Joint Count Transformation Models with Covariate-dependent Correlations

Abstract

Joint Species Distribution Models are essential for understanding how ecological covariates shape species communities. However, most existing approaches are limited by rigid parametric distributions for count data and the inability to model how interspecific associations change with those covariates. We introduce joint count transformation models, a novel framework designed to overcome these limitations. Our approach combines distribution-free marginal count transformation models for multiple species with a covariate-dependent latent Gaussian copula to model interspecific correlations, interpretable as Spearman's rank correlation on the observed count scale. All model parameters are estimated efficiently via joint maximum likelihood estimation, implemented in the R package tram. We apply this framework to model the joint abundance of three fish-eating bird species, using seasonality as the primary covariate. Our model successfully captured the complex, species-specific seasonal abundance patterns, including periods of high zero-counts and seasonal shifts in variance. Furthermore, the model revealed strong, seasonally-varying correlations between the species. These findings are consistent with an empirical approach and similar to those from the computationally expensive parametric Bayesian Hierarchical Modelling of Species Communities (HMSC) framework. Consistency, accuracy and feasibility of our approach are demonstrated in a simulation study for up to 10 species.