ALLOMETRIC CONSTRAINTS AND THE EVOLUTION OF ALLOMETRY

Morphological traits often covary within and among species according to simple power laws referred to as allometry. Such allometric relationships may result from common growth regulation, and this has given rise to the hypothesis that allometric exponents may have low evolvability and constrain trait evolution. We formalize hypotheses for how allometry may constrain morphological trait evolution across taxa, and test these using more than 300 empirical estimates of static (within‐species) allometric relations of animal morphological traits. Although we find evidence for evolutionary changes in allometric parameters on million‐year, cross‐species time scales, there is limited evidence for microevolutionary changes in allometric slopes. Accordingly, we find that static allometries often predict evolutionary allometries on the subspecies level, but less so across species. Although there is a large body of work on allometry in a broad sense that includes all kinds of morphological trait–size relationships, we found relatively little information about the evolution of allometry in the narrow sense of a power relationship. Despite the many claims of microevolutionary changes of static allometries in the literature, hardly any of these apply to narrow‐sense allometry, and we argue that the hypothesis of strongly constrained static allometric slopes remains viable.     

SEX‐SPECIFIC PATTERNS OF MORPHOLOGICAL DIVERSIFICATION: EVOLUTION OF REACTION NORMS AND STATIC ALLOMETRIES IN NERIID FLIES

The consequences of sex‐specific selection for patterns of diversification remain poorly known. Because male secondary sexual traits are typically costly to express, and both costs and benefits are likely to depend on ambient environment and individual condition, such traits may be expected to diversify via changes in reaction norms as well as the scaling of trait size with body size (static allometry). We investigated morphological diversification within two species of Australian neriid flies (Telostylinus angusticollis, Telostylinus lineolatus) by rearing larvae from several populations on larval diets varying sixfold in nutrient concentration. Mean body size varied among populations of T. angusticollis, but body size reaction norms did not vary within either species. However, we detected diversification of reaction norms for body shape in males and females within both species. Moreover, unlike females, males also diversified in static allometry slope and reaction norms for static allometry slope of sexual and nonsexual traits. Our findings reveal qualitative sex differences in patterns of morphological diversification, whereby shape–size relationships diversify extensively in males, but remain conserved in females despite extensive evolution of trait means. Our results highlight the importance of incorporating plasticity and allometry in studies of adaptation and diversification.     

Pitfalls in understanding the functional significance of genital allometry

The male genitalia of arthropods consistently show negative static allometry (the genitalia of small males of a species are disproportionally large, and those of large males are disproportionally small). We discuss relations between the ‘one‐size‐fits‐all’ hypothesis to explain this allometry and the regimes of selection that may be acting on genitalia. We focus on the contrasts between directional vs. stabilizing selection, and natural vs. sexual selection. In addition, we point out some common methodological problems in studies of genital allometry. One‐size‐fits‐all types of arguments for negative allometry imply net stabilizing selection, but the effects of stabilizing selection on allometry will be weaker when the correlation between body size and the trait size is weaker. One‐size‐fits‐all arguments can involve natural as well as sexual selection, and negative allometry can also result from directional selection. Several practical problems make direct tests of whether directional or stabilizing selection is acting difficult. One common methodological problem in previous studies has been concentration on absolute rather than relative values of the allometric slopes of genitalia; there are many reasons to doubt the usefulness of comparing absolute slopes with the usual reference value of 1.00. Another problem has been the failure to recognize that size and shape are independent traits of genitalia; rapid divergence in the shape of genitalia is thus not paradoxical with respect to the reduced variation in their sizes that is commonly associated with negative allometric scaling.     

The allometric pattern of sexually size dimorphic feather ornaments and factors affecting allometry

The static allometry of secondary sexual characters is currently subject to debate. While some studies suggest an almost universal positive allometry for such traits, but isometry or negative allometry for nonornamental traits, other studies maintain that any kind of allometric pattern is possible. Therefore, we investigated the allometry of sexually size dimorphic feather ornaments in 67 species of birds. We also studied the allometry of female feathers homologous to male ornaments (female ornaments in the following) and ordinary nonsexual traits. Allometries were estimated as reduced major axis slopes of trait length on tarsus length. Ornamental feathers showed positive allometric slopes in both sexes, although that was not a peculiarity for ornamental feathers, because nonsexual tail feathers also showed positive allometry. Migration distance (in males) and relative size of the tail ornament (in females) tended to be negatively related to the allometric slope of tail feather ornaments, although these results were not conclusive. Finally, we found an association between mating system and allometry of tail feather ornaments, with species with more intense sexual selection showing a smaller degree of allometry of tail ornaments. This study is consistent with theoretical models that predict no specific kind of allometric pattern for sexual and nonsexual characters.     

