Hierarchical Bayesian modeling of species richness in biological communities

The estimation of the number of species in biological communities has been an important topic for wildlife research, and is important for understanding wildlife conservation and biodiversity. The motivating data for this work consist of observational counts of bird species in a large-scaled survey of roadside routes in North America. The goal is to obtain accurate assessment of the number of species on those routes.;In this thesis, we reviewed a rich literature of species richness estimation, and investigated an existing hierarchical Bayesian approach (Dorazio and Royle (2005), Dorazio et al. (2006)) which models species occurrence rate and observer detection rate explicitly. We tuned and implemented this model. Compared to conventional jackknife estimates (Burnham and Overton (1979)), simulation studies showed that the Bayesian estimates are more accurate and more robust to certain assumptions.;This Bayesian model (Dorazio and Royle (2005), Dorazio et al. (2006)) only uses detection/non-detection information in the data, whereas abundance information (actual counts) is also available. To be able to utilize complete information in the data and therefore to obtain better estimates, we proposed a new hierarchical Bayesian model. Comparisons between our model and the existing Bayesian model were done both theoretically and via simulation. In general, we found it beneficial to make use of the abundance information in the data.;Using our Bayesian model for a single route as a building-block, we further developed hierarchical Bayesian spatial-temporal models to jointly model multiple routes and years in the data. We allowed for greater flexibility in spatial-temporal smoothing than existing approaches. We demonstrated the effectiveness of our spatial-temporal models via both simulations and real data analyses. Our models can be easily adapted to include observable spatial/temporal covariates as well as account for observer effects.