Generalized joint attribute modeling for biodiversity analysis: median-zero, multivariate, multifarious data

Probabilistic forecasts of species distribution and abundance require models that accommodate the range of ecological data, including a joint distribution of multiple species based on combinations of continuous and discrete observations, mostly zeros. We develop a generalized joint attribute model (GJAM), a probabilistic framework that readily applies to data that are combinations of presence-absence, ordinal, continuous, discrete, composition, zero-inflated, and censored. It does so as a joint distribution over all species providing inference on sensitivity to input variables, correlations between species on the data scale, prediction, sensitivity analysis, definition of community structure, and missing data imputation. GJAM applications illustrate flexibility to the range of species-abundance data. Applications to forest inventories demonstrate species relationships responding as a community to environmental variables. It shows that the environment can be inverse predicted from the joint distribution of species. Application to microbiome data demonstrates how inverse prediction in the GJAM framework accelerates variable selection, by isolating effects of each input variable's influence across all species.