Rensch's Rule Research Articles

Sexual size dimorphism as a determinant of fighting performance dimorphism in Anolis lizards.

Rensch's Rule describes a pattern of interspecific allometry in which sexual size dimorphism (SSD) increases with size among closely related species (i.e., among a group of related species, the largest ones tend to show more male-biased SSD). Sexual selection is often invoked to explain Rensch's Rule, as larger male body size is assumed to be favoured by sexual selection for increased fighting performance in contests for mating opportunities. Often, however, the correlation between size and performance is not well described. We studied a sexually selected performance trait, bite force in Anolis lizards, to determine whether patterns of SSD are linked to size-associated patterns of performance dimorphism at the macroevolutionary level, as expected under the sexual selection hypothesis for Rensch's Rule. Additionally, we tested whether allometric patterns of performance dimorphism differ between mainland and island species, as the latter have likely evolved under a stronger sexual selection regime. We found that SSD overwhelmingly explains the relationship between performance dimorphism and size in anoles, as expected under a sexual selection model for Rensch's Rule. However, residual performance dimorphism was higher in island than in mainland species, suggesting that these groups differ in performance dimorphism for reasons unrelated to size. Head size dimorphism was associated with residual performance dimorphism, but did not fully explain the difference in performance dimorphism between island and mainland species. Together, these findings highlight the need to interpret Rensch's Rule patterns of body size evolution cautiously, as allometric patterns of performance dimorphism and size dimorphism might not be equivalent.

Among-population variation in sexual size dimorphism of Nepa cinerea (Heteroptera: Nepomorpha)

AbstractNepa cinerea is a common aquatic predator. It is widely distributed in various aquatic biotopes of the Palaearctic. Body size is an important trait that impacts the fitness and survival of animals and thus their evolution. Like most insects, N. cinerea males are smaller than females, but sexual size dimorphism (SSD) has not been investigated. We investigated the extent of SSD, the validity of Rensch's rule, and morphological differences between nine populations based on 51 morphological parameters. Females were found significantly and marginally significantly larger than males in all but one population. However, no difference in body length was found between the populations. Population had a significant effect on 12 traits for females and only on 5 for males, showing that females are more variable than males. Specifically, differences were found in the length of the second and third leg pairs. We did not find any support for the Rensch's rule. Nevertheless, female body size and SDI (sexual dimorphism index) were positively correlated. We suggest that fecundity selection accounts for female-biased SSD in N. cinerea.

Sexual Size Dimorphism in 28 Neotropical Bat Species Fails to Obey Rensch's Rule

Sexual Size Dimorphism in 28 Neotropical Bat Species Fails to Obey 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.

The macroevolutionary dynamics of mammalian sexual size dimorphism.

Sexual size dimorphism (SSD) is a common phenomenon across the animal kingdom. Mammals are unusual in primarily displaying male-biased SSD, where males of a species are typically larger than females. The driving factors behind the evolution of this SSD have been much debated, with popular hypotheses invoking the influence of mating system and social organization via sexual selection, dietary niche divergence and broad-scale correlations with body size (Rensch's rule). Here, we investigate the macroevolutionary origins and maintenance of SSD among mammals, using phylogenetic general mixed linear models and a comprehensive global dataset to evaluate correlations of diet, body mass, seasonality, social organization and mating system with SSD type. We find that SSD as a whole is lost at a greater rate than it is gained, with female-biased SSD being particularly unstable. Non-monogamous mating systems, vertebrate prey consumption and temperature seasonality correlate with male-biased SSD, while polyandry correlates with female-biased SSD, and both types of SSD are positively correlated with body mass. This is in partial contrast to the predictions of Rensch's rule, which predicts that female-biased SSD would correlate negatively with body size. Taken together, our results highlight the importance of considering multiple ecological and social drivers when evaluating the macroevolutionary trajectory of sex differences in body size.

Rensch's rule: linking intraspecific to evolutionary allometry.

