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.     

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.     

The Evolution of Positive Allometry of Weaponry in Horned Lizards (Phrynosoma)

The allometry of weapons and other conspicuous structures has long fascinated biologists. Recently, a debate has arisen about the roles of sexual and natural selection in driving the allometry of structures, with some authors suggesting that positive allometry is exclusively the result of sexual selection. Although some studies, often focusing on weapons, support this hypothesis, others have shown that many naturally selected structures also exhibit positive allometry. We study the allometry of the cranial horns in 14 species of horned lizards (Phrynosoma). These horns are purely defensive weapons and so are under natural, as opposed to sexual, selection. In almost all cases, the length of these horns is positively allometric through ontogeny (intraspecifically) and through evolution (interspecifically). Our findings demonstrate that positive allometry can be the product of natural selection, suggesting that the function of structures may dictate allometry and not the type of selection. For example, it is possible that weapons tend to be positively allometric. Our findings also suggest that longer horns may arise through the prolongation of horn growth, and that the horns that are most effective at defense from predators attacking a lizard from above are integrated with one another. Finally, we find that species with unusual horn morphologies have diverged from other species in their horn allometries, indicating that the evolution of morphological diversity can be mediated through the evolution of allometry.     

Convergent evolution of sexual shape dimorphism in Diptera

Several patterns of sexual shape dimorphism, such as male body elongation, eye stalks, or extensions of the exoskeleton, have evolved repeatedly in the true flies (Diptera). Although these dimorphisms may have evolved in response to sexual selection on male body shape, conserved genetic factors may have contributed to this convergent evolution, resulting in stronger phenotypic convergence than might be expected from functional requirements alone. I compared phenotypic variation in body shape in two distantly related species exhibiting sexually dimorphic body elongation: Prochyliza xanthostoma (Piophilidae) and Telostylinus angusticollis (Neriidae). Although sexual selection appears to act differently on male body shape in these species, they exhibited strikingly similar patterns of sexual dimorphism. Likewise, patterns of within-sex shape variation were similar in the two species, particularly in males: relative elongation of the male head capsule, antenna, and legs was associated with reduced head capsule width and wing length, but was nearly independent of variation in thorax length. However, the two species presented contrasting patterns of static allometry: male sexual traits exhibited elevated allometric slopes in T. angusticollis, but not in P. xanthostoma. These results suggest that a shared pattern of covariation among traits may have channeled the evolution of sexually dimorphic body elongation in these species. Nonetheless, static allometries may have been shaped by species-specific selection pressures or genetic architectures.     

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.     

Weapon allometry varies with latitude in the New Zealand giraffe weevil

Animal body size commonly shows a relationship with latitude to the degree that this phenomenon is one of the few ‘rules’ discussed in evolutionary ecology: Bergmann's rule. Although exaggerated secondary sexual traits frequently exhibit interesting relationships with body size (allometries) and are expected to evolve rapidly in response to environmental variation, the way in which allometry might interact with latitude has not been addressed. We present data showing latitudinal variation in body size and weapon allometry for the New Zealand giraffe weevil (Lasiorhynchus barbicornis). Males display an extremely elongated rostrum used as a weapon during fights for access to females. Consistent with Bergmann's rule, mean body size increased with latitude. More interestingly, weapon allometry also varied with latitude, such that lower latitude populations exhibited steeper allometric slopes between weapon and body size. To our knowledge, this is the first study to document a latitudinal cline in weapon allometry and is therefore a novel contribution to the collective work on Bergmann's rule and secondary sexual trait variation.     

