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.     

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.     

Evolution of multivariate wing allometry in schizophoran flies (Diptera: Schizophora)

The proximate and ultimate mechanisms underlying scaling relationships as well as their evolutionary consequences remain an enigmatic issue in evolutionary biology. Here, I investigate the evolution of wing allometries in the Schizophora, a group of higher Diptera that radiated about 65 million years ago, by studying static allometries in five species using multivariate approaches. Despite the vast ecological diversity observed in contemporary members of the Schizophora and independent evolutionary histories throughout most of the Cenozoic, size‐related changes represent a major contributor to overall variation in wing shape, both within and among species. Static allometries differ between species and sexes, yet multivariate allometries are correlated across species, suggesting a shared developmental programme underlying size‐dependent phenotypic plasticity. Static allometries within species also correlate with evolutionary divergence across 33 different families (belonging to 11 of 13 superfamilies) of the Schizophora. This again points towards a general developmental, genetic or evolutionary mechanism that canalizes or maintains the covariation between shape and size in spite of rapid ecological and morphological diversification during the Cenozoic. I discuss the putative roles of developmental constraints and natural selection in the evolution of wing allometry in the Schizophora.     

Cryptic individual scaling relationships and the evolution of morphological scaling

Morphological scaling relationships between organ and body size—also known as allometries—describe the shape of a species, and the evolution of such scaling relationships is central to the generation of morphological diversity. Despite extensive modeling and empirical tests, however, the modes of selection that generate changes in scaling remain largely unknown. Here, we mathematically model the evolution of the group‐level scaling as an emergent property of individual‐level variation in the developmental mechanisms that regulate trait and body size. We show that these mechanisms generate a “cryptic individual scaling relationship” unique to each genotype in a population, which determines body and trait size expressed by each individual, depending on developmental nutrition. We find that populations may have identical population‐level allometries but very different underlying patterns of cryptic individual scaling relationships. Consequently, two populations with apparently the same morphological scaling relationship may respond very differently to the same form of selection. By focusing on the developmental mechanisms that regulate trait size and the patterns of cryptic individual scaling relationships they produce, our approach reveals the forms of selection that should be most effective in altering morphological scaling, and directs researcher attention on the actual, hitherto overlooked, targets of selection.     

The form of sexual selection on male genitalia cannot be inferred from within-population variance and allometry - a case study in Aquarius remigis

Male genital morphology in insects and arachnids is characterized by static hypoallometry and low intrapopulational levels of phenotypic variation relative to other male traits. The one-size-fits-all model of genital evolution attributes these patterns to stabilizing sexual selection. This model relies on the assumption that the observed patterns of variation and allometry reflect the form of sexual selection acting these traits. We test this by examining the patterns of scaling and trait variation for a set of genitalic and somatic morphological traits in male water striders (Aquarius remigis). This suite of traits is of particular interest because previous work has shown that the genitalic traits are under strong directional selection whereas the somatic traits are under either weak directional or stabilizing selection. Because the selection regime for these traits is known, we can, for the first time, test the purported relationship between trait variation, scaling, and the form of sexual selection. We show that the patterns of variation and scaling of these traits differ sharply from those predicted for traits experiencing strong directional sexual selection. Specifically, the male genital structures show static hypoallometry and low intrapopulational levels of phenotypic variation relative to other male traits, in spite of consistent, strong, directional sexual selection. These scaling relationships and levels of variation are typical of genital traits in other insect species, where they have been presumed to reflect stabilizing sexual selection. Our data clearly refute the assumption of the one-size-fits-all hypothesis that hypoallometric scaling of genitalic traits implies stabilizing selection. We discuss the implications of this finding and propose future directions for improving our current understanding of genital evolution in arthropods.     

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.     

