| Abstract |
Modelling the local density of tropical saplings can provide insights into the ecological processes that drive species regeneration and thereby help predict population recovery after disturbance. Yet, few studies have addressed the challenging issues in autocorrelation and zero-inflation of local density. This paper presents Hierarchical Bayesian Modelling (HBM) of sapling density that includes these two features. Special attention is devoted to variable selection, model estimation and comparison. We developed a Zero-Inflated Poisson (ZIP) model with a latent correlated spatial structure and compared it with non-spatial ZIP and Poisson models that were either autocorrelated (Spatial Generalized Linear Mixed, SGLM) or not (generalized linear models, GLM). In our spatial models, local density autocorrelation was modeled by a Conditional Auto-Regressive (CAR) process. 13 explicative variables described ecological conditions with respect to topography, disturbance, stand structure and intraspecific processes. Models were applied to six tropical tree species with differing biological attributes: Oxandra asbeckii, Eperua falcata, Eperua grandiflora, Dicorynia guianensis, Qualea rosea, and Tachigali melinonii. We built species-specific models using a simple method of variable selection based on a latent binary indicator. Our spatial models showed a close correlation between observed and estimated densities with site spatial structure being correctly reproduced. By contrast, the non-spatial models showed poor fits. Variable selection highlighted species-specific requirements and susceptibility to local conditions. Model comparison overall showed that the SGLM was the most accurate explanatory and predictive model. Surprisingly, zero-inflated models performed less well. Although the SZIP model was relevant with respect to data distribution, and more flexible with respect to response curves, its model complexity caused marked variability in parameter estimates. In the SUM, the spatial process alone accounted for zero-inflation in the data. A refinement of the hypotheses employed at the process level could compensate for distribution flaws at the data level. This study emphasized the importance of the HBM framework in improving the modelling of density-environment relationships. (C) 2008 Elsevier B.V. All rights reserved. |
