On the relationship between ontogenetic and static allometry

Endocranial shape variation and allometry in Euarchontoglires

While brain size in primates and their relatives within Euarchontoglires is well-studied, less research has examined brain shape, or the allometric trajectories that underlie the relationship between size and shape. Defining these patterns is key to understanding evolutionary trends. 3D geometric morphometric analyses of endocranial shape were performed on 140 species of extant euarchontoglirans using digital cranial endocasts. Principal component analyses on Procrustes shape variables show a clear phylogenetic pattern in endocranial shape, supported by an ANOVA which identified significant differences in shape among several groups (e.g., Platyrrhini, Strepsirrhini, Scandentia, Rodentia, and Lagomorpha). ANOVAs of shape and size also indicate that allometry has a small but significant impact on endocranial shape across Euarchontoglires, with homogeneity of slopes tests finding significant differences in the scaling relationship between shape and size among these same groups. While most of these clades possess a distinct endocranial morphotype, the highly derived platyrrhines display the strongest relationship between size and shape. Rodents show the most diversity in endocranial shape, potentially attributed to their comparatively weak relationship between shape and size. These results suggest fundamental differences in how shape and size covary among Euarchontoglires, which may have facilitated the adaptive radiations that characterize members of this group.

Facing the facts: adaptive trade-offs along body size ranges determine mammalian craniofacial scaling

The mammalian cranium (skull without lower jaw) is representative of mammalian diversity and is thus of particular interest to mammalian biologists across disciplines. One widely retrieved pattern accompanying mammalian cranial diversification is referred to as 'craniofacial evolutionary allometry' (CREA). This posits that adults of larger species, in a group of closely related mammals, tend to have relatively longer faces and smaller braincases. However, no process has been officially suggested to explain this pattern, there are many apparent exceptions, and its predictions potentially conflict with well-established biomechanical principles. Understanding the mechanisms behind CREA and causes for deviations from the pattern therefore has tremendous potential to explain allometry and diversification of the mammalian cranium. Here, we propose an amended framework to characterise the CREA pattern more clearly, in that 'longer faces' can arise through several kinds of evolutionary change, including elongation of the rostrum, retraction of the jaw muscles, or a more narrow or shallow skull, which all result in a generalised gracilisation of the facial skeleton with increased size. We define a standardised workflow to test for the presence of the pattern, using allometric shape predictions derived from geometric morphometrics analysis, and apply this to 22 mammalian families including marsupials, rabbits, rodents, bats, carnivores, antelopes, and whales. Our results show that increasing facial gracility with size is common, but not necessarily as ubiquitous as previously suggested. To address the mechanistic basis for this variation, we then review cranial adaptations for harder biting. These dictate that a more gracile cranium in larger species must represent a structural sacrifice in the ability to produce or withstand harder bites, relative to size. This leads us to propose that facial gracilisation in larger species is often a product of bite force allometry and phylogenetic niche conservatism, where more closely related species tend to exhibit more similar feeding ecology and biting behaviours and, therefore, absolute (size-independent) bite force requirements. Since larger species can produce the same absolute bite forces as smaller species with less effort, we propose that relaxed bite force demands can permit facial gracility in response to bone optimisation and alternative selection pressures. Thus, mammalian facial scaling represents an adaptive by-product of the shifting importance of selective pressures occurring with increased size. A reverse pattern of facial 'shortening' can accordingly also be found, and is retrieved in several cases here, where larger species incorporate novel feeding behaviours involving greater bite forces. We discuss multiple exceptions to a bite force-mediated influence on facial proportions across mammals which lead us to argue that ecomorphological specialisation of the cranium is likely to be the primary driver of facial scaling patterns, with some developmental constraints as possible secondary factors. A potential for larger species to have a wider range of cranial functions when less constrained by bite force demands might also explain why selection for larger sizes seems to be prevalent in some mammalian clades. The interplay between adaptation and constraint across size ranges thus presents an interesting consideration for a mechanistically grounded investigation of mammalian cranial allometry.

Ontogenetic shifts in body form in the bull shark Carcharhinus leucas

Recent studies have uncovered mosaic patterns of allometric and isometric growth underlying ontogenetic shifts in the body form of elasmobranch species (shark and rays). It is thought that shifts in trophic and spatial ecology through ontogeny drive these morphological changes; however, additional hypotheses relating to developmental constraints have also been posed. The bull shark (Carcharhinus leucas) is a large-bodied coastal shark that exhibits strong ontogenetic shifts in trophic and spatial ecology. In this study, we utilise a large data set covering a large number of morphological structures to reveal ontogenetic shifts in the body form of C. leucas, stratifying analyses by sex and size classes to provide fine-scale, more ecomorphologically relevant results. Our results indicate shifts in functional demands across the body through ontogeny, driven by selective pressures relating to trophic and spatial ecology driving the evolution of allometry. We also find significant differences in scaling trends between life stages, and between the sexes, highlighting the importance of utilising large, diverse datasets that can be stratified in this way to improve our understanding of elasmobranch morphological evolution. Ultimately, we discuss the implications of these results for existing ecomorphological hypotheses regarding the evolution of specific morphological structures, and pose novel hypotheses where relevant.

