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.     

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.     

Crown allometries are less responsive than stem allometry to tree size and habitat variations in an Indian monsoon forest

While theoretical allometric models postulate universal scaling exponents, empirical relationships between tree dimensions show marked variability that reflects changes in the biomass allocation pattern. As growth of the various tree compartments may be controlled by different functions, it is hypothesized that they may respond differently to factors of variation, resulting in variable tree morphologies and potentially in trade-offs between allometric relationships. We explore the variability of tree stem and crown allometries using a dataset of 1,729 trees located in an undisturbed wet evergreen forest of the Western Ghats, India. We specifically test whether species adult stature, terrain slope, tree size and crown light exposure affect the relationships between stem diameter and stem height (stem allometry), and between stem diameter and crown width, crown area and crown volume (crown allometries). Results show that both stem and crown allometries are subject to variations in relation to both endogenous (tree size, species adult stature) and exogenous (terrain slope, crown light exposure) factors. Stem allometry appears to be more affected by these factors than are crown allometries, including the stem diameter–crown volume relationship, which proved to be particularly stable. Our results support the idea that height is a prevailing adjustment factor for a tree facing variable growth (notably light) conditions, while stem diameter–crown volume allometry responds more to internal metabolic constraints. We ultimately discuss the various sources of variability in the stem and crown allometries of tropical trees that likely play an important role in forest community dynamics.     

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.     

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.     

Modes of ontogenetic allometric shifts in crocodylian vertebrae

During postnatal ontogeny of vertebrates, allometric trends in certain morphological units or dimensions can shift drastically among isometry, positive allometry, and negative allometry. However, detailed patterns of allometric transitions in certain timings have not been explored well. Identifying the presence and nature of allometric shifts is essential for understanding the patterns of changes in relative size and shape and the proximal factors that are controlling these changes mechanistically. Allometric trends in 10 selected vertebrae (cervical 2–caudal 2) from hatchlings to very mature individuals of Alligator mississippiensis (Archosauria, Crocodylia) are reported in the present study. Allometric coefficients in 12 vertebral dimensions are calculated and compared relative to total body length, including centrum, neural spine, transverse process, zygapophysis, and neural pedicle. During the postnatal growth, positive allometry is the most common type of relative change (10 of the 12 dimensions), although the diameter of the neural canal shows a negative allometric trend. However, when using spurious breaks (i.e. allometric trends subdivided into growth stages using certain growth events, and key body sizes and/or ages), vertebral parts exhibit various pathways of allometric shifts. Based on allometric trends in three spurious breaks, separated by the end of endochondral ossification (body length: approximnately 0.9 m), sexual maturity (1.8 m), and the stoppage of body size increase (2.8 m), six types of ontogenetic allometric shifts are established. Allometric shifts exhibit a wide range from positive allometry restricted only in the early postnatal stage (Type I) to life‐long positive allometry (Type VI). This model of ontogenetic allometric shifts is then applied to interpret potential mechanisms (causes) of allometric changes, such as (1) growth itself (when allometric trend gradually decreases to isometric or negative allometric change: Type II–IV allometric shift); (2) developmental constraint (when positive allometry is limited only in the early growth stage: Type I allometric shift); and (3) functional or biomechanical drive (when positive allometry continues throughout ontogeny: Type VI allometric shift).     

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.     

ARTIFICIAL SELECTION ON HORN LENGTH-BODY SIZE ALLOMETRY IN THE HORNED BEETLE ONTHOPHAGUS ACUMINATUS (COLEOPTERA: SCARABAEIDAE)

Males of the horned beetle Onthophagus acuminatus Har. (Coleoptera: Scarabaeidae) exhibit horn length dimorphism due to a sigmoidal allometric relationship between horn length and body size: the steep slope of the allometry around the inflection of the sigmoid curve separates males into two groups; those larger than this inflection possess long horns, and those smaller than this inflection have short horns or lack horns. I examined the genetic basis of the allometric relationship between horn length and body size by selecting males that produced unusually long horns, and males that produced unusually short horns, for their respective body sizes. After seven generations of selection, lines selected for relatively long horns had significantly longer horn lengths for a given body size than lines selected for relatively short horns, indicating a heritable component to variation in the allometry. The sigmoidal shape of the allometry was not affected by this selection regime. Rather, selected lines differed in the position of the allometry along the body size axis. One consequence of lateral shifts in this allometric relationship was that the body size separating horned from hornless males (the point of inflection of the sigmoid curve) differed between selection lines: lines in which males were selected for relatively long horns began horn production at smaller body sizes than lines selected for relatively short horns. These results suggest that populations can evolve in response to selection on male horn length through modification of the growth relationship between horn length and body size.     

