Scalable phylogenetic Gaussian process models improve the detectability of environmental signals on extinction risks for many Red List species

1. Conservation biologists have a daunting task of understanding the causes of species decline associated with anthropogenic factors and predicting the extinction risk of a growing number of endangered species. By stabilising estimates with information on closely related species, phylogenetic information among species can bridge gaps in information on species with small sample sizes when modelling large numbers of endangered species. However, modelling many species with the Gaussian process (GP), which underlies the evolutionary process of phylogenetic random effects, remains a challenge owing to the computational burden in estimating the large variance-covariance matrix. 2. Here, we applied a phylogenetic generalised mixed model with random slopes and random intercepts to 1,010 endangered vascular plant taxa in Japan following phylogenetic GPs implemented by nearest neighbour GP (NNGP) approximation. NNGP enables flexibility in changing the proximity on the phylogenetic tree of species from which information is borrowed to stabilise parameter estimates with a realistic computational burden. We evaluated the effectiveness of phylogenetic models by comparing the predictive performance and descriptive power of phylogenetic and non-phylogenetic models and identified the anthropogenic factors contributing to the decline of each of the studied endangered species. 3. We found that the model with phylogenetic information had better prediction performance than the model without phylogenetic information. The results showed that across all explanatory variables, the phylogenetic model could detect interspecific differences in response to environmental factors in a number of species more clearly. Combined with the phylogenetic signal results, we could also detect a phylogenetic bias in the species that could benefit from the positive effects of protected areas but reduce the extinction risk of 95% of all studied taxa. 4. In conclusion, our model, considering phylogenetic information with NNGP, allows the elucidation of factors causing the decline of many endangered species. In future analyses, the estimation of extinction probability linked to environmental change using such modelling might be applied to future climate-land use scenarios, advancing the comprehensive assessment of biodiversity degradation and threats to species at multiple scales.