Sexual selection and allometry: a critical reappraisal of the evidence and ideas

One of the most pervasive ideas in the sexual selection literature is the belief that sexually selected traits almost universally exhibit positive static allometries (i.e., within a sample of conspecific adults, larger individuals have disproportionally larger traits). In this review, I show that this idea is contradicted by empirical evidence and theory. Although positive allometry is a typical attribute of some sexual traits in certain groups, the preponderance of positively allometric sexual traits in the empirical literature apparently results from a sampling bias reflecting a fascination with unusually exaggerated (bizarre) traits. I review empirical examples from a broad range of taxa illustrating the diversity of allometric patterns exhibited by signal, weapon, clasping and genital traits, as well as nonsexual traits. This evidence suggests that positive allometry may be the exception rather than the rule in sexual traits, that directional sexual selection does not necessarily lead to the evolution of positive allometry and, conversely, that positive allometry is not necessarily a consequence of sexual selection, and that many sexual traits exhibit sex differences in allometric intercept rather than slope. Such diversity in the allometries of secondary sexual traits is to be expected, given that optimal allometry should reflect resource allocation trade-offs, and patterns of sexual and viability selection on both trait size and body size. An unbiased empirical assessment of the relation between sexual selection and allometry is an essential step towards an understanding of this diversity.     

Phylogenetic analysis of sexual dimorphism and eye-span allometry in stalk-eyed flies (Diopsidae)

Eye stalks and their scaling relationship with body size are important features in the mating system of many diopsid species, and sexual selection is a critical force influencing the evolution of this exaggerated morphology. Interspecific variation in eye span suggests there has been significant evolutionary change in this trait, but a robust phylogenetic hypothesis is required to determine its rate and direction of change. In this study, the pattern of morphological evolution of eye span is assessed in a phylogenetic framework with respect to its function in the sexual system of these flies. Specifically, we examine within the family Diopsidae the pattern of increase and decrease in sexual dimorphism, the morphological coevolution of eye span between males and females, and the evolutionary flexibility of eye-span allometry. Based on several different methods for reconstructing morphological change, results suggest a general pattern of evolutionary flexibility, particularly for eye-span allometry. Sexual dimorphism in eye span has evolved independently at least four times in the family and this trait also has undergone several reductions within the genus Diasemopsis. Despite most species being dimorphic, there is a strong phylogenetic correlation between males and females for mean eye span. The coevolution between the sexes for eye-span allometry, however, is significantly weaker. Overall, eye-span allometry exhibits significantly more change on the phylogeny than the other morphological traits. The evolutionary pattern in eye-span allometry is caused primarily by changes in eye-span variance. Therefore, this pattern is consistent with recent models that predict a strong relationship between sexual selection and the variance of ornamental traits and highlights the significance of eye-span allometry in intersexual and intrasexual signaling.     

Evolutionary allometry reveals a shift in selection pressure on male horn size

How selection pressures acting within species interact with developmental constraints to shape macro‐evolutionary patterns of species divergence is still poorly understood. In particular, whether or not sexual selection affects evolutionary allometry, the increase in trait size with body size across species, of secondary sexual characters, remains largely unknown. In this context, bovid horn size is an especially relevant trait to study because horns are present in both sexes, but the intensity of sexual selection acting on them is expected to vary both among species and between sexes. Using a unique data set of sex‐specific horn size and body mass including 91 species of bovids, we compared the evolutionary allometry between horn size and body mass between sexes while accounting for both the intensity of sexual selection and phylogenetic relationship among species. We found a nonlinear evolutionary allometry where the allometric slope decreased with increasing species body mass. This pattern, much more pronounced in males than in females, suggests either that horn size is limited by some constraints in the largest bovids or is no longer the direct target of sexual selection in very large species.     