Sexual dimorphism describes phenotypic differences between the sexes; the most prominent of which is sexual size dimorphism (SSD). Rensch's rule (RR) is an allometric trend in which SSD increases in male-larger taxa and decreases in female-larger ones. Covariation between a trait and overall size within and across species can both be affected by sexual and natural selection. Thus, intraspecific allometric variation could influence the expression of RR. Here we used computer simulations to dissect how RR emerges under specific allometric patterns of intraspecific sexual differentiation in a trait. We found that sexual differentiation in static allometric slopes is the main determinant of RR. Based on our findings, RR and its converse can manifest in both body size and other traits. As a realistic showcase, we also examined RR and static allometry of different body parts in Mediterranean green lizards to establish whether intraspecific and evolutionary allometry are linked. Here, we identified RR and its converse for different traits, where the amount of sexual differentiation in static allometric slopes within species had a significant contribution to RR. Integrating the simulations and the empirical case we corroborate that sexual differentiation in static allometric slopes is a major parameter affecting evolutionary allometry.

Morphological variability or inter-observer bias? A methodological toolkit to improve data quality of multi-researcher datasets for the analysis of morphological variation.

The investigation of morphological variation in animals is widely used in taxonomy, ecology, and evolution. Using large datasets for meta-analyses has dramatically increased, raising concerns about dataset compatibilities and biases introduced by contributions of multiple researchers. We compiled morphological data on 13 variables for 3073 individual mouse lemurs (Cheirogaleidae, Microcebus spp.) from 25 taxa and 153 different sampling locations, measured by 48 different researchers. We introduced and applied a filtering pipeline and quantified improvements in data quality (Shapiro-Francia statistic, skewness, and excess kurtosis). The filtered dataset was then used to test for genus-wide sexual size dimorphism and the applicability of Rensch's, Allen's, and Bergmann's rules. Our pipeline reduced inter-observer bias (i.e., increased normality of data distributions). Inter-observer reliability of measurements was notably variable, highlighting the need to reduce data collection biases. Although subtle, we found a consistent pattern of sexual size dimorphism across Microcebus, with females being the larger (but not heavier) sex. Sexual size dimorphism was isometric, providing no support for Rensch's rule. Variations in tail length but not in ear size were consistent with the predictions of Allen's rule. Body mass and length followed a pattern contrary to predictions of Bergmann's rule. We highlighted the usefulness of large multi-researcher datasets for testing ecological hypotheses after correcting for inter-observer biases. Using genus-wide tests, we outlined generalizable patterns of morphological variability across all mouse lemurs. This new methodological toolkit aims to facilitate future large-scale morphological comparisons for a wide range of taxa and applications.

When Rensch meets Foster: insular gigantism may reduce sexual dimorphism in anurans

According to the Island rule, insular populations exhibit gigantism in small species and dwarfism in large species. These contexts offer opportunities to test for complementary aspects pertaining to the evolution of body size, and particularly sexual size dimorphism (SSD). ‘Rensch's rule' states that SSD should vary with increasing body size, depending on the larger sex. As a consequence, it is expected that dwarfism or gigantism occurring in insular populations should influence the magnitude of SSD. Using anuran amphibians as a study system (because most anuran species express a female‐biased SSD and a marked lability in size), we investigated our hypothesis both in a specific comparison of continental and insular populations of a widespread coastal amphibian, and using a large‐scale analysis across anurans (10 species across 62 sites). Both datasets yielded similar results, with increasing body size in insular populations reducing the magnitude of SSD through an increase of male body size, as expected by Rensch's rule. Detailed data on insular populations considering both sexes are scarce, and future studies are required to complement the existing literature in order to test for the validity of our hypothesis at a wider scale and to infer the mechanistic causes of size variations, which remain unknown. In addition, further investigations are required to explore the consequences of insularity on the magnitude of SSD including various taxa (e.g. mammals, birds, lizards and snakes) in which the Island rule has found support, and considering taxa in which males are the larger sex.Keywords: amphibians, body size, insularity, Island rule, Rensch's rule, sexual dimorphism

Sexual dimorphism in body size and some exterior traits of pigeon breed groups

In this study, sexual dimorphism in pigeons was investigated. Rensch's rule was evaluated across pigeon breeds. Body weight, body length, beak length, wingspan, tail length, and tarsus length were used for the analysis. We have divided the breeds in the five groups (form, frills and owls, tumbler and rollers, homer and highflyer, feral). The allometric relation in the traits between female and male measures were analyzed. The measure of sexual size dimorphism was measured for each trait as a simple male size divided by female size (Sexual Size Index, SSI). On average across traits, male birds have higher values than female birds, both across breed groups and overall. No deviation from isometric allometry can be observed except the tail length. No trends towards logarithmic female values according to the SSI could be identified. According to the results, the rules of Rensch for pigeon breeds are rejected. Sexual dimorphism exists between breeds and traits, mainly in favor of the male birds. In most cases, allometric relationships between breeds change, as do traits.

