Fig. 3. Bill and body size variation in birds reveals alternative pathways of thermal adaptation.

a Bill size scales allometrically with body size (brighter colors indicate higher species counts; N = 6,974). b In analyses with relative bill sizes, we detect no correlation between the strength of Bergmann’s rule (i.e., −1 times the family-wise slope estimates from a model of body size as a function of mean annual temperature) and that of Allen’s rule (i.e., family-wise slope estimates from a model of bill size as a function of mean annual temperature; metaregression slope = 0.006; 95% CI = −0.074 to 0.089) and we find that 17 families conform to Allen’s rule (blue circles), 2 conform to Bergmann’s rule (red circles), 2 conform to both rules (purple), and 78 conform to neither (gray). c In contrast, similar analyses with absolute bill size, a better proxy for surface area, indicate that more pronounced changes in one trait are correlated with more muted changes in the other (solid black line depicts the metaregression fit: slope = −0.232; 95% CI = −0.322 to −0.150). In this version of our analysis, the number of families that do not exhibit any significant morphological changes increases to 87 and no families simultaneously conform to both rules. Circle sizes in b and c depict the number of species sampled within a family, whereas vertical and horizontal whiskers depict the 95% posterior credible interval of the estimated slopes.