Baculum variation and allometry in the muskrat (Ondatra zibethicus): a case for sexual selection

Sexual selection is a powerful force that influences the evolution of a variety of traits associated with female mate choice and male–male competition. Although other factors have been implicated, sexual selection may be particularly important in the evolution of the genitalia. Traits under sexual selection typically have high phenotypic variance and positive allometry relative to non-sexual traits. Here, we test the hypothesis that the baculum (os penis) of the muskrat (Ondatra zibethicus) is under sexual selection by examining phenotypic variance and allometry relative to non-sexual traits. Muskrats were sampled from Ontario, Canada, and a variety of traits measured. Measurements included baculum length and width, and three non-sexual traits (skull length, skull width, hind foot length). We used coefficient of variation (CV) and allometric slopes calculated using reduced major axis regression to test our hypotheses. Baculum traits had significantly higher CV’s relative to non-sexual traits. Baculum traits also showed positive allometry, whereas all non-sexual traits had negative allometric relationships. In addition, baculum width had higher CV’s and steeper allometric slopes than baculum length, indicating that, in muskrat, baculum width may be more influenced by sexual selection than baculum length. Positive allometry of the baculum is consistent with other examples of mammalian genitalia, but contrasts with negative allometry found in many insects. Other examples of positive allometry and high phenotypic variance of the baculum have suggested that females may use the baculum as an indicator of male quality. “Good genes” indicator traits may be particularly important in species that mate in an environmental context that prohibits female assessment of male quality. Muskrats mate aquatically, and thus females may be unable to properly assess males prior to copulation.     

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.     

Internal and external constraints in the evolution of morphological allometries in a butterfly

Much diversity in animal morphology results from variation in the relative size of morphological traits. The scaling relationships, or allometries, that describe relative trait size can vary greatly in both intercept and slope among species or other animal groups. Yet within such groups, individuals typically exhibit low variation in relative trait size. This pattern of high intra- and low intergroup variation may result from natural selection for particular allometries, from developmental constraints restricting differential growth among traits, or both. Here we explore the relative roles of short-term developmental constraints and natural selection in the evolution of the intercept of the allometry between the forewing and hindwing of a butterfly. First, despite a strong genetic correlation between these two traits, we show that artificial selection perpendicular to the forewing-hindwing scaling relationship results in rapid evolution of the allometry intercept. This demonstrates an absence of developmental constraints limiting intercept evolution for this scaling relationship. Mating experiments in a natural environment revealed strong stabilizing selection favoring males with the wild-type allometry intercept over those with derived intercepts. Our results demonstrate that evolution of this component of the forewing-hindwing allometry is not limited by developmental constraints in the short term and that natural selection on allometry intercepts can be powerful.     

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.     

Ontogenetic allometry, heterochrony, and interspecific differences in the skull of African apes, using tridimensional Procrustes analysis

Ontogenetic studies of African ape skulls lead to an analysis of morphological differences in terms of allometry, heterochrony, and sexual dimorphism. The use of geometric morphometrics allows us 1) to define size and shape variations as independent factors (an essential but seldom respected condition for heterochrony), and 2) to calculate in percentage of shape changes and to graphically represent the parts of shape variation which are related to various biological phenomena: common allometry, intraspecific allometry, and allometric and nonallometric shape discrimination. Three tridimensional Procrustes analyses and the calculation of multivariate allometries, discriminant functions, and statistical tests are used to compare the skulls of 50 Pan troglodytes, and 50 Gorilla gorilla of different dental stages. The results both complement and modify classical results obtained from similar material but with different methods. Size and Scaling in Primate Morphology, New York: Plenum, p. 175-205). As previously described by Shea, the common growth allometric pattern is very important (64% of total shape variation). It corresponds to a larger increase of facial volume than of neurocranial volume, a more obliquely oriented foramen magnum, and a noticeable reshaping of the nuchal region (higher inion). However, the heterochronic interpretation based on common allometry is rather different from Shea. Gorillas differ from chimpanzees not only with a larger magnitude of allometric change (rate peramorphosis), as is classically said, but also grow more in size than in shape (size acceleration). In other words, for a similar stage of growth, gorillas have the size and shape corresponding to older chimpanzees, and for a similar shape, gorillas have a larger size than chimpanzees. In contrast, sexual dimorphism actually corresponds to allometric changes only, as classically demonstrated (time hypermorphosis). Sexual dimorphism is here significant in adult gorillas alone, and solely in terms of allometry (size-related shape and size, given that sagittal and nuchal crests are not taken into account). The study also permits us to differentiate two different shape variations that are classically confused in ontogenetic studies: a very small part of allometric shape change which is specific to each species (1% of the total shape variation), and nonallometric species-specific traits independent of growth (8% of total shape change). When calculated in terms of intraspecific allometries (including common allometry and noncommon allometry), shape changes are more extensive in gorillas (36% of total shape change) than in chimpanzees (29% of total shape change). The allometric differences mainly concern the inion, which becomes higher; the position of the foramen magnum, more dorsally oriented; and the palate, more tilted in adult gorillas than in adult chimpanzees. In contrast, nonallometric species-specific traits in gorillas are the long and flat vault characterized by a prominent occipital region, the higher and displaced backward glabella, and the protrusive nose. Biomechanical schemes built from shape partition suggest that the increased out-of-plumb position of the head during growth is partially compensated in gorillas by a powerful nuchal musculature due to the peculiar shape of the occipital region.     