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.     

Testing heterochrony: Connecting skull shape ontogeny and evolution of feeding adaptations in baleen whales

Ontogeny plays a key role in the evolution of organisms, as changes during the complex processes of development can allow for new traits to arise. Identifying changes in ontogenetic allometry—the relationship between skull shape and size during growth—can reveal the processes underlying major evolutionary transformations. Baleen whales (Mysticeti, Cetacea) underwent major morphological changes in transitioning from their ancestral raptorial feeding mode to the three specialized filter-feeding modes observed in extant taxa. Heterochronic processes have been implicated in the evolution of these feeding modes, and their associated specialized cranial morphologies, but their role has never been tested with quantitative data. Here, we quantified skull shapes ontogeny and reconstructed ancestral allometric trajectories using 3D geometric morphometrics and phylogenetic comparative methods on sample representing modern mysticetes diversity. Our results demonstrate that Mysticeti, while having a common developmental trajectory, present distinct cranial shapes from early in their ontogeny corresponding to their different feeding ecologies. Size is the main driver of shape disparity across mysticetes. Disparate heterochronic processes are evident in the evolution of the group: skim feeders present accelerated growth relative to the ancestral nodes, while Balaenopteridae have overall slower growth, or pedomorphosis. Gray whales are the only taxon with a relatively faster rate of growth in this group, which might be connected to its unique benthic feeding strategy. Reconstructed ancestral allometries and related skull shapes indicate that extinct taxa used less specialized filter-feeding modes, a finding broadly in line with the available fossil evidence.     

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.     

Problems of ontogeny and phylogeny in brain-size evolution

Fundamental ambiguities in the interpretation of brain/body allometric trends can only be resolved by analyzing relationships between ontogenetic brain/body growth processes in different groups. The ambiguous concept of adult encephalization confuses at least three distinct types of transformation of a common mammalian growth curve: scalar magnification, total curve didplacement, and changes in proportions of the pre- and postnatal phases of the curve. The conservative ratio between pre- and postnatal growth phases determines the apparent linearity of comparative brain/body allometry and can be explained by assuming that embyological neurogenetic processes ultimately determine both target brain and body size—the first directly and the second indirectly via neurohormonal regulation of somatic growth. Uneven taxonomic distribution of different ontogenetic growth patterns may explain many differences in the allometric trends at different taxonomic levels of analysis. The human brain grows exactly as if it was in a giant ape body; however, because of decoupled growth in different brain regions, it regulates body growth as though it were the size of a chimpanzee brain. Human encephalization exhibits an ontogenetic transformation not found in other mammalian groups.     

Relative growth of the skull and postcranium in giant transgenic mice

Cross-sectional allometric growth patterns of the cranial and postcranial skeleton were compared between giant transgenic (MT-rGH) mice and their normal littermate controls. Body weights, external body dimensions, and a series of cranial and postcranial linear dimensions of the skeleton were determined for samples of known age. Comparative bivariate and multivariate allometric analyses were completed in order to determine whether (1) the larger transgenic mice differed significantly from the normal controls in aspects of body and skeletal proportions, and (2) any such proportion differences resulted from general allometric effects of overall weight or skeletal size increase. Results demonstrate that the transgenic mice do exhibit significantly different body and skeletal proportions than normal control adults. Allometric comparisons of the skeletal dimensions relative to body weight reveal similar coefficients of growth allometry but several differences in gamma-intercept values in the transgenic vs. control groups. The comparisons among the skeletal dimensions of the skull and postcranium generally reveal the sharing and differential extension of common growth allometries in the two groups. Thus, the elevated levels of growth hormone (GH) and insulin-like growth factor I (IGF-I) in the transgenic mice appear to result in increased overall growth for the various skeletal elements, but in the relative proportions determined by intrinsic growth controls within that system.     