Influence of microhabitat, fecundity, and parental care on the evolution of sexual size dimorphism in Caribbean Eleutherodactylus frogs.

Rensch's rule suggests that sexual size dimorphism (SSD) increases with species size when males are the larger sex, whereas it decreases when females are the larger sex. However, the process responsible for this pattern remains obscure. SSD can result from sexual selection, such as intrasexual competition for access to mates, or from natural selection, due to resource partitioning or fecundity selection. We studied SSD in Caribbean Eleutherodactylus frogs using phylogenetic comparative methods to investigate the influence of microhabitat, fecundity, and parental care. Our results show that in Caribbean Eleutherodactylus females tend to be larger and, contrary to Rensch's rule, dimorphism increases with species size. SSD was not related to microhabitat use. However, SSD was positively correlated with fecundity, mediated by a greater increase in female size. SSD was also influenced by parental care, suggesting that male care promotes larger male size and reduces the female bias in SSD. As suggested for other anurans, female-biased SSD in Caribbean Eleutherodactylus results from fecundity selection, although the magnitude is countered by increased male size in species with paternal care. Our results highlight the importance of considering various selective forces that may act in concert to influence the evolution of SSD.

Converse of Rensch's Rule is not Necessarily True in Millipedes

Previous studies on Rensch's rule showed tests in the Diplopoda. These produced correct results of hypo-allometry however they were somewhat misinterpreted. The original corroboration of the rule appeared to be incorrect.

Does sexual size dimorphism vary with female size in forest millipedes Centrobolus Cook, 1897?

This study aimed to determine whether the variation responsible for breaking Rensch's Rule when Sexual Size Dimorphism (SSD) increased with body size was due to male-biased or female-biased variation by studying a sex-based set of morphological characters. Variation in female volume based on length and width measurements was associated with the SSD in the forest millipede genus Centrobolus. There was a significant positive correlation between SSD and female size (r=0.56, Z score=2.76, n=22, p

Evolution of sexual dimorphism in an endemic toad of the Qinghai–Tibet plateau fails to obey Rensch’s rule

According to Rensch's rule, sexual size dimorphism (SSD) decreases with increasing body size in species where females are larger than males, whereas SSD increases with body size when males are larger than females. In this study, we examined body size from 15 populations of Bufo minshanicus in the Qinghai–Tibet plateau in China. We estimated the age of the individuals from eight populations to evaluate Rensch's rule and possible causes of variation in SSD. After or before correcting male and female body size for age differences, the patterns of SSD failed to obey Rensch's rule or its inverse, even though fecundity selection in toads tends to favor larger female body size. We also found that the degree of SSD was positively correlated with the operational sex ratio in the field across B. minshanicus populations. Thus, sexual and fecundity selection play an equal role driving the evolution of SSD within toads. In addition, sex-specific growth rate and age structure explain part of the variation observed in SSD across populations.

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.

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

In many species, sexual dimorphism increases with body size when males are the larger sex but decreases when females are the larger sex, a macro-evolutionary pattern known as Rensch's rule (RR). Although empirical studies usually focus exclusively on body size, Rensch's original proposal included sexual differences in other traits, such as ornaments and weapons. Here, we used a clade of harvestmen to investigate whether two traits follow RR: body size and length of the fourth pair of legs (legs IV), which are used as weapons in male-male fights. We found that males were slightly smaller than females and body size did not follow RR, whereas legs IV were much longer in males and followed RR. We propose that sexual selection might be stronger on legs IV length than on body size in males, and we discuss the potential role of condition dependence in the emergence of RR.

Sexual size dimorphism and its allometry in Chinese lizards

Rensch's rule is an allometric rule on sexual size dimorphism. It states that in small-sized species, females are larger than males, whereas in larger species, males are relatively larger than females. Several studies have explored this pattern, and its inverse in lizard species. China has a unique and high diversity of species, with a variety of ecological systems which shape diversity of phenotypes. In this study, sexual size dimorphism and Rensch’s rule were determined using a dataset of Chinese lizard species. The findings show that Chinese lizards generally exhibit female-biased sexual size dimorphism. In addition, clutch size was positively correlated with sexual size dimorphism. Agamidae species were the only taxa that followed Rensch’s rule (slope of males against females was steeper than 1). Clutch size was correlated with sexual size dimorphism in groups that do not follow Rensch's rule. This finding implies that strong fecundity selection limits application of Rensch's rule in these groups.

