  Species distribution models usually attempt to explain presence-absence or
abundance of a species at a site in terms of the environmental features
(socalled abiotic features) present at the site. Historically, such models have
considered species individually. However, it is well-established that species
interact to influence presence-absence and abundance (envisioned as biotic
factors). As a result, there has been substantial recent interest in joint
species distribution models with various types of response, e.g.,
presence-absence, continuous and ordinal data. Such models incorporate
dependence between species response as a surrogate for interaction.
  The challenge we focus on here is how to address 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. Again, there is some recent literature to address this; we adopt
a dimension reduction approach. The novel wrinkle we add here is spatial
dependence. That is, we have a collection of sites over a relatively small
spatial region so it is anticipated that species distribution at a given site
would be similar to that at a nearby site. Specifically, we handle dimension
reduction through Dirichlet processes joined with spatial dependence through
Gaussian processes.
  We use both simulated data and a plant communities dataset for the Cape
Floristic Region (CFR) of South Africa to demonstrate our approach. The latter
consists of presence-absence measurements for 639 tree species on 662
locations. Through both data examples we are able to demonstrate improved
predictive performance using the foregoing specification.