Does allometry of a sexually selected ornamental trait vary with sexual selection intensity? A multi‐species test in damselflies

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The limits of elaboration: curved allometries reveal the constraints on mandible size in stag beetles

Many studies have demonstrated the adaptive advantage of elaborate secondary sexual traits, but few if any have shown compelling evidence for the limits to the elaboration of these traits that must exist. We describe such evidence in the exaggerated mandibles of stag beetles. In 1932, Huxley showed that the slope of the allometric relationship between mandible length and body size in some stag beetles declines in the largest males. We show that this curvature is most pronounced in species with relatively long mandibles, consistent with the hypothesis that the decrease in slope is caused by the increasing costs of large mandibles, which ultimately limit their size. Increasing depletion of resources in the prepupa and pupa by the rapidly growing mandibles is the most likely way in which these costs are manifested. The curved allometries have two components: intraspecific mandible allometry is steepest among small males of the species with the longest mandibles, but shallowest among the largest males of those same species. These patterns suggest that selection continues to favour positive allometry in species that invest relatively more in weaponry despite the limits to mandible exaggeration being reached in the largest males.     

Relationships among ontogenetic,static, and evolutionary allometry

The relationship between ontogenetic, static, and evolutionary levels of allometry is investigated. Extrapolation from relative size relationships in adults to relative growth in ontogeny depends on the variability of slopes and intercepts of ontogenetic vectors relative to variability in length of the vector. If variability in slopes and intercepts is low relative to variability in length, ontogenetic and static allometries will be similar. The similarity of ontogenetic and static allometries was tested by comparing the first principal component, or size vector, for correlations among 48 cranial traits in a cross-sectional ontogenetic sample of rhesus macaques from Cayo Santiago with a static sample from which all age- and sex-related variation had been removed. The vector correlation between the components is high but significantly less than one while two of three allometric patterns apparent in the ontogenetic component are not discernable in the static component. This indicates that there are important differences in size and shape relationships among adults and within ontogenies. Extrapolation from intra- or interspecific phenotypic allometry to evolutionary allometry is shown to depend on the similarity of genetic and phenotypic allometry patterns. Similarity of patterns was tested by comparing the first principal components of the phenotypic, genetic, and environmental correlation matrices calculated using standard quantitative genetic methods. The patterns of phenotypic, genetic, and environmental allometry are dissimilar; only the environmental allometries show ontogenetic allometric patterns. This indicates that phenotypic allometry may not be an accurate guide to patterns of evolutionary change in size and shape.     

Allometry of the baculum and sexual size dimorphism in American martens and fishers (Mammalia: Mustelidae)