Rensch’s rule—Definitions and statistics

AbstractIssueSexual size dimorphism is thought to vary in a predictable manner with overall body size, a pattern named “Rensch's rule”. The rule is thought to suggest different predictions for taxa with female‐ and male‐biased dimorphism. This leaves taxa where both types of dimorphism are common in limbo. Rensch's rule is usually estimated using the reduced major axis (RMA) slope of a regression of male size on female size. A slope steeper than one shows support for the rule.EvidenceWe show that the predictions of Rensch's rule for male‐ and female‐biased taxa are, in fact, the same and offer a unified definition of the rule. Using numerical examples and data from the literature, we show that RMA and ordinary least squares (OLS) methods of line fitting can produce conflicting results, suggesting that RMA is a less conservative way to test the rule.ConclusionWe recommend that both line‐fitting methods are used to estimate Rensch's rule, with strong support being claimed only when the results of both agree with each other. Alternatively, we suggest that tests are conducted in a way that agrees with the definition of the rule (i.e., that size dimorphism is regressed on the mean size of males and females of the species).

Is body size a good indicator of fecundity in the genus Thaumetopoea? A story told by two intrageneric Mediterranean forest defoliators

Abstract Body size correlates with several factors such as reproductive fitness, environmental changes, the quality and quantity of food during critical development stages, and the feeding season. For the Palearctic moths of the genus Thaumetopoea (Lepidoptera; Notodontidae), the larval development is crucial and differs between species according to their feeding season; larvae of the pine processionary moth Thaumetopoea pityocampa (Denis & Schiffermüller 1775) feed during winter while larvae of its congeneric cedar processionary moth Thaumetopoea bonjeani (Powell 1922) develop during summer in North Africa. This discrepancy in lifecycles leads to different reproductive traits such as egg batch length, number of eggs per batch, eggs protection mechanisms and female body size. According to Darwin's fecundity advantage hypothesis (1871), female body size should have a positive influence on reproductive fitness, since larger females supposedly have higher fecundity. The universal allometric scaling phenomenon rule proposed by Rensch (1950) predicts that the degree of sexual size dimorphism tends to decrease with the increase of female body size. Here, two morphometrical parameters that is, body size and scale size, estimated from body measurements of individuals of both species, feeding on the same host Atlantic cedar Cedrus atlantica (Manetti & Carrière 1855) (Pinales; Pinaceae) in Algeria were proposed. The aim was to find out traits that might rule the competition for food and space, in particularly fecundity and body size. Results of the present study highlight a female‐biased sexual size dimorphism in both species. The positive correlation between female body size and fecundity shown in this study weakly supports Darwin's hypothesis. Finally, the intrageneric test performed leads to conclude that Rensch's rule does not hold in the considered species.

Not playing by the rules: mixed support of ecogeographic rules in an arid‐adapted African ground squirrel

AbstractBody size impacts nearly all aspects of an animal's life and can be subject to considerable variation in response to differences in climate and resource availability. We studied the impact of temperature and resource availability on arid‐living Cape ground squirrels (Xerus inauris), relative to body size and degree of sexual dimorphism, over three locations differing in annual rainfall and temperature to test Bergmann's rule, the resource rule and Rensch's rule. We found that squirrels were the largest where resources were the highest and temperatures were the lowest but squirrels were similar in mass where resources were medium or low and temperatures medium and highest, partially supporting Bergmann's rule and the resource rule. Hind‐feet were the largest where resources were medium and temperatures were medium and similarly small in low and high resource and high‐ and low‐temperature areas. The degree of sexual dimorphism of hind‐foot and mass was constant no matter the resource abundance or temperature, suggesting no impact of resource availability or temperature on the degree of sexual dimorphism, contradicting Rensch's rule. Our findings suggest that, while resource availability and temperature may have an impact on body size, other mechanisms may be important in limiting both body size and degree of sexual dimorphism in this species.

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 underliethem.