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.     

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.     

Variation in the ontogenetic allometry of horn length in bovids along a body mass continuum

Allometric relationships describe the proportional covariation between morphological, physiological, or life‐history traits and the size of the organisms. Evolutionary allometries estimated among species are expected to result from species differences in ontogenetic allometry, but it remains uncertain whether ontogenetic allometric parameters and particularly the ontogenetic slope can evolve. In bovids, the nonlinear evolutionary allometry between horn length and body mass in males suggests systematic changes in ontogenetic allometry with increasing species body mass. To test this hypothesis, we estimated ontogenetic allometry between horn length and body mass in males and females of 19 bovid species ranging from ca. 5 to 700 kg. Ontogenetic allometry changed systematically with species body mass from steep ontogenetic allometries over a short period of horn growth in small species to shallow allometry with the growth period of horns matching the period of body mass increase in the largest species. Intermediate species displayed steep allometry over long period of horn growth. Females tended to display shallower ontogenetic allometry with longer horn growth compared to males, but these differences were weak and highly variable. These findings show that ontogenetic allometric slope evolved across species possibly as a response to size‐related changes in the selection pressures acting on horn length and body mass.     

Walk the line: 600000 years of molar evolution constrained by allometry in the fossil rodent Mimomys savini

The allometric-constraint hypothesis states that evolutionary divergence of morphological traits is restricted by integrated growth regulation. In this study, we test this hypothesis on a time-calibrated and well-documented palaeontological sequence of dental measurements on the Pleistocene arvicoline rodent species Mimomys savini from the Iberian Peninsula. Based on 507 specimens representing nine populations regularly spaced over 600 000 years, we compare static (within-population) and evolutionary (among-population) allometric slopes between the width and the length of the first lower molar. We find that the static allometric slope remains evolutionary stable and predicts the evolutionary allometry quite well. These results support the hypothesis that the macroevolutionary divergence of molar traits is constrained by static allometric relationships.     

Artificial selection on allometry: change in elevation but not slope

To what extent within-species (static) allometries constitute a constraint on evolution is the subject of a long-standing debate in evolutionary biology. A prerequisite for the constraint hypothesis is that static allometries are hard to change. Several studies have attempted to test this hypothesis with artificial-selection experiments, but their results remain inconclusive due to various methodological issues. Here, we present results from an experiment in which we selected independently on the slope and the elevation of the allometric relationship between caudal-fin size and body size in male guppies (Poecilia reticulata). After three episodes of selection, the allometric elevation (i.e. intercept at constant slope) had diverged markedly between the lines selected to increase or decrease it, and showed a realized heritability of 50%. In contrast, the allometric slope remained unaffected by selection. These results suggest that the allometric elevation is more evolvable than the allometric slope, this latter representing a potential constraint on adaptive trait evolution. To our knowledge, this study is the first artificial-selection experiment that directly tests the evolvability of static allometric slopes.     

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.     

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.     

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.     

Size and shape interspecific divergence patterns partly reflect phylogeny in an Onthophagus species‐complex (Coleoptera: Scarabaeidae)

