Multi-species count transformation models

Joint Species Distribution Models are essential for understanding how ecological drivers shape species communities. However, most existing approaches are limited by rigid parametric distributions for count data and the inability to model how interspecific interactions change in response to those drivers. We introduce multi-species count transformation models, a novel framework designed to overcome these limitations. Our approach combines flexible, distribution-free marginal species count transformation models for each species' count abundance, with a driver-dependent latent Gaussian copula modelling interspecific correlations, interpretable as Spearman's rank correlation on the scale of the counts. All model parameters are estimated efficiently via joint maximum likelihood estimation, implemented in the R package cotram. We apply this framework to model the joint abundance of three fish-eating bird species, using seasonality as the primary driver. 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.