Ontogenetic progression of individual head size in the larvae of the beetle Trypoxylus dichotomus (Coleoptera: Scarabaeidae): catch-up growth within stages and per-stage growth rate changes across stages

The ontogenetic progression of insect larval head size has received much attention due to its fundamental and practical importance. However, although previous studies have analyzed the population mean head size, such an approach may not be appropriate for developmental studies of larval head sizes when the trajectory of individual head size growth is correlated with pre-molt head size and developmental stage. Additionally, there is covariation between the head and body sizes; however, few studies have compared the ontogenetic progression of individual head sizes with that of individual body sizes. In this investigation, the per-stage growth rates (PSGRs) for head width (HW) and cubic-rooted body mass at the beginning of each instar (body size, BS) were assessed in Trypoxylus dichotomus. Linear models were used to test the size- and instar-dependence of the ontogenetic progression of individual HW and BS. The individual PSGRs of the HW (iPSGR_H) and BS (iPSGR_B) were then compared. In addition, the allometric relationship between HW and BS was examined. The iPSGR_H was negatively correlated with the pre-molt HW at every instar (i.e., head catch-up growth). Furthermore, the mean iPSGR_H at L2 was relatively higher than that at L1 when the pre-molt HW was used as covariate in the analysis (i.e., instar-effect), whereas the mean iPSGR_H decreased ontogenetically. The iPSGR_B showed catch-up growth and instar-effects similar to those of iPSGR_H; however, iPSGR_H was found to be lower than iPSGR_B. Due to the differences between the PSGRs for the larval head and body, the larval head size showed negative ontogenetic allometry against body size.

Environmental selection, rather than neutral processes, best explain regional patterns of diversity in a tropical rainforest fish

To conserve the high functional and genetic variation in hotspots such as tropical rainforests, it is essential to understand the forces driving and maintaining biodiversity. We asked to what extent environmental gradients and terrain structure affect morphological and genomic variation across the wet tropical distribution of an Australian rainbowfish, Melanotaenia splendida splendida. We used an integrative riverscape genomics and morphometrics framework to assess the influence of these factors on both putative adaptive and non-adaptive spatial divergence. We found that neutral genetic population structure was largely explainable by restricted gene flow among drainages. However, environmental associations revealed that ecological variables had a similar power to explain overall genetic variation, and greater power to explain body shape variation, than the included neutral covariables. Hydrological and thermal variables were the strongest environmental predictors and were correlated with traits previously linked to heritable habitat-associated dimorphism in rainbowfishes. In addition, climate-associated genetic variation was significantly associated with morphology, supporting heritability of shape variation. These results support the inference of evolved functional differences among localities, and the importance of hydroclimate in early stages of diversification. We expect that substantial evolutionary responses will be required in tropical rainforest endemics to mitigate local fitness losses due to changing climates.

Exploring potential drivers of brain size variation in the electric fish Brachyhypopomus occidentalis

Characterizing the factors that shape variation in brain size in natural populations is crucial to understanding the evolution of brain size in animals. Here, we explore how relative brain size and brain allometry vary with drainage, predation risk and sex in natural populations of the electric knifefish Brachyhypopomus occidentalis. Fish were sampled from high and low predation risk sites within two independent river drainages in eastern and central Panamá. Overall, we observed low variation in brain-body size allometric slopes associated with drainage, predation risk and sex category. However, we observed significant differences in allometric intercepts between predation risk sites. We also found significant differences in relative brain mass associated with drainage, as well as significant differences in absolute brain mass associated with drainage, predation risk and sex category. Our results suggest potential constraints in brain-body allometry across populations of B. occidentalis. However, both drainage and predation risk may be playing a role in brain mass variation among populations. We suggest that variation in brain mass in electric fishes is affected by multiple extrinsic and intrinsic factors, including geography, environmental complexity, social interaction and developmental or functional constraints.

Sex differences in allometry for phenotypic traits in mice indicate that females are not scaled males

Sex differences in the lifetime risk and expression of disease are well-known. Preclinical research targeted at improving treatment, increasing health span, and reducing the financial burden of health care, has mostly been conducted on male animals and cells. The extent to which sex differences in phenotypic traits are explained by sex differences in body weight remains unclear. We quantify sex differences in the allometric relationship between trait value and body weight for 363 phenotypic traits in male and female mice, recorded in >2 million measurements from the International Mouse Phenotyping Consortium. We find sex differences in allometric parameters (slope, intercept, residual SD) are common (73% traits). Body weight differences do not explain all sex differences in trait values but scaling by weight may be useful for some traits. Our results show sex differences in phenotypic traits are trait-specific, promoting case-specific approaches to drug dosage scaled by body weight in mice.

