Pie, M. R.

Climate is a strong predictor of global species richness, but the effects of climatic conditions are difficult to separate from the geography of the climates themselves. Recent work in climate space has shown that the area and isolation of discrete climatic conditions explain broad-scale richness gradients, yet the internal spatial cohesion of those climates remains poorly characterized. Here, we introduce climate percolation as a complementary descriptor of climate geography, measuring the degree to which the total area of a climate bin is concentrated within effectively connected fragments. Using global range maps for amphibians, birds, mammals and reptiles, we quantified species richness across a two-dimensional climate space defined from 12 climatic variables and evaluated the independent and joint effects of climate area, climate isolation and climate percolation across multiple climate-space resolutions. Climate isolation and percolation were strongly coupled: their first joint axis explained, on average, more than 95% of their shared variation, revealing a dominant gradient of climate fragmentation along which geographically isolated climates are also internally subdivided. Despite this collinearity, percolation consistently outperformed isolation in cross-validation across all four vertebrate groups, with particularly strong predictive gains for birds and mammals. The largest improvements, however, came from the shared isolation percolation axis, indicating that vertebrate richness in climate space is more strongly associated with the integrated geographical structure of climates than with either inter-fragment distance or internal cohesion alone. These results suggest that climate fragmentation is a multidimensional property of environmental space, combining both the distance among climate fragments and the dominance structure of connected areas. By extending climate-space approaches from area and isolation to percolation, our framework provides a more complete description of how the geography of climate may shape global richness gradients and offers a structural basis for anticipating how future changes in climate connectivity could alter biodiversity patterns.