Genitalia are among the most variable of morphological traits, and recent research suggests that this variability may be the result of sexual selection. For example, large bacula may undergo post‐copulatory selection by females as a signal of male size and age. This should lead to positive allometry in baculum size. In addition to hyperallometry, sexually selected traits that undergo strong directional selection should exhibit high phenotypic variation. Nonetheless, in species in which pre‐copulatory selection predominates over post‐copulatory selection (such as those with male‐biased sexual size dimorphism), baculum allometry may be isometric or exhibit negative allometry. We tested this hypothesis using data collected from two highly dimorphic species of the Mustelidae, the American marten (Martes americana) and the fisher (Martes pennanti). Allometric relationships were weak, with only 4.5–10.1% of the variation in baculum length explained by body length. Because of this weak relationship, there was a large discrepancy in slope estimates derived from ordinary least squares and reduced major axis regression models. We conclude that stabilizing selection rather than sexual selection is the evolutionary force shaping variation in baculum length because allometric slopes were less than one (using the ordinary least squares regression model), a very low proportion of variance in baculum length was explained by body length, and there was low phenotypic variability in baculum length relative to other traits. We hypothesize that this pattern occurs because post‐copulatory selection plays a smaller role than pre‐copulatory selection (manifested as male‐biased sexual size dimorphism). We suggest a broader analysis of baculum allometry and sexual size dimorphism in the Mustelidae, and other taxonomic groups, coupled with a comparative analysis and with phylogenetic contrasts to test our hypothesis. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 104 , 955–963.     

SEXUALLY SELECTED TRAITS EVOLVE POSITIVE ALLOMETRY WHEN SOME MATINGS OCCUR IRRESPECTIVE OF THE TRAIT

Positive allometry of secondary sexual traits (whereby larger individuals have disproportionally larger traits than smaller individuals) has been called one of the most pervasive and poorly understood regularities in the study of animal form and function. Its widespread occurrence is in contrast with theoretical predictions that it should evolve only under rather special circumstances. Using a combination of mathematical modeling and simulations, here we show that positive allometry is predicted to evolve under much broader conditions than previously recognized. This result hinges on the assumption that mating success is not necessarily zero for males with the lowest trait values: for example, a male who lacks horns or antlers might still be able to copulate if encountering an unguarded female. We predict the strongest positive allometry when males typically (but not always) compete in large groups, and when trait differences decisively determine the outcome of competitive interactions.     

Sexual dimorphism in chelicerae size in three species of nuptial-gift spiders: a discussion of possible functions and driving selective forces

Positive allometric patterns observed for intersexual signalling characters are related to directional sexual selection, and supported by theoretical and empirical data. Recent models have shown that positive allometry may not hold as a rule if the influence of natural selection is added to the model. Here we tested these models applying traditional morphometrical techniques for the analysis of chelicerae sexual dimorphism and allometric patterns within the genus Paratrechalea : Paratrechalea azul , Paratrechalea galianoae and Paratrechalea ornata . Spider chelicerae are basically used for prey capture, but males of Paratrechalea also use the chelicerae to offer a nuptial gift during courtship, also presenting a clear size and colour sexual dimorphism supporting a possible role as a signal. Chelicerae size was male biased for all the variables studied and showed an isometric pattern, while females showed a higher variation. Our findings are in accordance with models of viability-related function for prey capture, questioning some statements proposed by the positive allometry model.     

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.     

Developmental causes of allometry: new models and implications for phenotypic plasticity and evolution

Shapes change during development because tissues, organs, and various anatomical features differ in onset, rate, and duration of growth. Allometry is the study of the consequences of differences in the growth of body parts on morphology, although the field of allometry has been surprisingly little concerned with understanding the causes of differential growth. The power-law equation y?=?ax(b), commonly used to describe allometries, is fundamentally an empirical equation whose biological foundation has been little studied. Huxley showed that the power-law equation can be derived if one assumes that body parts grow with exponential kinetics, for exactly the same amount of time. In life, however, the growth of body parts is almost always sigmoidal, and few, if any, grow for exactly the same amount of time during ontogeny. Here, we explore the shapes of allometries that result from real growth patterns and analyze them with new allometric equations derived from sigmoidal growth kinetics. We use an extensive ontogenetic dataset of the growth of internal organs in the rat from birth to adulthood, and show that they grow with Gompertz sigmoid kinetics. Gompertz growth parameters of body and internal organs accurately predict the shapes of their allometries, and that nonlinear regression on allometric data can accurately estimate the underlying kinetics of growth. We also use these data to discuss the developmental relationship between static and ontogenetic allometries. We show that small changes in growth kinetics can produce large and apparently qualitatively different allometries. Large evolutionary changes in allometry can be produced by small and simple changes in growth kinetics, and we show how understanding the development of traits can greatly simplify the interpretation of how they evolved.