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.

Testing Rensch’s rule in Acanthoscelides macrophthalmus, a seed-feeding beetle infesting Leucaena leucocephala plants

Rensch’s rule states that males vary more in size than females when body size increases. The main cause of Rensch’s rule has been credited to sexual selection. However, different degrees of plasticity between the sexes have also been proven to be useful for describing variations in sexual size dimorphism, particularly within an intraspecific context. For insects, in general, this rule has rarely been tested within species. Here, we tested whether Acanthoscelides macrophthalmus (Schaeffer, 1907) (Coleoptera: Chrysomelidae: Bruchinae) followed Rensch’s rule when individuals emerged from seeds immediately after fruit collection and when they were reared for one generation, by measuring three morphological traits. Rensch’s rule was not followed for any of the morphological traits. Variations in body size were similar in males and females for bruchines that first emerged from seeds and for those that were reared for one generation. These findings suggest that environmental conditions (e.g., temperature, humidity, and seasonality) are unlikely to drive differential plasticity in males and females of this seed-feeding beetle. It is possible that changes in the body size of A. macrophthalmus have a genetic basis. However, regardless of whether variations in body size have a genetic basis, our findings provide no support for Rensch’s rule.

Lack of support for Rensch's rule in an intraspecific test using red flour beetle (Tribolium castaneum) populations

Rensch's rule proposes a universal allometric scaling phenomenon across species where sexual size dimorphism (SSD) has evolved: in taxa with male-biased dimorphism, degree of SSD should increase with overall body size, and in taxa with female-biased dimorphism, degree of SSD should decrease with increasing average body size. Rensch's rule appears to hold widely across taxa where SSD is male-biased, but not consistently when SSD is female-biased. Furthermore, studies addressing this question within species are rare, so it remains unclear whether this rule applies at the intraspecific level. We assess body size and SSD within Tribolium castaneum (Herbst), a species where females are larger than males, using 21 populations derived from separate locations across the world, and maintained in isolated laboratory culture for at least 20 years. Body size, and hence SSD patterns, are highly susceptible to variations in temperature, diet quality and other environmental factors. Crucially, here we nullify interference of such confounds as all populations were maintained under identical conditions (similar densities, standard diet and exposed to identical temperature, relative humidity and photoperiod). We measured thirty beetles of each sex for all populations, and found body size variation across populations, and (as expected) female-biased SSD in all populations. We test whether Rensch's rule holds for our populations, but find isometry, i.e. no allometry for SSD. Our results thus show that Rensch's rule does not hold across populations within this species. Our intraspecific test matches previous interspecific studies showing that Rensch's rule fails in species with female-biased SSD.

Allometry for Sexual Size Dimorphism in Stoneflies Defies the Rensch's Rule

The Rensch's rule predicts that male-biased sexual size dimorphism (SSD) increases with body size, while female-biased SSD (FBSSD) decreases. In insects, many groups follow this rule, but the evidence suggests that it is taxon dependent and that the inverse of the rule can occur in species with FBSSD. Therefore, we conducted this study with Gripopterygidae stoneflies (Plecoptera) to describe their pattern of SSD and determine if they follow the Rensch's rule. Our data suggest that stoneflies exhibit FBSSD and do not follow the rule, but a reverse pattern. Our results corroborate other studies that suggest that the Rensch's rule is taxon based and that groups with FBSSD usually fail to obey the rule.

Proximate Causes of Rensch’s Rule: Does Sexual Size Dimorphism in Arthropods Result from Sex Differences in Development Time?

A prominent interspecific pattern of sexual size dimorphism (SSD) is Rensch's rule, according to which male body size is more variable or evolutionarily divergent than female body size. Assuming equal growth rates of males and females, SSD would be entirely mediated, and Rensch's rule proximately caused, by sexual differences in development times, or sexual bimaturism (SBM), with the larger sex developing for a proportionately longer time. Only a subset of the seven arthropod groups investigated in this study exhibits Rensch's rule. Furthermore, we found only a weak positive relationship between SSD and SBM overall, suggesting that growth rate differences between the sexes are more important than development time differences in proximately mediating SSD in a wide but by no means comprehensive range of arthropod taxa. Except when protandry is of selective advantage (as in many butterflies, Hymenoptera, and spiders), male development time was equal to (in water striders and beetles) or even longer than (in drosophilid and sepsid flies) that of females. Because all taxa show female-biased SSD, this implies faster growth of females in general, a pattern markedly different from that of primates and birds (analyzed here for comparison). We discuss three potential explanations for this pattern based on life-history trade-offs and sexual selection.

Selection on body size and sexual size dimorphism differs between host species in a seed-feeding beetle

Sexual size dimorphism varies substantially among populations and species but we have little understanding of the sources of selection generating this variation. We used path analysis to study how oviposition host affects selection on body size in a seed-feeding beetle (Stator limbatus) in which males contribute large ejaculates (nuptial gifts) to females. Females use nutrients in these ejaculates for egg production. Male body size, which affects ejaculate size, affects female fecundity and is thus under fecundity selection similar in magnitude to the fecundity selection on female body size. We show that when eggs are laid on a host on which larval mortality is low (seeds of Acacia greggii) fecundity predicts fitness very well and fecundity selection is the major source of selection on both male and female adult size. In contrast, when eggs are laid on a host on which larval mortality is high (seeds of Parkinsonia florida) fecundity poorly predicts fitness such that fecundity selection is relaxed on both male and female size. However, because egg size affects larval mortality on this poor host (P. florida) there is selection on female size via the female size --> egg size --> fitness path; this selection via egg size offsets the reduction in fecundity selection on female, but not male, body size. Thus, differences in host suitability (due to differences in larval mortality) affect the relative importance of two sources of selection on adult body size; fecundity selection on both male and female body size is lower on the poor quality host (P. florida) relative to the high quality host (A. greggii) whereas selection on female body size via effects of egg size on offspring survival (body size --> egg size --> fitness) is greater on the poor quality host relative to the high quality host. Because selection via the egg size path affects only females the difference in larval survival between hosts shifts the relative magnitude of selection on female vs. male size. Researchers working on other study systems should be alerted to the possible importance of subtle, but consequential, indirect selection on their study organisms.

Proximate mechanisms that contribute to female-biased sexual size dimorphism in an anguid lizard

Various proximate mechanisms have been proposed to explain sexual size dimorphism (SSD) in vertebrates. Identifying the proximate causation of SSD allows insight into the ultimate reasons why SSD exists. I explored whether differential growth rates and (or) mortality explain SSD in the lizard Elgaria coerulea (Baird and Girard, 1852). I estimated growth parameters for males and females using the logistic-by-weight growth curves and determined survivorship using two complimentary methods: standard life-table calculations and capture–recapture methods. The former calculated age-specific survivorship, whereas the latter tested for differences in survivorship between males and females while considering differences in their recapture rates. I considered age-specific SSD as further evidence of SSD independent of differential mortality. Differences in growth asymptote, not intrinsic growth rate, contribute to SSD in this population. SSD is not due to differential mortality, as there is no difference in survivorship of males and females over 3 years of age. In addition, there is age-specific SSD with females larger than males for individuals 4 years of age and greater. The female-biased SSD may be a result of selection for large body size, although further studies are necessary to identify the ultimate cause of SSD in this species.