our results support the hypothesis that the relationship between owl distribution and older forest varies with latitude. A quadratic relationship between owl abundance and older forest was evident in the southern portion of the range, and a pseudothreshold relationship was evident in the northern portion of the range. Our results suggest that proposed changes to the network of owl habitat reserves would reduce the proportion of the population protected by up to one-third, and that proposed guidelines for forest management within reserves underestimate the proportion of older forest associated with maximum owl abundance and inappropriately generalize threshold relationships among subregions. Bayesian spatial models can greatly enhance the utility of habitat analysis for conservation planning because they add the statistical flexibility necessary for analyzing regional survey data while retaining the interpretability of simpler models.     

A distributed-delay model to predict ageing and survival rates of adults of Cryptolestes ferrugineus (Stephens) (Coleoptera: Laemophloeidae) in granaries filled with wheat

A time-varying distributed-delay model simulating effects of multifactors was developed. Prediction of the ageing rate and survival distribution of adults of the rusty grain beetle, Cryptolestes ferrugineus (Stephens) (Coleoptera: Laemophloeidae) in various environments found in wheat-filled granaries was conducted as an example to illustrate the application of this developed model. Published adult mortalities, determined at different temperatures, relative humidities, and food sources, were directly used to find the average ageing rate and family of cumulative function of adult mortality. The developed model could predict the adult survival rate at constant or transient temperatures with different relative humidities. This model could also simulate the effect of adult acclimation to their environment when they experience temperature and moisture fluctuations inside granaries. To validate the developed model, the simulation results were compared with available experimental data from the literature. There was no difference between predicted and measured mortalities in two granaries in which the mortalities were determined in a 4-month experiment.