Complementarity in Allen's and Bergmann's rules among birds

Abstract

Biologists have long noted that endotherms tend to have larger bodies (Bergmann's rule) and shorter appendages (Allen's rule) in colder environments. Nevertheless, many taxonomic groups appear not to conform to these 'rules', and general explanations for these frequent exceptions are currently lacking. Here we note that by combining complementary changes in body and extremity size, lineages could theoretically respond to thermal gradients with smaller changes in either trait than those predicted by either Bergmann's or Allen's rule alone. To test this idea, we leverage geographic, ecological, phylogenetic, and morphological data on 6,974 non-migratory terrestrial bird species, and show that stronger family-wide changes in bill size over thermal gradients are correlated with more muted changes in body size. Additionally, we show that most bird families exhibit weak but appropriately directed changes in both traits, supporting the notion of complementarity in Bergmann's and Allen's rules. Finally, we show that the few families that exhibit significant gradients in either bill or body size, tend to be more speciose, widely distributed, or ecologically constrained. Our findings validate Bergmann's and Allen's logic and remind us that body and bill size are simply convenient proxies for their true quantity of interest: the surface-to-volume ratio.

Fig. 1. Complementarity between Bergmann’s and Allen’s rules.

While some bird families conform to either Bergmann’s rule or Allen’s rule, most families conform to neither. For example, while owls exhibit significant changes in body but not bill size (red in a and b) and flycatchers exhibit significant changes in bill but not body size (blue in a and c), ducks exhibit instead complementary changes in both body and bill size that are subtle and difficult to detect statistically even though they exhibit the same trends that were predicted by Bergmann and Allen (purple in a and d). Symbols in scatterplots depict the species highlighted in a. Regression lines highlight conformance to rules (solid red/blue—significant conformance; loosely dashed black– non-significant change in one of bill or body size; densely dashed purple—non-significant trend in both bill and body sizes). We thank Gregory “Slobirdr” Smith, Ayna Cumplido, Félix Uribe, N. Hanuise, Ron Knight, John G. Keulemans, xgirouxb, and Andy Wilson for making their artwork and photos available on Wikimedia Commons and Phylopic under Creative Commons license CC-BY-SA (see Supplemental Information; https://creativecommons.org/licenses/by-sa/4.0/).

Fig. 2. Potential effects of complementarity in Bergmann’s and Allen’s rules.

Bergmann noted that changes in surface and volume typically accrue at different rates such that when body size decreases, the surface-to-volume ratio, SVR—and thereby the ability to dissipate heat—also increases (a). Similarly, Allen noted that appendages like the beak already have high SVRs so that when they become larger, SVR also increases (b). Here we note that by combining small changes in both traits, lineages can achieve comparable changes in their SVR without drastically altering their morphology and, presumably, their ecology (c). Depicted examples were simulated by approximating a bird’s body with two spheres and one cone (cartoon depictions were drawn to exemplify the potential subtlety of these changes). Parameter values: Body size reduction factor in a = 1%; Beak size increase factor in b = 13.7% (volume to volume); Body size reduction factor in c = 0.5%; and beak size increase factor in c = 5.5%.

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.

Fig. 4. Family-level traits are associated with conformity to Bergmann’s and Allen’s rules.

Cladogram without branch-length information showing family-level conformity to Bergmann’s (red) and Allen’s rule (blue). Icons depict representative taxa from conforming families and the asterisk denotes the ancestral node of passerines. Bill specialization can be estimated through bill shape characterization through a geometric morphometrics approach (see methods, i.e., contour lines for kernel densities in a–c indicate the rarity of a given shape). Silhouettes represent bill shapes that correspond to positions in PC 1 and 2. Families that conform to Bergmann’s rule (red circles) tend to occur in the periphery of bill morphospace (a), whereas families that either conform to Allen’s rule (blue circles) or neither rule (gray circles) tend to be more centrally located (b, c). Randomization models indicate that family-level factors that increase statistical power (i.e., extent of the temperature gradient for Bergmann, d, and sample size for both Bergmann and Allen, e) or that indicate bill specialization (f) tend to be higher in families that conform to these biological rules. Column heights in d–f depict family means and violin plots depict variation in the number of species per family across the range of each variable of interest. Randomization tests (g–i) confirm findings in a–f by showing that the corresponding observed values for these traits (arrows) lie outside the 95% interval of their expected null distribution (gray dashed lines). We thank Andy Wilson, xgirouxb, Ferran Sayol, Margot Michaud, Liftarn, Abraão B. Leite, Michael Scroggie, Metallura and Martin Bulla making their artwork available on Phylopic under Creative Commons licenses (CC-BY-SA, CC-BY, CC0—see Supplemental Information; https://creativecommons.org/licenses/by-sa/4.0/).