  Joint species distribution modeling is attracting increasing attention these
days, acknowledging the fact that individual level modeling fails to take into
account expected dependence/interaction between species. These models attempt
to capture species dependence through an associated correlation matrix arising
from a set of latent multivariate normal variables. However, these associations
offer little insight into dependence behavior between species at sites.
  We focus on presence/absence data using joint species modeling which
incorporates spatial dependence between sites. For pairs of species, we
emphasize the induced odds ratios (along with the joint probabilities of
occurrence); they provide much clearer understanding of joint presence/absence
behavior. In fact, we propose a spatial odds ratio surface over the region of
interest to capture how dependence varies over the region.
  We illustrate with a dataset from the Cape Floristic Region of South Africa
consisting of more than 600 species at more than 600 sites. We present the
spatial distribution of odds ratios for pairs of species that are positively
correlated and pairs that are negatively correlated under the joint species
distribution model.
  The multivariate normal covariance matrix associated with a collection of
species is only a device for creating dependence among species but it lacks
interpretation. By considering odds ratios, the quantitative ecologist will be
able to better appreciate the practical dependence between species that is
implicit in these joint species distribution modeling specifications.
