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.     

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.     

Quantitative genetic variation in static allometry in the threespine stickleback

The common pattern of replicated evolution of a consistent shape-environment relationship might reflect selection acting in similar ways within each environment, but divergently among environments. However, phenotypic evolution depends on the availability of additive genetic variation as well as on the direction of selection, implicating a bias in the distribution of genetic variance as a potential contributor to replicated evolution. Allometry, the relationship between shape and size, is a potential source of genetic bias that is poorly understood. The threespine stickleback, Gasterosteus aculeatus, provides an ideal system for exploring the contribution of genetic variance in body shape allometry to evolutionary patterns. The stickleback system comprises marine populations that exhibit limited phenotypic variation, and young freshwater populations which, following independent colonization events, have often evolved similar phenotypes in similar environments. In particular, stickleback diversification has involved changes in both total body size and relative size of body regions (i.e., shape). In a laboratory-reared cohort derived from an oceanic Alaskan population that is phenotypically and genetically representative of the ancestor of the diverse freshwater populations in this region, we determined the phenotypic static allometry, and estimated the additive genetic variation about these population-level allometric functions. We detected significant allometry, with larger fish having relatively smaller heads, a longer base to their second dorsal fin, and longer, shallower caudal peduncles. There was additive genetic variance in body size and in size-independent body shape (i.e., allometric elevation), but typically not in allometric slopes. These results suggest that the parallel evolution of body shape in threespine stickleback is not likely to have been a correlated response to selection on body size, or vice versa. Although allometry is common in fishes, this study highlights the need for additional data on genetic variation in allometric functions to determine how allometry evolves and how it influences phenotypic evolution.     

Geographical variation in allometry in the guppy (Poecilia reticulata)

Variation in static allometry, the power relationship between character size and body size among individuals at similar developmental stages, remains poorly understood. We tested whether predation or other ecological factors could affect static allometry by comparing the allometry between the caudal fin length and the body length in adult male guppies (Poecilia reticulata) among populations from different geographical areas, exposed to different predation pressures. Neither the allometric slopes nor the allometric elevations (intercept at constant slope) changed with predation pressure. However, populations from the Northern Range in Trinidad showed allometry with similar slopes but lower intercepts than populations from the Caroni and the Oropouche drainages. Because most of these populations are exposed to predation by the prawn Macrobrachium crenulatum, we speculated that the specific selection pressures exerted by this predator generated this change in relative caudal fin size, although effects of other environmental factors could not be ruled out. This study further suggests that the allometric elevation is more variable than the allometric slope.     

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.     

Does allometry account for shape variability in <Emphasis Type="Italic">Ephedrus persicae</Emphasis> Froggatt (Hymenoptera: Braconidae: Aphidiinae) parasitic wasps?

We analysed linear measurements on various parts of the body and the configuration of 11 landmarks on the wing in a large sample of Ephedrus persicae that had emerged from 13 aphid host species, to assess whether static allometry (a measure of the scaling relationship between traits in a population of individuals at the same ontogenetic stage) accounts for variation in body shape. The analysed specimens came from several localities in Europe, Asia Minor, Japan and South America, and cover a large portion of the distribution area of E. persicae. We found that allometry accounts for variation in body shape among different biotypes within the E. persicae group. The allometric slopes for head size (HD), petiolus width (PETW), mesoscutum width (MSC), and ovipositor sheath length (OVPL) diverged significantly among biotypes, indicating biotype-specific allometries. The analysis of allometric variation in wing shape showed that the pattern and direction of allometric changes also differed among individuals that had emerged from different hosts. Our results (observed divergences in the directions of allometric slopes of particular morphometric traits and wing shape) suggest that allometric relations within E. persicae are not conserved, so that allometry itself changes, evolving differently in aphid parasitoids that emerge from different hosts.     

