The role of odds ratios in joint species distribution modeling

Abstract

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 joint models capture species dependence through an associated correlation matrix arising from a set of latent multivariate normal variables. However, these associations offer limited insight into realized dependence behavior between species at sites. We focus on presence/absence data using joint species modeling, which, in addition, incorporates spatial dependence between sites. For pairs of species selected from a collection, we emphasize the induced odds ratios (along with the joint occurrence probabilities); they provide a better appreciation of the practical dependence between species that is implicit in these joint species distribution modeling specifications. For any pair of species, the spatial structure enables a spatial odds ratio surface to illuminate how dependence varies over the region of interest. 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.