Additive Multivariate Gaussian Processes for Joint Species Distribution Modeling with Heterogeneous Data

Abstract

Species distribution models (SDM) are a key tool in ecology, conservation and management of natural resources. Two key components of the state-ofthe-art SDMs are the description for species distribution response along environmental covariates and the spatial random effect that captures deviations from the distribution patterns explained by environmental covariates. Joint species distribution models (JSDMs) additionally include interspecific correlations which have been shown to improve their descriptive and predictive performance compared to single species models. However, current JSDMs are restricted to hierarchical generalized linear modeling framework. Their limitation is that parametric models have trouble in explaining changes in abundance due, for example, highly nonlinear physical tolerance limits which is particularly important when predicting species distribution in new areas or under scenarios of environmental change. On the other hand, semi-parametric response functions have been shown to improve the predictive performance of SDMs in these tasks in single species models.Here, we propose JSDMs where the responses to environmental covariates are modeled with additive multivariate Gaussian processes coded as linear models of coregionalization. These allow inference for wide range of functional forms and interspecific correlations between the responses. We propose also an efficient approach for inference with Laplace approximation and 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 semi-parametric single species models and parametric single and joint species models in interpolation and extrapolation tasks. The proposed model outperforms the alternative models in all cases. We also show that the proposed model can be seen as an extension of the current state-of-the-art JSDMs to semi-parametric models.MSC 2010 subject classifications: Primary 60G15, 60K35; secondary 62P12.

On the Interpretations of Joint Modeling in Community Ecology

“…As a result, rare species could 'borrow strength' from common species if they do not behave fundamentally differently [17]. JSDMs, as a further extension of GLMs (but see [22,23] for other approaches), infer a correlation matrix from the residuals (hereafter residual correlation matrix) that reflects species co-occurrence patterns not explained by the environmental predictors [24]. Residual correlations may arise from model mis-specifications, missing covariates or species interactions (Box 2, review in [25][26][27]).…”

Modelling spatial patterns in host‐associated microbial communities

“…Likewise, a number of extensions and modifications to JSDMs could likely improve their performance for the high number of taxa that characterizes microbial studies. While a generalized linear modelling framework is usually at the core of JSDM models, their performance can be further improved by using Gaussian processes instead (Ingram et al ., 2020; Vanhatalo et al ., 2020). Advanced computational techniques such as Integrated Nested Laplace Approximation (Blangiardo et al ., 2013) could also be used to enhance their computational efficiency.…”

Clustering Species With Residual Covariance Matrix in Joint Species Distribution Models

“…While SDMs could be used to study species assemblages (a technique commonly called stacked SDM (sSDM), see Ferrier and Guisan, 2006;Calabrese et al, 2014), they were meant to model and predict the distribution of individual species. To model species assemblages, recent statistical advances yield to Joint Species Distribution Models (JSDMs) (Pollock et al, 2014;Warton et al, 2015;Clark et al, 2017;Ovaskainen et al, 2017b), which are multivariate extensions of generalized linear regression models (GLM) (other approaches can be found in Harris, 2015;Vanhatalo et al, 2020). In JSDMs, the regression coefficients are related to the response of species to the environment, as in SDMs, while the correlation among the residuals describe the pairwise-species dependencies not explained by the environment.…”