Ontogeny,function, and scaling of the mandibular symphysis in papionin primates

In vivo study of mastication in adult cercopithecine primates demonstrates a link between mandibular symphyseal form and resistance to “wishboning,” or lateral transverse bending. Mechanical consideration of wishboning at the symphysis indicates exponentially higher stresses along the lingual surface with increasing symphyseal curvature. Lengthening the anteroposterior width of the symphysis acts to resist these higher loads. Interspecific adult cercopithecine allometries show that both symphyseal curvature and symphyseal width exhibit positive allometry relative to body mass. The experimental and allometric data support an hypothesis that the cercopithecine mandibular symphysis is designed to maintain functional equivalence—in this case dynamic strain similarity—in wishboning stress and strain magnitudes across adult cercopithecines. We test the hypothesis that functional equivalence during masticatory wishboning is maintained throughout ontogeny by calculating relative stress estimates from morphometric dimensions of the mandibular symphysis in two cercopithecine primates, Macaca fascicularis and M. nemestrina. Results indicate no significant differences in relative stress estimates among the two macaque ontogenies and an interspecific sample of adult papionin primates. Further, relative stress estimates do not change significantly throughout ontogeny in either species. These results offer the first evidence for the maintenance of functional equivalence in stress and strain levels during postnatal growth in a habitually loaded cranial structure. Scaling analyses demonstrate significant slope differences for both symphyseal curvature and width between the ontogenetic and interspecific samples. The distinct interspecific cercopithecine slopes are realized by a series of ontogenetic transpositions in both symphyseal curvature and width. Throughout papionin ontogeny, symphyseal curvature increases with less negative allometry, while symphysis width increases with less positive allometry versus the interspecific pattern. As symphyseal curvature and width are inversely proportional to one another in estimating relative stresses, functionally equivalent stress levels are maintained both ontogenetically and interspecifically, because the relatively slower rate of allometric increase in symphyseal curvature during growth is compensated for by a slower rate of allometric increase in symphyseal width. These results indicate the primacy of maintaining functional equivalence during growth and the need for ontogenetic data in understanding the evolutionary processes that affect form–function relations as well as the interspecific patterning of adult form across a clade. J. Morphol. 235:157–175, 1998. © 1998 Wiley-Liss, Inc.     

Allometric relations in three species of finches (Aves: Fringillidae)

Static nestling, adult and ontogenetic allometry were analysed in three species of finches. Static nestling allometry was very similar across age in early ontogeny and among species and could be approximated by a single matrix of phenotypic variances and covariances. The first eigenvector of this matrix showed negative allometry of bill and tarsus to mass, but positive for wing length to mass. Adult static allometry was also very similar among species, but differed from nestling pattern. In adults the bill had a positive allometry in relation to tarsus and wing, but negative to mass, while tarsus and wing were unrelated to mass. The ontogenetic allometry in each species was very similar to nestling static allometry. Viewed in relation to final size, bill characters grew more slowly than body characters, but for a longer time, which created the difference between adult and nestling allometric patterns. There were differences among species both with regard to elevation and slope of allometric coefficients, suggesting that the differences among species came about by changes in the three fundamental ontogenetic parameters namely growth rate, onset of growth and offset of growth.     

Geometric Morphometric Analysis of Body-Form Variability in Cichlasoma minckleyi, the Cuatro Cienegas cichlid

In this study, I investigate body-form variability in the trophically polymorphic Cuatro Cienegas cichlid, Cichlasoma minckleyi. I use geometric morphometrics to assess and compare size, shape, and allometric patterns within and between dental morphs (distinguished by differences in pharyngeal bones and papilliform or molariform dentitions). I find that dental morphs do not differ significantly in size, shape, or allometric slopes, but do differ in allometric intercepts; thus, dental morphs exhibit different patterns of body-form variability. Within each morph, body-form varies between more fusiform 'piscivores' and deeper-bodied dietary generalists. However, papilliform individuals show a continuous distribution of body-forms, whereas molariform individuals exhibit a discontinuity. I compare results from geometric analyses with those from a traditional (distance-based) morphometric analysis, finding that geometric techniques more clearly recognize discontinuities in shape. Finally, I suggest explanations for observed differences in body-form variability between dental morphs, concluding that the best explanation hinges on the relative importance of genetic and environmental factors in influencing body-form.     

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.     

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.     

