Extended Data Fig. 7: Effects of sample size differences, spatial autocorrelation and phylogeny on estimates of S_space and S_time.

Comparison of S_space and S_time estimates obtained by (a) homogenizing sample sizes among species, (b) accounting for spatial autocorrelation among observations and (c) accounting for phylogenetic relationships among species against estimates generated ignoring these factors (as those presented in the main text). In (a, b), we fit the model presented in the main text using a thinned dataset were each species was represented by 300 specimens, comparing its output to that of the model in the main text. In (c, d), we compared the results of models omitting or accounting for phylogenetic relationships. We selected a random subset of 300 species from which to generte a phylogeny, thinning these data to include only 300 specimens for each species (to make the model computationally tractable). S_space and S_time estimates that did not account for phylogeny were obtained using the model described in the main text. In turn, the model accounting for phylogeny included a prior for the covariance structure of species-specific parameters consisting of the evolutionary distance between each pair of species as estimated from a phylogenetic hypothesis and a model of trait divergence among species. The phylogenetic tree (or hypothesis) was generated using the R package ‘v.PhyloMaker’ version 0.1.0⁷¹ and generated a phylogeny resovled to the genus level. Using this tree, we then calculated the variance–covariance phylogenetic matrix predicted by a Brownian model of trait evolution using the R package ‘ape’ version 5.6-2⁷². Finally, both models were implemented using the ‘brms’ package version 2.18.0⁷³. Finally, in (e, f) we compared estimates obtained from models ignoring or accounting for spatial autocorrelation of the residuals. All S_space and S_time estimates were obtained using single-species models, but those accounting for spatial autocorrelation included a covariance structure for the residuals determined by the geographic distance between each pair of points. All models were fitted using the’nlme’ package version 3.1⁷⁴ in R. Estimates of S_space and S_time obtained accounting for or ignoring spatial autocorrelation were nearly indentical across species. Across panels, the x-axes show the estimates obtained when omitting the focal factor (sample size, phylogeny, or spatial autocorrelation), whereas the y-axes show estimates obtained when accounting for it. Solid black lines represent a 1:1 line, representing perfect agreement in magnitude and direction between estimates. S_space and S_time estimates obtained ignoring sample size differences, phylogeny and spatial autocorrelation where highly correlated to estimates obtained from models accounting for these factors. Accordingly, we consider it unlikely that omitting these factors could have biased our results.