EVOLUTION OF STATIC ALLOMETRIES: ADAPTIVE CHANGE IN ALLOMETRIC SLOPES OF EYE SPAN IN STALK‐EYED FLIES

Julian Huxley showed that within‐species (static) allometric (power‐law) relations can arise from proportional growth regulation with the exponent in the power law equaling the factor of proportionality. Allometric exponents may therefore be hard to change and act as constraints on the independent evolution of traits. In apparent contradiction to this, many empirical studies have concluded that static allometries are evolvable. Many of these studies have been based, however, on a broad definition of allometry that includes any monotonic shape change with size, and do not falsify the hypothesis of constrained narrow‐sense allometry. Here, we present the first phylogenetic comparative study of narrow‐sense allometric exponents based on a reanalysis of data on eye span and body size in stalk‐eyed flies (Diopsidae). Consistent with a role in sexual selection, we found strong evidence that male slopes were tracking “optima” based on sexual dimorphism and relative male trait size. This tracking was slow, however, with estimated times of 2–3 million years for adaptation to exceed ancestral influence on the trait. Our results are therefore consistent with adaptive evolution on million‐year time scales, but cannot rule out that static allometry may act as a constraint on eye‐span adaptation at shorter time scales.     

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.     

Developmental constraints on the evolution of wing-body allometry in Manduca sexta

Artificial selection on body size in Manduca sexta produced genetic strains with large and small body sizes. The wing-body allometries of these strains differed significantly from the wild type. Selection on small body size led to a change in the scaling of wing and body size without changing the allometry: the wings were smaller relative to the body, but to the same degree at all body sizes. Selection for large body size led to a change in allometry with a decrease in the allometric coefficient, wing size becoming progressively smaller relative to body as body size increased. When larvae were deprived of food so as to produce adults of a range of small body sizes, all strains retained the same allometric coefficient but showed an increase in the scaling factor. Thus individuals starved as larvae had a smaller adult body size but had proportionally larger wings than fed individuals. We analyzed the developmental processes that could give rise to this pattern of allometries. Differences in the relative growth of body and wing disks can account for the differences in the allometric coefficients among the three body size strains. The change in wing-body allometry at large body sizes was primarily due to an insufficient time period for growth. The available time period for growth of the wing imaginal disks poses a significant constraint on the proportional growth of wings, and thus on the evolution of large body size.     

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.     

Evolution of Allometry in Antirrhinum

Correlated variation in shape and size (allometry) is a major component of natural diversity. We examined the evolutionary and genetic basis for allometry using leaves and flower petals of snapdragon species (Antirrhinum). A computational method was developed to capture shape and size variation in both types of organ within the Antirrhinum species group. The results show that the major component of variation between species involves positively correlated changes in leaf and petal size. The correlation was maintained in an F2 population derived from crossing two species with organs of different sizes, suggesting that developmental constraints were involved. Identification of the underlying genes as quantitative trait loci revealed that the larger species carried alleles that increased organ size at all loci. Although this was initially taken as evidence that directional selection has driven diversity in both leaf and petal size, simulations revealed that evolution without consistent directional selection, an undirected walk, could also account for the parental distribution of organ size alleles.     

CONDITION DEPENDENCE OF A SEXUALLY SELECTED TRAIT IN A CRUSTACEAN SPECIES COMPLEX: IMPORTANCE OF THE ECOLOGICAL CONTEXT

The genic capture model offers a promising solution to the lek paradox. Heightened condition dependency of sexually selected traits is a prerequisite of this model. Condition dependency is empirically inferred by the sensitivity of traits to stressors. The magnitude of ecological stress (e.g., competition and predation) experienced by populations varies considerably. Thus, condition dependence should manifest more in populations experiencing higher levels of stress. We experimentally assessed the sensitivity of a sexually selected trait (posterior gnathopod) to food resource stress in an amphipod species. We found that gnathopod size variation was 59% higher under food stress, with no corresponding effect on nonsexually selected traits. In addition, we assessed levels of gnathopod variation and the allometry of gnathopods for males sampled from natural populations for two amphipod species that experience different levels of stress (driven by contrasting size‐selective predation and associated life‐history trade‐offs). Populations that experience higher resource stress had both steeper allometries and greater gnathopod size variation. These results suggest that the magnitude of ecological stress experienced by natural populations strongly impacts condition dependency of sexually selected traits, and could play an important role in shaping trait variation and thus the opportunity for sexual selection.     

