Female-biased gape and body-size dimorphism in the New World watersnakes (tribe: Thamnophiini) oppose predictions from Rensch's rule

Sharks Violate Rensch's Rule for Sexual Size Dimorphism

Systematic trends in body size variation exist in a multitude of vertebrate radiations, however their underlying ecological and evolutionary causes remain poorly understood. Rensch's rule describes one such trend-in which the scaling of sexual size dimorphism (SSD) depends on which sex is larger. Where SSD is male-biased, SSD should scale hyperallometrically, as opposed to hypoallometrically where SSD is female-biased. The evidence for Rensch's rule is mixed, and comes from a small subset of total vertebrate diversity. We conducted the first empirical test of Rensch's rule in sharks, seeking to confirm or refute a long-hypothesied trend. We find that sharks violate Rensch's rule, as the magnitude of SSD increases with body size despite sharks predominantly exhibiting female-biased SSD. This adds to a growing literature of vertebrate clades that appear not to follow Rensch's rule, suggesting the absence of a single, conserved scaling trend for SSD amongst vertebrates. It is likely that selection associated with fecundity results in the "inverse Rensch's rule" observed in sharks, although additional studies will be required to fully reveal the factors underlying SSD variation in this clade.

Sex estimation from morphology in living animals and dinosaurs

Sexual dimorphism is a prevalent feature of sexually reproducing organisms yet its presence in dinosaurs has recently been questioned. However, the inferred absence of sexual dimorphism may be a methodological artefact, rooted in the lack of systematic knowledge concerning how sexual dimorphism of living animals behaves statistically. To start building such knowledge, I re-analysed published data of 139 species of living animals that are sexually dimorphic. The previous method used for dinosaurs recognized only 5% of the living species correctly as dimorphic. This low rate is largely caused by the tilting of ordinated multivariate space due to interactions between size and shape dimorphisms, low signal/noise ratios and inclusion of outliers. The rate can be improved to 50% by modifying the method but not further, unless the information on the sex of individual specimens is used. Such information is unavailable in dinosaurs, so sexual dimorphism probably cannot be established for a large proportion of sexually dimorphic dinosaurs. At the same time, about 32% of the 139 are strongly sexually dimorphic, and can be re-sexed from shape with misclassification rates below 0.05. A reassessment of dinosaurian data suggests that sexual dimorphism likely existed at least in some species, such as Allosaurus fragilis.

Sexual size dimorphism in lizards: Rensch's rule, reproductive mode, clutch size, and line fitting method effects

Rensch's rule relates to a pattern whereby sexual size dimorphism is more female-biased in small-sized species and more male-biased in large-sized ones. We collected literature and museum data on the body size of males and females belonging to 4032 lizard species, as well as data on their reproductive modes and clutch sizes. We used phylogenetic comparative analyses, and general linear mixed models, to test Rensch's rule and examined how reproductive mode and clutch size affect sexual size dimorphism. Sexual size dimorphism was independent of clutch size in lizard species with variable clutch sizes and in oviparous lizards. Large litters were associated with female-biased sexual dimorphism in viviparous and in scincomorph lizards. Inference regarding Rensch's rule depended on the analytical method used to identify it. The widely used, but less conservative, reduced major axis regression usually support Rensch's rule while ordinary least squares regressions mostly show isometric relationships. The rule tended to apply more to oviparous than to viviparous lizards. We infer that Rensch's rule is, at best, a weak pattern in lizards. This is especially true in viviparous lineages where females reproduce infrequently and therefore evolve large sizes to maximise fecundity, resulting in female-biased dimorphism.

Sex-specific growth is mirrored in feeding rate but not moulting frequency in a sexually dimorphic snake

Sexual size dimorphism (SSD), commonly observed in snakes, may arise from a different growth rate between the sexes. This indicates a sex-specific resource intake that is in fact observable in free-living snakes. It is not so well known whether the sexes can express differential feeding rates under conditions unconstrained by spatial accessibility, competition, etc. Here, I studied sex-specific variation in growth, its correlate-moulting frequency, and feeding rate in a captive group of sexually dimorphic banded water snakes (Nerodia fasciata) with access to food unconstrained by predation, competition or space. I showed that the sexes did indeed differ in relative mass growth in that females grew faster than males (p = 0.02), but such differences were not apparent in the moulting rate (p = 0.19). Such differential growth was mirrored in the sex-specific feeding rate, with females ingesting a larger number of meals than males (p = 0.004). Such variation in feeding rate may be governed by an individual's energy expenditure and can be interpreted as a behavioural tendency that contributes to SSD development, independently of other behavioural characteristics. Sex-specific resource demands may drive the differential effects of increasing resource scarcity on both sexes.

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

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.