Bayesian Analysis

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

Jarno Vanhatalo, Marcelo Hartmann, and Lari Veneranta

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Abstract

Species distribution models (SDM) are a key tool in ecology, conservation and management of natural resources. Two key components of the state-of-the-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 non-linear 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.

Article information

Source
Bayesian Anal., Advance publication (2018), 33 pages.

Dates
First available in Project Euclid: 3 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.ba/1559548823

Digital Object Identifier
doi:10.1214/19-BA1158

Subjects
Primary: 60G15: Gaussian processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 62P12: Applications to environmental and related topics

Keywords
linear model of coregionalization hierarchical model heterogeneous data spatial prediction model comparison Laplace approximation covariance transformation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Vanhatalo, Jarno; Hartmann, Marcelo; Veneranta, Lari. Additive Multivariate Gaussian Processes for Joint Species Distribution Modeling with Heterogeneous Data. Bayesian Anal., advance publication, 3 June 2019. doi:10.1214/19-BA1158. https://projecteuclid.org/euclid.ba/1559548823


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Supplemental materials

  • Supplementary Material: Additive multivariate Gaussian process for joint species distribution modeling with heterogeneous data. The supplementary material contains additional mathematical formulation of the methodology proposed in this paper and additional figures and tables for the case study analysis.