Sexual selection,phenotypic variation,and allometry in genitalic and non‐genitalic traits in the sexually size‐dimorphic stick insect Micrarchus hystriculeus

The mobility hypothesis could explain the evolution of female‐biased size dimorphism if males with a smaller body size and longer legs have an advantage in scramble competition for mates. This hypothesis is tested by performing a selection analysis in the wild on Micrarchus hystriculeus (Westwood) (Phasmatodea), a sexually size dimorphic stick insect endemic to New Zealand. This analysis examined the form and strength of sexual selection on body size, leg lengths (front, mid and hind), and clasper size (a genitalic trait), and also quantified the degree of phenotypic variation and the allometric scaling pattern of these traits. By contrast to the mobility hypothesis, three lines of evidence were found to support significant stabilizing sexual selection on male hind leg length: a significant nonlinear selection gradient, negative static allometry, and a low degree of phenotypic variation. Hind leg length might be under stabilizing selection in males if having average‐sized legs facilitates female mounting or improves a male's ability to achieve the appropriate copulation position. As predicted, a negative allometric scaling pattern and low phenotypic variation of clasper size is suggestive of stabilizing selection and supports the ‘one‐size‐fits‐all’ hypothesis. Opposite to males, the mid and hind leg lengths of females showed positive static allometry. Relatively longer mid and hind leg lengths in larger females might benefit individuals via the better support of their larger abdomens. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 113 , 471–484.     

Evolution of brain–body allometry in Lake Tanganyika cichlids

Brain size is strongly associated with body size in all vertebrates. This relationship has been hypothesized to be an important constraint on adaptive brain size evolution. The essential assumption behind this idea is that static (i.e., within species) brain–body allometry has low ability to evolve. However, recent studies have reported mixed support for this view. Here, we examine brain–body static allometry in Lake Tanganyika cichlids using a phylogenetic comparative framework. We found considerable variation in the static allometric intercept, which explained the majority of variation in absolute and relative brain size. In contrast, the slope of the brain–body static allometry had relatively low variation, which explained less variation in absolute and relative brain size compared to the intercept and body size. Further examination of the tempo and mode of evolution of static allometric parameters confirmed these observations. Moreover, the estimated evolutionary parameters indicate that the limited observed variation in the static allometric slope could be a result of strong stabilizing selection. Overall, our findings suggest that the brain–body static allometric slope may represent an evolutionary constraint in Lake Tanganyika cichlids.     

Sexual selection and the allometry of earwig forceps

Summary Positive intraspecific allometry, the tendency for large individuals to have relatively larger morphological traits, is thought to be more likely for secondary sexual traits than naturally selected traits. This is because secondary sexual traits are often used to signal individual quality and positive allometry should arise where the costs and/or benefits of signalling are size dependent. Here we examine the allometric relationships between forceps length, a sexually selected trait and elytra length, a naturally selected trait, in 42 species of earwig. Both forceps and elytra showed positive allometry. However, the degree of allometry was greater for forceps as predicted. If allometry arises due to sexual selection we would predict a greater degree of allometry in species with more exaggerated secondary sexual traits. Across species, the degree of forcep allometry did increase with forcep exaggeration. The relevance of positive allometry to reliable signalling is discussed.     

The static allometry of sexual and nonsexual traits in vervet monkeys

Sexual traits vary tremendously in static allometry. This variation may be explained in part by body size‐related differences in the strength of selection. We tested this hypothesis in two populations of vervet monkeys, using estimates of the level of condition dependence for different morphological traits as a proxy for body size‐related variation in the strength of selection. In support of the hypothesis, we found that the steepness of allometric slopes increased with the level of condition dependence. One trait of particular interest, the penis, had shallow allometric slopes and low levels of condition dependence, in agreement with one of the most consistent patterns yet detected in the study of allometry, namely that of genitalia exhibiting shallow allometries. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2015, 114 , 527–537.     

Is allometry of sexual traits adaptive? A field test with territorial damselflies

Recent studies have linked static allometry of sexual traits to selective advantages, in terms of sexual selection. An underlying, yet untested, assumption is that the allometry of sexual traits confers higher mating success and/or survival. Here, we investigated whether the allometry of two sexual traits is related to male mating success and survival in two species of damselflies: wing size in Paraphlebia zoe and the red‐pigmented wing spot in Hetaerina americana. We used large field‐based data sets of marked‐recaptured animals, in which we recorded male mating success and survival. Both sexual traits exhibited hyperallometric patterns; however, allometry was not linked to either mating success or survival. These results indicate that, at least during the period of sexual competition, allometry does not seem to be adaptive. Although our results may only apply to our damselfly study subjects (which nevertheless would require further tests in different seasons and/or study sites), our findings should encourage researchers to evaluate at least whether the assumed adaptiveness of sexual trait allometry holds for their study animals. © 2015 The Linnean Society of London, Biological Journal of the Linnean Society, 2015, 114 , 327–334.     

