Modeling species abundance patterns using local environmental features is an
important, current problem in ecology. The Cape Floristic Region (CFR) in South
Africa is a global hot spot of diversity and endemism, and provides a rich
class of species abundance data for such modeling. Here, we propose a
multi-stage Bayesian hierarchical model for explaining species abundance over
this region. Our model is specified at areal level, where the CFR is divided
into roughly 37,000 one minute grid cells; species abundance is observed at
some locations within some cells. The abundance values are ordinally
categorized. Environmental and soil-type factors, likely to influence the
abundance pattern, are included in the model. We formulate the empirical
abundance pattern as a degraded version of the potential pattern, with the
degradation effect accomplished in two stages. First, we adjust for land use
transformation and then we adjust for measurement error, hence
misclassification error, to yield the observed abundance classifications. An
important point in this analysis is that only 28 of the grid cells have been
sampled and that, for sampled grid cells, the number of sampled locations
ranges from one to more than one hundred. Still, we are able to develop
potential and transformed abundance surfaces over the entire region. In the
hierarchical framework, categorical abundance classifications are induced by
continuous latent surfaces. The degradation model above is built on the latent
scale. On this scale, an areal level spatial regression model was used for
modeling the dependence of species abundance on the environmental factors.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS335 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org