  By extending single-species distribution models, multi-species distribution
models and joint species distribution models are able to describe the
relationship between environmental variables and a community of species. It is
also possible to model either the marginal distribution of each species
(multi-species models) in the community or their joint distribution (joint
species models) under certain assumptions, but a model describing both entities
simultaneously has not been available. We propose a novel model that allows
description of both the joint distribution of multiple species and models for
the marginal single-species distributions within the framework of multivariate
transformation models. Model parameters can be estimated from abundance data by
two approximate maximum-likelihood procedures.
  Using a model community of three fish-eating birds, we demonstrate that
inter-specific food competition over the course of a year can be modeled using
count transformation models equipped with three time-dependent Spearman's rank
correlation parameters. We use the same data set to compare the performance of
our model to that of a competitor model from the literature on species
distribution modeling. Multi-species count transformation models provide an
alternative to multi- and joint- species distribution models. In addition to
marginal transformation models capturing single-species distributions, the
interaction between species can be expressed by Spearman's rank correlations in
an overarching model formulation that allows simultaneous inferences for all
model parameters. A software implementation is available in the "cotram" add-on
package to the R system for statistical computing.
