Measuring the evolution of <i>n</i> ‐dimensional environmental niches

The study of species' environmental niches underpins numerous questions in ecology and evolution and has increasing relevance in a rapidly changing world. Environmental niches, characterized by observations of organisms, inform about a species' specialization in multivariate environment space and help assess their exposure and sensitivity to changing conditions. Environmental niches are also the central concept behind species distribution models (SDMs), which quantify and predict the geographic variation in environmental suitability. Despite the clear role of past evolutionary processes in shaping contemporary biodiversity distribution, the assessment of multivariate or n ‐dimensional (where n is the number of environmental axes) niches in a phylogenetic framework has remained limited and constrained by restrictive assumptions. This hampers important existing and emerging applications, such as assessments of niche conservatism, estimates of species' adaptive potential under changing climates, and prediction of niches in less‐studied parts of the tree of life. Here, we introduce a framework that extends SDMs to estimate n ‐dimensional environmental niches jointly with underlying evolutionary processes. Specifically, we fit the relationship between niche similarity and phylogenetic distance as a latent Gaussian process across all species in a clade. We demonstrate mathematically how the parameters of the Gaussian process can be linked to existing traditional evolutionary models. Simulations indicate that the approach successfully recovers niche and evolutionary parameters. Applied to two clades of hummingbirds, the presented joint framework uncovers the relationships among species' niches in phylogenetic space and supports the quantification and hypothesis testing of niche evolution. A key advantage of the presented framework is its joint estimation of the evolutionary process alongside niches directly from species observations with uncertainty propagated to evolutionary model parameters. The proposed approach has the potential to increase the robustness of inference about niche evolution and improve understanding of how the processes of niche formation and evolution interact.