Anole Bites Help Us Rediscover Rensch’s Rule

What Rensch (really) found there

Rensch’s rule is one of the great macroevolutionary patterns studied by evolutionary biologists. It describes the positive association between male-biased sexual size dimorphism (SSD) and species size, a relationship that has been observed in many different taxa (although it is certainly not a generalizable pattern). Since 1950, year in which Bernhard Rensch described the rule for the first time, different hypotheses for its emergence have been proposed and tested, those involving sexual selection being the most popular. For example, male-biased SSD is likely to evolve in species where larger sizes provide males of fighting advantages in encounters with other males. Moreover, female size might subsequently evolve to be larger (although to a lesser extent) due to correlated selection and/or genetic correlation. In the end, the average size of the species increases together with male-biased SSD, and we could expect this effect to be stronger in species experiencing intense sexual selection regimes.

The study of Rensch’s rule patterns has increased exponentially in the last decades, providing us with important insights about the evolution of body size and sexual dimorphism. However, I recently found out that the definition of Rensch’s rule used by most researchers is not accurate. Rensch’s rule was an important concept during my PhD so I got interested in its history and particularly in its origin. After some time spent checking old books and papers (and getting some of them translated from German) I found the truth! Rensch was not only interested in the relationship between SSD and size, but in the relationship between ANY relative sexual difference and size. The Rensch’s rule we know of today is just a special case of a more general rule! And most people seem to have ignored this for decades!

Although I was not the first to notice this inconsistency between past and present definitions (e.g., see Adams et al., 2020), I realized that a concrete presentation of this problem was needed, especially because the frequency at which Rensch’s rule studies are being published is increasing. For this reason, I decided to write a historical perspective on Rensch’s rule with a detailed explanation of this historical inaccuracy and its possible consequences (see Toyama, 2024). Part of that work is also about how testing Rensch’s rule in traits other than body size (as Rensch originally did) might illuminate other aspects of sexual dimorphism. And here is where anoles can help us, keeping the tradition of being great systems for pretty much everything.

As shown in a later figure below, anoles follow Rensch’s rule (or better said, anole body size follows Rensch’s rule). Knowing that, in many species, males fight other males for access to females (specifically biting each other), sexual selection is a likely explanation for the emergence of this pattern in anoles. But testing Rensch’s rule solely in body size might not tell us much about the nature of the performance advantage provided by a size increase. Are patterns of size dimorphism mirrored by patterns of performance (i.e., biting) dimorphism? We tested this with the help of anoles in a recent paper (Toyama et al., 2024).

Testing the original Rensch’s rule in anole bite force

First, we proposed that, given a system in which body size follows Rensch’s rule (like anoles), at least 3 alternatives are possible regarding relative sexual differences in performance (e.g., bite force):

The top row shows 3 different scenarios regarding the evolutionary allometries of male and female performance. Notice how none of them is incompatible with Rensch’s rule in body size. The bottom row shows the allometry of relative (i.e., size-corrected) performance dimorphism. Does this sound familiar? Maybe not, but the bottom row can actually show whether performance follows Rensch’s rule! Remember, Rensch’s originally rule was concerned with the relationship between ANY relative sexual difference and size. The first column shows what happens when males and females follow the same allometric relationship across species (same slope and intercept, panel A). In this case, relative performance dimorphism should be zero across species sizes (D), because once size is corrected for, no other factor can result in differences between sexes. In this first scenario size is the only factor behind performance dimorphism. Notice that Rensch’s rule is not observed in performance (no positive association in the lower panel), meaning that, if anoles were to follow this scenario, males from larger species would not bite disproportionately harder than females given their size difference (although it would still be true that the difference in raw bite force would be higher in species with higher SSD).

