Trait measures are affected by intra- and interspecific variability. Most studies aggregate species-level data to averages to analyze patterns of interspecific variation. Reliable per-species averages require data for many individuals per species, which leads to insurmountable measuring effort when studying species-rich assemblages. Here we argue that across a large number of species, patterns and relationships can be precisely recovered even if they are based on measures from a single individual per species. While these deviate to an unknown degree from the true per-species averages, randomly distributed errors will level out across many species. We used subsamples of body size data along elevational gradients for moths and small mammals (dozens to several hundred species per dataset), as well as simulated species assemblages, to illustrate this effect and explore some of its consequences. Single-individual measures correlated well with “true” (i.e., full data) averages. Furthermore, single-individual measures recovered the same conclusions on elevation-body size relationships as true data. Randomly removing individuals per species recovered true elevation-body size relationships very well, while randomly dropping species quickly led to high random variability in relationships across subsampling runs. Simulated species assemblages illustrated how the ratio of intraspecific to interspecific variability affects the correlation between singleton-based and true data. We conclude that trait measures based on single individuals are a viable alternative to multi-individual averages when analyzing assemblages of medium to high species richness. Reducing study effort by limiting the measurement of individuals per species, while retaining all species, is a much more reliable approach than restricting the number of species included in a study.

We introduce a novel framework for conceptualising, quantifying and unifying discordant patterns of species richness along geographical gradients. While not itself explicitly mechanistic, this approach offers a path towards understanding mechanisms. In this study, we focused on the diverse patterns of species richness on mountainsides. We conjectured that elevational range midpoints of species may be drawn towards a single midpoint attractor - a unimodal gradient of environmental favourability. The midpoint attractor interacts with geometric constraints imposed by sea level and the mountaintop to produce taxon-specific patterns of species richness. We developed a Bayesian simulation model to estimate the location and strength of the midpoint attractor from species occurrence data sampled along mountainsides. We also constructed midpoint predictor models to test whether environmental variables could directly account for the observed patterns of species range midpoints. We challenged these models with 16 elevational data sets, comprising 4500 species of insects, vertebrates and plants. The midpoint predictor models generally failed to predict the pattern of species midpoints. In contrast, the midpoint attractor model closely reproduced empirical spatial patterns of species richness and range midpoints. Gradients of environmental favourability, subject to geometric constraints, may parsimoniously account for elevational and other patterns of species richness.