Sexual Selection on Accessory Glands, Genitalia and Protarsal Pads in the Whirligig Beetle Dineutus nigrior Roberts (Coleoptera: Gyrinidae)

Sexual selection is a potent force in the evolution of morphology in sexually reproducing species. When large size in a trait is favored by sexual selection the trait often exhibits positive allometry. Mating behavior in whirligig beetles consists of males attempting to grasp reluctant females using enlarged protarsi (protarsal pads). Here we use allometry and a mating experiment to investigate sexual selection pressures on accessory glands, intromittant genitalia (aedeagus), and protarsal pads in males of the whirligig beetle Dineutus nigrior Roberts. Accessory gland size exhibited positive allometry and males with larger accessory glands were more likely to copulate suggesting that larger size in this trait is favored by sexual selection. Males with larger accessory glands attempted to copulate more often but did not exhibit fewer failed mating attempts before copulating. This suggests that the increased probability of mating in males with large accessory glands is due to higher mating attempt frequency and not to increased ability to overcome female resistance. The length of the aedeagus exhibited negative allometry and males with a longer aedeagus did not have increased mating success. This is consistent with stabilizing selection favoring an intermediate size in this trait. The allometric slope of the protarsal pad did not differ from isometry and males with larger protarsal pads did not have increased mating success. This suggests that larger protarsal pads are not favored by sexual selection.     

Sex combs,allometry, and asymmetry in Drosophila

There has been recent debate about the expected allometry of sexually‐selected traits. Although sexually‐selected traits exhibit a diversity of allometric patterns, signalling characters are frequently positively allometric. By contrast, insect genitalia tend to be negatively allometric, although the allometry of nongenital sexually‐selected characters in insects is largely unknown (with some notable exceptions). It has also been suggested that there should be a negative association between the asymmetry and size of bilaterally‐paired, sexually‐selected traits, although this claim is controversial. We assessed the allometry and asymmetry (fluctuating asymmetry, FA) of a nongenital contact–courtship structure, the sex comb, in replicate populations of three species of Drosophila (we also measured wing FA). Sex combs are sexually‐selected characters used to grasp the female's abdomen and genitalia and to spread her wings prior to and during copulation. Although species differed in the size of the sex combs, all combs were positively allometric, and comb allometry did not generally differ significantly between species or populations. Comb and wing asymmetry did vary across species, although not across populations of the same species. However, FA was trait specific and was never negatively associated with trait size. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 103 , 923–934.     

Life-history variation and allometry for sexual size dimorphism in Pacific salmon and trout

Allometry for sexual size dimorphism (SSD) is common in animals, but how different evolutionary processes interact to determine allometry remains unclear. Among related species SSD (male : female) typically increases with average body size, resulting in slopes of less than 1 when female size is regressed on male size: an allometric relationship formalized as 'Rensch's rule' . Empirical studies show that taxa with male-biased SSD are more likely to satisfy Rensch's rule and that a taxon's mean SSD is negatively correlated with allometric slope, implicating sexual selection on male size as an important mechanism promoting allometry for SSD. I use body length (and life-history) data from 628 (259) populations of seven species of anadromous Pacific salmon and trout (Oncorhynchus spp.) to show that in this genus life-history variation appears to regulate patterns of allometry both within and between species. Although all seven species have intraspecific allometric slopes of less than 1, contrary to expectation slope is unrelated to species' mean SSD, but is instead negatively correlated with two life-history variables: the species' mean marine age and variation in marine age. Second, because differences in marine age among species render SSD and body size uncorrelated, the interspecific slope is isometric. Together, these results provide an example of how evolutionary divergence in life history among related species can affect patterns of allometry for SSD across taxonomic scales.     

