Interspecific allometry for sexual shape dimorphism: Macroevolution of multivariate sexual phenotypes with application to Rensch's rule

Abstract

Allometric trends in the degree of sexual dimorphism with body size have long fascinated evolutionary biologists. Many male‐biased clades display more prominent sexual dimorphism in larger taxa (Rensch's rule), with most examples documenting this pattern for body size dimorphism. Although sexual dimorphism in traits other than body size is equally functionally relevant, characterizing allometric patterns of sexual dimorphism in such traits is hampered by lack of an analytical framework that can accommodate multivariate phenotypes. In this article, we derive a multivariate equivalency for investigating trends in sexual dimorphism—relative to overall body size—across taxa and provide a generalized test to determine whether such allometric patterns correspond with Rensch's rule. For univariate linear traits such as body size, our approach yields equivalent results to those from standard procedures, but our test is also capable of detecting trends in multivariate datasets such as shape. Computer simulations reveal that the method displays appropriate statistical properties, and an empirical example in Mediterranean lizards provides the first demonstration of Rensch's rule in a multivariate phenotype (head shape). Our generalized procedure substantially extends the analytical toolkit for investigating macroevolutionary patterns of sexual dimorphism and seeking a better understanding of the processes that underlie them.

Evolutionary allometry of sexual dimorphism of jumping performance in anurans

“…test to determine if the true slope differs from b 0 1 = . There has been considerable discussion in the allometric literature as to whether model I or model II regression is more appropriate, in part because species values for both males and females are measured with error (see e.g., Wharton et al 2006;Bonduriansky 2007;Ives et al 2007;Hansen and Bartoszek 2012;Killmer and Rodríguez 2017;Adams et al 2020). However, as pointed out by Kilmer and Rodríguez (2017), when measurement error variance is small in proportion to total variance, slope attenuation is limited, and slopes from model I regression are robust.…”

“…However, natural and sexual selection may result in sexual dimorphism in traits other than body size. These include, for example, coloration, behavioral, physiological traits, or shape (Endler 1984;Price and Birch 1996;Adams et al 2020;Logan et al 2021). Importantly, behavioral or functional traits, such as climbing or jumping, which are typically characterized as measures of maximum or 'peak' performance, will respond directly to selection (Arnold 1983).…”

It is not always about body size: evidence of Rensch's rule in a male weapon

“…The two hypotheses above should also apply to traits other than body size. When a sexually dimorphic trait occurs in both sexes, but is under directional sexual selection in males only, a pattern consistent with RR should emerge [10]. In fact, although almost all studies on RR focus on body size, Rensch's original proposal was broad in scope and included sexual differences in other traits [1,10].…”

“…In fact, although almost all studies on RR focus on body size, Rensch's original proposal was broad in scope and included sexual differences in other traits [1,10]. Accordingly, recent studies with sexually selected male traits, such as wing pigmentation in dragonflies [11] and head shape in lizards [10], showed patterns consistent with RR. To our knowledge, however, there are no studies showing that RR applies to sexually selected traits that are present in both © 2021 The Author(s) Published by the Royal Society.…”

“…When a sexually dimorphic trait occurs in both sexes, but is under directional sexual selection in males only, a pattern consistent with RR should emerge [10]. In fact, although almost all studies on RR focus on body size, Rensch's original proposal was broad in scope and included sexual differences in other traits [1,10]. Accordingly, recent studies with sexually selected male traits, such as wing pigmentation in dragonflies [11] and head shape in lizards [10], showed patterns consistent with RR.…”