Biomass increases attributed to both faster tree growth and altered allometric relationships under long‐term carbon dioxide enrichment at a temperate forest

Increases in atmospheric carbon dioxide (CO₂) concentrations are expected to lead to increases in the rate of tree biomass accumulation, at least temporarily. On the one hand, trees may simply grow faster under higher CO₂ concentrations, preserving the allometric relations that prevailed under lower CO₂ concentrations. Alternatively, the allometric relations themselves may change. In this study, the effects of elevated CO₂ (eCO₂) on tree biomass and allometric relations were jointly assessed. Over 100 trees, grown at Duke Forest, NC, USA, were harvested from eight plots. Half of the plots had been subjected to CO₂ enrichment from 1996 to 2010. Several subplots had also been subjected to nitrogen fertilization from 2005 to 2010. Allometric equations were developed to predict tree height, stem volume, and aboveground biomass components for loblolly pine (Pinus taeda L.), the dominant tree species, and broad‐leaved species. Using the same diameter‐based allometric equations for biomass, it was estimated that plots with eCO₂ contained 21% more aboveground biomass, consistent with previous studies. However, eCO₂ significantly affected allometry, and these changes had an additional effect on biomass. In particular, P. taeda trees at a given diameter were observed to be taller under eCO₂ than under ambient CO₂ due to changes in both the allometric scaling exponent and intercept. Accounting for allometric change increased the treatment effect of eCO₂ on aboveground biomass from a 21% to a 27% increase. No allometric changes for the nondominant broad‐leaved species were identified, nor were allometric changes associated with nitrogen fertilization. For P. taeda, it is concluded that eCO₂ affects allometries, and that knowledge of allometry changes is necessary to accurately compute biomass under eCO₂. Further observations are needed to determine whether this assessment holds for other taxa.     

Allometry and ontogeny in Callibia diana Stål (Mantodea: Acanthopidae)

The life-cycle of Callibia diana St?l is described and linear and geometric morphometrics are used for studying allometrics and shape changes throughout this neotropical mantid species' life-cycle. Significant changes were expected in the allometry and shape of the raptorial leg and abdomen, given the importance of hunting and reproduction. The allometric slopes were obtained by using total length as the independent variable. Geometric morphometrics of landmarks were used for frontal femur and tibia. Hunting and reproduction-related structures had the steepest slopes and positive allometries. Negative growth of both disc width and head width found in the last moulting event may be a consequence of prothoracic muscle growth which is responsible for predatory strike strength. The tibial claw and femur of the raptorial leg become larger, while their spines become more orthogonal to the longitudinal axes which may facilitate prey retention. These changes in mantid shape throughout ontogeny were consistent and suggested the resource allocation and development programming of the body that improved reaching distance and prey retention.     

On a polyploid complex of freshwater snails (Planorbidae: Bulinus) in Ethiopia

Allometric growth of the postembryonic stages of Ectobius lapponicus (Linn.) and E. panzeri Stephens is described and analysed. Alternative methods of computing the allometric growth equation are discussed and applied, with the necessary significance tests, to a large number of skeletal structures in all developmental stages of each sex. The validity of Dyar's Law and its modifications are assessed quantitatively.  

Summary:

The growth in linear dimensions of 74 exosketetal structures has been studied quantitatively in all instars of both sexes of Ectobius lapponicus and E. panzeri.
Almost all the investigated structures show some statistically significant degree of allometric growth, but relatively few of them grow by simple allometry. Some possible reasons for this are indicated.
Well-defined growth gradients exist in the appendages and along the main axis of the body. Allometric growth contours, showing sexual and specific differences, express the temporal and spatial variations in the allometric growth ratio.
The limitations of Dyar's Law and Przibram's Rule are discussed and it is shown that conformity with Dyar's Law is not improved by allowing for differences in the duration of the instars.
It is emphasized that allometric growth studies should involve the choice of a suitable reference dimension and the selection of an appropriate statistical model to which the growth data are fitted. The estimation of the allometry parameters a and b , as well as the appropriate significance tests, depend on the model chosen, though the two models compared in this study do not yield appreciably different estimates.