Polyphenism has been suggested as an accelerator for morphological evolution and speciation. In the dung beetles of the genus Onthophagus, horn expression is polyphenic: large males develop horns whereas smaller males express greatly reduced or no horns. Horn static allometries seem to diverge rapidly amongst extant taxa, a process which might trigger changes in the male genital morphology, thus possibly promoting speciation as a by‐product. It can therefore be hypothesized that interspecific distances in allometries and, possibly, in other morphological traits mirror phylogenetic distances. In this study we first assessed the phylogenetic relationships amongst three closely related taxa belonging to the so‐called ‘Onthophagus fracticornis‐similis‐opacicollis’ species‐complex by sequencing the mitochondrial gene cytochrome oxidase subunit 1 (cox1). Biomolecular results indicated three independent lineages, the closest relationships being found between Onthophagus similis and Onthophagus opacicollis. Then we assessed the extent to which divergence pattern of horn static allometries and size and shape divergence patterns of one genital (paramere) and two nongenital (head and epipharynx) structures mirrored the phylogenetic relationships. Interspecific divergence patterns of horn static allometries, paramere, and head shape were found to be congruent with the evolutionary relationships inferred from biomolecular data. Nevertheless, paramere size and epipharynx shape showed patterns not consistent with the phylogeny. Furthermore, the relative size of nongenital structures showed little interspecific divergence compared to their shapes. Our results suggest that size and shape interspecific divergence mirror phylogeny only in part; they also indicate that distinct morphological traits may differ in their tendency to evolve in concert, and that size and shape of the same trait can evolve independently across species. © 2011 The Linnean Society of London, Zoological Journal of the Linnean Society, 2011, 162 , 482–498.     

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.     

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 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.     

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.     

A matter of measurements: challenges and approaches in the comparative analysis of static allometries

Comparisons of static allometries are frequently used to gain insights into patterns and processes underlying morphological and developmental evolution. A study by J. L. Tomkins and coworkers, recently published in the American Naturalist, examined complex nonlinear allometries in three insect species in which males are dimorphic in the expression of secondary sexual traits. Employing a novel approach to analyzing male allometries in these organisms, the authors were able to show that developmental reprogramming of trait primordia is not necessary to explain allometric scaling in two of the species examined, contrary to several previous studies on the same species. Instead, male dimorphisms could be explained by simple exponential growth, an important result that carries with it major evolutionary and developmental implications. Using this study as an example, I highlight some of the methodological challenges involved in analyzing and comparing static allometries and in inferring the developmental processes that underlie them. I end by discussing how correct application of hypothesis testing, on one side, and basic anatomy and developmental biology, on the other, should guide how morphology is measured.     

Evolution of extreme ontogenetic allometric diversity and heterochrony in pythons,a clade of giant and dwarf snakes

Ontogenetic allometry, how species change with size through their lives, and heterochony, a decoupling between shape, size, and age, are major contributors to biological diversity. However, macroevolutionary allometric and heterochronic trends remain poorly understood because previous studies have focused on small groups of closely related species. Here, we focus on testing hypotheses about the evolution of allometry and how allometry and heterochrony drive morphological diversification at the level of an entire species‐rich and diverse clade. Pythons are a useful system due to their remarkably diverse and well‐adapted phenotypes and extreme size disparity. We collected detailed phenotype data on 40 of the 44 species of python from 1191 specimens. We used a suite of analyses to test for shifts in allometric trajectories that modify morphological diversity. Heterochrony is the main driver of initial divergence within python clades, and shifts in the slopes of allometric trajectories make exploration of novel phenotypes possible later in divergence history. We found that allometric coefficients are highly evolvable and there is an association between ontogenetic allometry and ecology, suggesting that allometry is both labile and adaptive rather than a constraint on possible phenotypes.     

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.     

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.     

No evidence for condition-dependent expression of male genitalia in the dung beetle Onthophagus taurus

We examine the condition-dependence of male genitalia in the dung beetle Onthophagus taurus by manipulating the quality of dung provided for larval growth and development. We show that the influence of larval nutrition differed considerably across three different trait classes (sexual, nonsexual and genital). The size of all nonsexual traits varied with dung quality but their allometric slopes remained unchanged. Relative horn length and allometry, but not absolute horn length, showed a high degree of plasticity with differences in dung quality. In contrast, both absolute size and allometry of genitalia were largely unresponsive to changes in dung quality. Male genitalia exhibited intermediate levels of phenotypic variation and lower allometric slopes than both horns and nonsexual traits. Thus, our findings provide little support for good genes hypotheses of genital evolution. We use our findings to discuss a developmental mechanism and selection pressures that may prevent the condition-dependent expression of genitalia.