Things change in the next two columns. In the second one (B), performance trajectories in males and females still have the same allometric slope. However, the intercept is higher for males. Size-correcting performance and calculating dimorphism will result again in no relationship between relative performance dimorphism and size (i.e., no Rensch’s rule in performance), but the intercept difference will result in relative dimorphism being higher than zero (E). Finally, in the last scenario males and females show different allometric slopes (C). In this case, the more positive slope of males results in a positive relationship between relative performance dimorphism and species size (F). In other words, Rensch’s rule is true for body size AND performance. In anoles, this would mean that males from larger species are (1) larger in size than females and (2) bite disproportionately harder than females given their size difference when compared to males from smaller species.

In summary, testing Rensch’s rule in body size and performance tells us whether size differences imply, or not, disproportionate differences in performance. Now that we know the theory, let’s test what’s the case for anoles. First, we confirmed that Rensch’s rule is followed by body size in anoles (notice how I specify body size), but we also found that island and mainland anoles show separate relationships (see figure below). Island and mainland anole species likely experience different sexual selection regimes (Andrews, 1976, 1979), so we included insularity as a term in our analyses.

The next step was to test Rensch’s rule in bite force, a measure of fighting performance in anoles. Which of the three scenarios will anoles follow? Surprise! In spite of what we found for body size, biting performance did not follow Rensch’s rule in anoles. See that there is no relationship between relative bite force dimorphism and species size (see figure below). However, we found that island and mainland anoles seem to follow different scenarios. Mainland anoles (in green) seem to be following the first scenario: body size is the only determinant of sexual performance differences (compare with panel D in the 2nd figure above). Island anoles (blue), on the other hand, follow the second scenario. Although independent of species size, relative bite force dimorphism is higher than zero (compare with panel E in the 2nd figure above).

The second scenario implies that there is “something” causing an intercept difference between the performance allometries of males and females (see panel B in the 2nd figure above). Robust heads are known to be associated with bite force in different lizard species, and head shape might not be adequately represented by traditional measures of body size like SVL, so relative head size seemed to be a good candidate to explain this difference between island and mainland species. Let’s see…

Our tests showed that, although relative head size dimorphism explained relative bite force dimorphism to some extent (see the significant positive relationship between them), some residual difference in performance dimorphism between island and mainland species was still left unexplained. Muscle morphology? Physiology? Behaviour? Seems that additional factors not considered by us also contribute to this difference, pointing towards future opportunities for exploration.

In summary, our results show how male biting performance is influenced by SSD in Anolis lizards. It seems that, relative to females, male anoles do not get disproportionate evolutionary enhancements in biting performance through an increase in size (i.e., the sexual differences in bite force are proportional to the sexual differences in size). However, we found that a robust head seems to be a size-independent fighting adaptation in insular male anoles that causes a difference in the degree of relative performance dimorphism shown by island and mainland species. These results illustrate well how testing Rensch’s rule in body size AND other traits, including performance, can increase our understanding of the functional drivers and consequences of the evolution of sexual dimorphism. The rediscovery of Rensch’s original rule presents innumerable opportunities for future research, and anoles have just shown us one of them!

 

References

Adams, D. C., Glynne, E., & Kaliontzopoulou, A. (2020). Interspecific allometry for sexual shape dimorphism: Macroevolution of multivariate sexual phenotypes with application to Rensch’s rule. Evolution, 74(9), 1908-1922. https://doi.org/10.1111/evo.14049

Andrews, R. M. (1976). Growth rate in island and mainland anoline lizards. Copeia, 1976(3), 477–482. https://doi.org/10.2307/1443362

Andrews, R. M. (1979). Evolution of life histories: A comparison of Anolis lizards from matched island and mainland habitats. Breviora, 454, 1–51.

Toyama, K. S. (2024). Beyond size dimorphism: the past, present, and future of Rensch’s Rule. bioRxiv, 2024-10. https://doi.org/10.1101/2024.10.30.621038

Toyama, K. S., Losos, J. B., Herrel, A., & Mahler, D. L. (2024). Sexual size dimorphism as a determinant of fighting performance dimorphism in Anolis lizards. Journal of Evolutionary Biology, voae148. https://doi.org/10.1093/jeb/voae148