SEXUAL SIZE DIMORPHISM AND EGG-SIZE ALLOMETRY IN BIRDS

We tested the hypothesis that egg size should evolve in sexually dimorphic birds to reduce costs associated with more rapid growth by nestlings of the larger sex. Consistent with this hypothesis, we found that in species in which males were larger, females laid proportionately larger eggs as sexual size dimorphism increased. However, this result was also consistent with the hypothesis that egg size varied allometrically with both male and female body size. Furthermore we found that in species in which females were larger, relative egg size decreased as size dimorphism increased, which is consistent with the “allometry hypothesis” but not the “cost-reduction hypothesis. That male body size contributes to the allometric relationship between egg size and body size suggests that the basis for the allometric relationship is not wholly a mechanical one stemming from the physical requirements of developing, transporting, and laying an egg of a particular size. Rather, the relationship seems likely to be tied more directly to body size itself the tact that male body size influences a female trait suggests that egg size–body size relationships otter some scope for investigating the basis for allometric relationships in general.     

Extreme Eye Projection in the Male Weevil <Emphasis Type="Italic">Exechesops leucopis</Emphasis> (Coleoptera: Anthribidae): Its Effect on Intrasexual Behavioral Interferences

Fungus weevils, Exechesops leucopis (Anthribidae), are sexually dimorphic in the degree of eye protrusion and antenna elongation. I examined the allometric relationships of eye span, eyestalk length, antenna length, elytra width, and wing length against body size (pronotum width), and their effects on the outcome of male-male combat in the laboratory. Male eye span, eyestalk length, and antenna length indicated positive allometry, while elytra width showed isometry, and wing length showed negative allometry. In male-male combat, males with a larger eye span, antenna length, and body size defeated those with smaller attributes. However, when males fought experimentally males of similar body size, only eye span affected the outcome of combat, independent of body size and antenna length. In the female-female contests, the prior residency was an important determinant of victory the other than any morphological traits.     

The evolution of static allometry in sexually selected traits

Although it has been the subject of verbal theory since Darwin, the evolution of morphological trait allometries remains poorly understood, especially in the context of sexual selection. Here we present an allocation trade-off model that predicts the optimal pattern of allometry under different selective regimes. We derive a general solution that has a simple and intuitive interpretation and use it to investigate several examples of fitness functions. Verbal arguments have suggested cost or benefit scenarios under which sexual selection on signal or weapon traits may favor larger individuals with disproportionately larger traits (i.e., positive allometry). However, our results suggest that this is necessarily true only under a precisely specified set of conditions: positive allometry will evolve when the marginal fitness gains from an increase in relative trait size are greater for large individuals than for small ones. Thus, the optimal allometric pattern depends on the precise nature of net selection, and simple examples readily yield isometry, positive or negative allometry, or polymorphisms corresponding to sigmoidal scaling. The variety of allometric patterns predicted by our model is consistent with the diversity of patterns observed in empirical studies on the allometries of sexually selected traits. More generally, our findings highlight the difficulty of inferring complex underlying processes from simple emergent patterns.     

Allometry and sexually dimorphic traits in male anurans

Allometry of secondary sexual traits has been the subject of recent debate, and the generality of positive allometry and its association with sexual selection have been recently questioned. Whereas some studies suggest an almost universal positive allometry for traits under sexual selection and isometry or a negative allometry for traits not under such pressure, other studies argue that this pattern results from the study of exaggerated (ornamental) traits. To answer the call for an examination of the allometry of less-exaggerated sexually selected traits, we have examined morphological data from 14 sexually dimorphic traits and six monomorphic traits from three anuran species. Although we found evidence of positive allometry in male secondary sexual traits of several species and populations, not all nonsexual traits were isometric or exhibited negative allometry. Furthermore, our results indicate that larger traits in the populations that we studied were not associated with greater allometric slopes. Therefore, our study is in line with the contention suggesting no specific kind of allometric pattern for sexual and nonsexual characters, and we can only advocate for further investigation of trait allometry and sexual selection to understand the complexity underlying the evolution of allometry in sexual traits.     

Life history patterns in birds and mammals and their evolutionary interpretation

Summary It is argued that allometric principles account for most of the observed variation in the life history patterns amongst birds. To test this contention it is shown that traits such as incubation time, growth rates, age at first reproduction, lifespan, clutch weight and egg weight all scale to body weight with exponents similar to those found for analogous traits in mammals. It is then shown that most of the variation amongst bird taxa and between birds and mammals based on body weight allometry can be explained by variations in brain size, body temperature and metabolic rate, consistent with theories of growth and ageing derived from mammalian studies. Finally, it is suggested that the evidence for life histostory allometry is sufficiently strong that it argues for a more epigenetic view of life history patterns and their evolution than is generally conceded in most adaptation theories.