A TWO-STEP ESTIMATOR FOR A SPATIAL LAG MODEL OF COU TS: THEORY, SMALL SAMPLE PERFORMA CE A D A APPLICATIO by
Modelling the local densityof tropical saplings canprovide insights into theecological processes thatdrive 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 LinearMixed, SGLM) or not (generalized linearmodels, GLM). In our spatialmodels, 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 spatialmodels showed a close correlation between observed and estimated densitieswith 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 SGLMwas themost accurate explanatory and predictivemodel. Surprisingly, zero-inflated models performed less well. Although the SZIP model was relevant with respect to data distribution, andmore flexible with respect to response curves, its model complexity caused marked variability in parameter estimates. In the SGLM, 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.