Space-time modeling for the Missouri Turkey Hunting Survey

The Missouri Turkey Hunting Survey (MTHS) is a postseason mail survey conducted by the Missouri Department of Conservation. The 1996 MTHS provides information concerning the number of turkeys harvested by hunters on each day and the total number of trips made to the counties by these hunters on each day of the hunting season. The success rates are then found from this information. Small sample sizes produce large standard errors for the estimates at the county level. We use a Bayesian hierarchical generalized linear model to estimate daily hunting success rates at the county level. The model includes an autoregressive process for the days of the hunting season and spatially correlated random geographic effects. The computations are performed using Gibbs sampling and adaptive rejection sampling techniques. Results show that there are significant spatial corelations between counties and correlations between days of the hunting season. The estimates are close to the frequency estimates at the state level and much more stable at the county level.     

An individual-based stochastic hazard model of eastern king prawn (Melicertus plebejus) migration with spatially and temporally varying fishing effort

This paper describes an individual-based stochastic model of eastern king prawn migration along the eastern Australian coast. Migration is treated as one-dimensional diffusion with drift. Capture of a prawn is seen as a failure event driven by movement through a spatially and temporally variable fishing mortality hazard. This hazard is combined with a uniform natural mortality hazard. We use a Monte Carlo method to estimate parameters by comparing expected numbers of tag-returns predicted from the model with previously published tag-release data. As the previous study used a discrete compartmental model, with compartments corresponding to zones of constant fishing effort, we used the same zones and fishing effort in our comparison. The marginal distribution of yield in each zone per single recruit is determined, providing more information compared with the deterministic approach to yield-per-recruit. Using our model we also derive the constant fishing mortality rate equivalent to a spatially variable fishing mortality rate in its impact on the proportion of prawns surviving the migration to reach spawning grounds. Determination of this proportion could contribute significantly to a sustainability assessment of the fishery. It is demonstrated using the AIC that better fits to the data of the previous study and greater parsimony are obtained using our model than were found in the deterministic compartmental analysis of that study. This improvement results from the ability of our model to account separately for average speed of movement and average dispersal rate, whereas in the previous deterministic compartmental model, movement is governed by just one parameter. Our individual-based model includes a parameter that explicitly accounts for dispersal of prawns in migration, so it can distinguish between speed effects and dispersal effects in the data. It also models both types of mortality as processes distinct from those of movement. This enables it to better separate movement and mortality effects compared to the compartmental approach, in which movement and mortality are treated as similar departure processes from a compartment. This separation reduces confounding of movement and mortality effects when parameters are estimated.     

Modelling the distribution of plant species using the autologistic regression model

For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation and real data examples. As examples, we use the proposed methodology to model the distributions of two plant species in the state of Florida.     

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.