Additive multivariate Gaussian processes for joint species distribution modeling with heterogeneous data
Jarno Vanhatalo, Marcelo Hartmann, Lari Veneranta
备注：
Accepted for publication in Bayesian Analysis. First available in Project Euclid: 3 June 2019. Permanent link to the BA article: https://projecteuclid.org/euclid.ba/1559548823 Digital Object Identifier: doi:10.1214/19-BA1158
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. 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. Current JSDMs are restricted to hierarchical generalized linear modeling framework. These parametric models have trouble in explaining changes in abundance due, e.g., 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.
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Faculty of Economics, Keio University（庆应义塾大学经济学部）；Research School of Finance, Actuarial Studies and Statistics, The Australian National University（澳大利亚国立大学金融、精算与统计研究学院）
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Tokyo University of Science（东京理科大学）；Meisei University（明海大学）；Keio University（庆应义塾大学）；Institute of Marine Research（海洋研究所）；RIKEN Center for Brain Science（理化学研究所脑科学中心）
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