Abstract: Species distribution models usually attempt to explain the presence-absence or abundance of a species at a site in terms of the environmental features (so-called abiotic features) present at the site. Historically, such models have considered species individually. However, it is well established that species interact to influence the presence-absence and abundance (envisioned as biotic factors). As a result, recently joint species distribution models with various types of responses, such as presence-absence, continuous, and ordinal data have attracted a significant amount of interest. Such models incorporate the dependence between species' responses as a proxy for interaction. We address the accommodation of such modeling in the context of a large number of species (e.g., order 10²) across sites numbering in the order of 10² or 10³ when, in practice, only a few species are found at any observed site. To do so, we adopt a dimension-reduction approach. The novelty of our approach is that we add spatial dependence. That is, we consider a collection of sites over a relatively small spatial region. As such, we anticipate that the species distribution at a given site will be similar to that at a nearby site. Specifically, we handle dimension reduction using Dirichlet processes, which enables the clustering of species, and add spatial dependence across sites using Gaussian processes. We use simulated data and a plant communities data set for the Cape Floristic Region (CFR) of South Africa to demonstrate our approach. The latter consists of presence-absence measurements for 639 tree species at 662 locations. These two examples demonstrate the improved predictive performance of our method using the aforementioned specification.

Key words and phrases: Dimension reduction; Gaussian processes; high-dimensional covariance matrix; spatial factor model; species dependence.