Joint Spatial and Temporal Generalized Dissimilarity Mixed Modeling (stGDMM) for Beta Diversity

Abstract

Generalized dissimilarity models (GDMs) have emerged as a valuable tool for formal statistical analysis of biodiversity. In particular, beta diversity, measured using dissimilarity measures, e.g., the Bray-Curtis dissimilarity in our case, provides a statistical summary of the difference in species composition between sites. It also provides novel data for spatial and spatio-temporal modeling as it resides over the product space of one space-time pair and a second space-time pair. In earlier work we developed the spatial generalized dissimilarity mixed model (spGDMM) to remedy some of the stochastic issues concerned with the foundational GDM in the literature. Here, we extend that work to include dynamics. We find much richer modeling opportunities as we consider beta diversity with regard to change in time as well as space. We illustrate with a dataset from the Cape Floristic Region (CFR) in South Africa.