Exaggerated Trait Allometry,Compensation and Trade-Offs in the New Zealand Giraffe Weevil (Lasiorhynchus barbicornis)

Sexual selection has driven the evolution of exaggerated traits among diverse animal taxa. The production of exaggerated traits can come at a cost to other traits through trade-offs when resources allocated to trait development are limited. Alternatively some traits can be selected for in parallel to support or compensate for the cost of bearing the exaggerated trait. Male giraffe weevils (Lasiorhynchus barbicornis) display an extremely elongated rostrum used as a weapon during contests for mates. Here we characterise the scaling relationship between rostrum and body size and show that males have a steep positive allometry, but that the slope is non-linear due to a relative reduction in rostrum length for the largest males, suggesting a limitation in resource allocation or a diminishing requirement for large males to invest increasingly into larger rostra. We also measured testes, wings, antennae, fore- and hind-tibia size and found no evidence of a trade-off between these traits and rostrum length when comparing phenotypic correlations. However, the relative length of wings, antennae, fore- and hind-tibia all increased with relative rostrum length suggesting these traits may be under correlational selection. Increased investment in wing and leg length is therefore likely to compensate for the costs of flying with, and wielding the exaggerated rostrum of larger male giraffe weevils. These results provide a first step in identifying the potential for trait compensation and trades-offs, but are phenotypic correlations only and should be interpreted with care in the absence of breeding experiments.     

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.     

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.     

Many ways to be small: different environmental regulators of size generate distinct scaling relationships in Drosophila melanogaster

Static allometries, the scaling relationship between body and trait size, describe the shape of animals in a population or species, and are generated in response to variation in genetic or environmental regulators of size. In principle, allometries may vary with the different size regulators that generate them, which can be problematic since allometric differences are also used to infer patterns of selection on morphology. We test this hypothesis by examining the patterns of scaling in Drosophila melanogaster subjected to variation in three environmental regulators of size: nutrition, temperature and rearing density. Our data indicate that different environmental regulators of size do indeed generate different patterns of scaling. Consequently, flies that are ostensibly the same size may have very different body proportions. These data indicate that trait size is not simply a read-out of body size, but that different environmental factors may regulate body and trait size, and the relationship between the two, through different developmental mechanisms. It may therefore be difficult to infer selective pressures that shape scaling relationships in a wild population without first elucidating the environmental and genetic factors that generate size variation among members of the population.     

Distinct evolutionary patterns of morphometric sperm traits in passerine birds

The striking diversity of sperm shape across the animal kingdom is still poorly understood. Postcopulatory sexual selection is an important factor driving the evolution of sperm size and shape. Interestingly, morphometric sperm traits, such as the length of the head, midpiece and flagellum, exhibit a strong positive phenotypic correlation across species. Here we used recently developed comparative methods to investigate how such phenotypic correlations between morphometric sperm traits may evolve. We compare allometric relationships and evolutionary trajectories of three morphometric sperm traits (length of head, midpiece and flagellum) in passerine birds. We show that these traits exhibit strong phenotypic correlations but that allometry varies across families. In addition, the evolutionary trajectories of the midpiece and flagellum are similar while the trajectory for head length differs. We discuss our findings in the light of three scenarios accounting for correlated trait evolution: (i) genetic correlation; (ii) concerted response to selection acting simultaneously on different traits; and (iii) phenotypic correlation between traits driven by mechanistic constraints owing to selection on sperm performance. Our results suggest that concerted response to selection is the most likely explanation for the phenotypic correlation between morphometric sperm traits.     

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.