Joint species distribution modeling with additive multivariate Gaussian process priors and heteregenous data

In this work, we propose JSDMs where the responses to environmental covariates are modeled with multivariate additive Gaussian processes. These allow inference for wide range of functional forms and interspecific correlations between the responses. We propose also an efficient approach for inference by utilizing Laplace approximation with a parameterization of the interspecific covariance matrices on the euclidean space. We demonstrate the benefits of our model with two small scale examples and one real world case study. We use cross-validation to compare the proposed model to analogous single species models in interpolation and extrapolation tasks. The proposed model outperforms the single species models in both cases. We also show that the proposed model can be seen as an extension of the current state-of-the-art JSDMs to semiparametric models.