Abstract

To assess the current and future health of ecosystems under climate change, we need to understand how plants can adapt to shifting environmental conditions. Phylogenetic models that capture the co-evolution of species allow us to link genetic and functional traits to climate tolerance, helping to predict how plant communities may respond to future change. The UK’s Natural History Museum holds plant records extending back to the voyages of James Cook and beyond, and hundreds of millions of further records sit on the Global Biodiversity Information Facility (GBIF), but these observations do not span the full range of environmental conditions under which species can persist. Creating models that allow information to be shared across related species, can fill these gaps and thus improve inference about species responses to climate.

With an estimated 400,000 plant species worldwide, modelling multiple co-evolving traits on large phylogenies is computationally demanding. This is due to the resulting covariance matrices that scale with the number of species. Ho and Ané (2014) showed that these matrices have a three-point structure, enabling linear time algorithms for computing determinants and inverses. While existing methods do make use of these algorithms, their current software implementations are not computationally efficient, are largely restricted to frequentist inference, and do not support multiple observations per species with appropriate uncertainty quantification at scale.

In this work, we propose a new Bayesian phylogenetic modelling framework that addresses these limitations. It enables large scale inference on species traits with appropriate uncertainty quantification. We develop a computationally optimised implementation of the phylogenetic model that is an order of magnitude faster than existing software. This is embedded within a Bayesian framework, which easily allows us to accommodate multiple observations per species through a latent variable approach. Hence, we can capture within-species trait variation at scale, without inflating the dimensionality of the phylogenetic covariance matrix.

Through comparative analysis of our approach, we show that the model reliably recovers evolutionary and co-evolutionary rates. We then apply the method to a subset of the plant family, integrating multiple observations per species and multiple traits to produce species-level estimates with calibrated uncertainty. Together, these results provide new insight into how these species and their traits have evolved and how they are likely to respond to future climate change. Future work will allow us to scale the method to all plant species, supporting the identification of the species that are the most at risk under climate change and thus informing conservation priorities.