The ontogeny of sexual dimorphism in the cranium of Bornean orang-utans (Pongo pygmaeus pygmaeus) as detected by principal-components analysis

The ontogeny of cranial sexual dimorphism in the Bornean orang-utan (Pongo pygmaeus pygmaeus) is examined by means of principal-components analysis (PCA). Normalized first components are called allometry vectors or vectors of relative growth and show that sexual dimorphism is present at all stages of growth. Two patterns of sexual dimorphism are present: (1) sexual differences at age groups 2 and 3 are the result primarily of differences in principal component II scores, reflecting mainly shape-related differences, and (2) age groups 5, 6, and 7 show a trend of stronger size-related shape differences with increasing age in the allometry vector along with decreasing differences in principal component II scores, reflecting an increase in size-related shape differences between the sexes. Age group 4 shows a combination of both patterns. Our results support Shea's hypothesis (1985a) that when using multigroup PCAs in closely related taxa, the allometry vector will generally estimate the shape variation resulting from the extension of common growth allometry patterns (ontogenetic scaling). The second and subsequent components summarize shape variation from slope and intercept differences between the groups, provided that ontogenetic scaling is not solely responsible for all the shape differences present. Subanalyses of those dimensions previously found to show ontogenetic scaling and acceleration follow this pattern well. The total sample provides a pattern whereby ontogenetically scaled dimensions possess a stronger influence over accelerated dimensions but still generally follow Shea's hypothesis. Finally, variously derived coefficients provided several interesting findings: (1) strong evidence was found against multivariate isometry for both the pooled and the separate samples, (2) multivariate allometric coefficients for both sexes follow the general growth pattern of negative scaling in neurocranial dimensions and positive scaling in the viscerocranium, and (3) multivariate slopes have a very high correlation with bivariate slopes relative to the same independent X variable, thereby lending further support to Jolicoeur's (1963a, b) allometry generalization.     

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.     

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.     

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.     

Morphology and diet are decoupled in nearshore notothenoids from King George Island,West Antarctica

Antarctic notothenioid fishes show wide adaptive morphological radiation, linked to habitat preferences and food composition. However, direct comparisons of phenotypic variability and feeding habits are still lacking, particularly in stages inhabiting nearshore areas. To assess these relationships, we collected juveniles and adults of the most common benthic species inhabiting shallow waters off the South Shetland Islands within a similar size range, the plunderfish Harpagifer antarcticus, the black rockcod Notothenia coriiceps, and the marbled rockcod Notothenia rossii. Individual size ranges varied from 44.0 to 98.9 mm standard length (LS) (H. antarcticus), from 95.8 to 109.3 mm LS (N. coriiceps), and from 63.0 to 113.0 mm LS (N. rossii). Notothenioid fish showed different morphospace variability, being larger for H. antarcticus than the other Notothenia species and associated with the position of the posterior end of the operculum, along with the location and relative size of the eye. The evolutionary allometry was low, but the static allometry was much higher, especially for H. antarcticus and N. rossii. The diet was mainly carnivorous, consisting of amphipods and euphausiids. Macroalgae were scarce or totally absent in the gut contents of all species. Only H. antarcticus showed an increase in the prey number and ingested prey volume with fish size. Finally, there was a significant covariation between shape changes and LS in all species (allometric effects), however, not with prey composition, probably due to the small size range or ontogenetic stage and the relative similarity (or lack of contrast) in the benthic environment that they utilized.     

Phylogenetic and size constrains on cranial ontogenetic allometry of spiny rats (Echimyidae,Rodentia)

Analysis of ontogenetic development is crucial for understanding the emergence of phenotypic discrepancies between animal taxa. The study of allometric trajectories within a phylogenetic context is a feasible approach to assess the morphological change across different evolutionary lineages. Here, we report the disparity of multivariate ontogenetic allometry in the Echimyidae, a taxonomically diverse rodent family, as well as the effects of size on the evolution of skull ontogeny. The ontogenetic trajectories of 15 echimyid operational taxonomic unities (12 genera plus one genus with three species) belonging to all subfamilies and major clades, when plotted in allometric space, revealed strong and significant phylogenetic signals. Allometric trajectories were found to be constrained by phylogenetic ancestry, with changes approximately adjusting to a Brownian motion model of evolution. Moreover, the occupation of allometric space by echimyid taxa was significantly correlated with adult size rather than with shape, suggesting that the variation in adult size might result in critically intrinsic and structural constraints on allometric coefficients. These findings disagreed with the hypothesis that allometric disparities might be mainly adaptive with undetectable phylogenetic signals.     

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.