Signal detection shapes ornament allometry in functionally convergent Caribbean Anolis and Southeast Asian Draco lizards

Visual ornaments have long been assumed to evolve hyper-allometry as an outcome of sexual selection. Yet growing evidence suggests many sexually selected morphologies can exhibit other scaling patterns with body size, including hypo-allometry. The large conspicuous throat fan, or dewlap, of arboreal Caribbean Anolis lizards was one ornament previously thought to conform to the classical expectation of hyper-allometry. We re-evaluated this classic example alongside a second arboreal group of lizards that has also independently evolved a functionally equivalent dewlap, the Southeast Asian Draco lizards. Across multiple closely related species in both genera, the Anolis and Draco dewlaps were either isometric or had hypo-allometric scaling patterns. In the case of the Anolis dewlap, variation in dewlap allometry was predicted by the distance of conspecifics and the light environment in which the dewlap was typically viewed. Signal efficacy, therefore, appears to have driven the evolution of hypo-allometry in what was originally thought to be a sexually selected ornament with hyper-allometry. Our findings suggest that other elaborate morphological structures used in social communication might similarly exhibit isometric or hypo-allometric scaling patterns because of environmental constraints on signal detection.

A Revision of the Traditional Analysis Method of Allometry to Allow Extension of the Normality-Borne Complexity of Error Structure: Examining the Adequacy of a Normal-Mixture Distribution-Driven Error Term

Huxley’s model of simple allometry provides a parsimonious scheme for examining scaling relationships in scientific research, resource management, and species conservation endeavors. Factors including biological error, analysis method, sample size, and overall data quality can undermine the reliability of a fit of Huxley’s model. Customary amendments enhance the complexity of the power function-conveyed systematic term while keeping the usual normality-borne error structure. The resulting protocols bear multiple-parameter complex allometry forms that could pose interpretative shortcomings and parameter estimation difficulties, and even being empirically pertinent, they could potentially bear overfitting. A subsequent heavy-tailed Q-Q normal spread often remains undetected since the adequacy of a normally distributed error term remains unexplored. Previously, we promoted the advantages of keeping Huxley’s model-driven systematic part while switching to a logistically distributed error term to improve fit quality. Here, we analyzed eelgrass leaf biomass and area data exhibiting a marked size-related heterogeneity, perhaps explaining a lack of systematization at data gathering. Overdispersion precluded adequacy of the logistically adapted protocol, thereby suggesting processing data through a median absolute deviation scheme aimed to remove unduly replicates. Nevertheless, achieving regularity to Huxley’s power function-like trend required the removal of many replicates, thereby questioning the integrity of a data cleaning approach. But, we managed to adapt the complexity of the error term to reliably identify Huxley’s model-like systematic part masked by variability in data. Achieving this relied on an error term conforming to a normal mixture distribution which successfully managed overdispersion in data. Compared to normal-complex allometry and data cleaning composites present arrangement delivered a coherent Q-Q normal mixture spread and a remarkable reproducibility strength of derived proxies. By keeping the analysis within Huxley’s original theory, the present approach enables substantiating nondestructive allometric proxies aimed at eelgrass conservation. The viewpoint endorsed here could also make data cleaning unnecessary.

Within-individual leaf allometry and the evolution of leaf morphology: A multilevel analysis of leaf allometry in temperate Viburnum (Adoxaceae) species

A critical issue in evolutionary biology is understanding the relationship between macroevolutionary patterns of diversity and the origin of variation at the organismal level. Among-individual allometry, the relationship between the size and shape of a structure among organisms at a fixed developmental stage, is often similar to evolutionary allometry, the relationship between the size and shape of a structure among populations or species, and the genetic and developmental process that underlie allometric relationships at both levels are thought to influence evolutionary diversification. Metameric organisms present an additional level of allometry: the relationship between the size and shape of structures within individuals. We propose that within-individual allometry is also related to evolutionary diversification among metameric organisms. We explore this idea in temperate deciduous Viburnum (Adoxaceae) species that bear two types of leaves, that is, preformed and neoformed leaves, with contrasting patterns of development. Examination of within-individual, among-individual, among-population, and among-species allometry of leaf shape in both leaf types showed that the slopes of all allometric relationships were significantly different from isometry, and their sign was consistent across allometric hierarchies. Although the allometric slope of preformed leaves was constant across allometry levels, the allometric slope of neoformed leaves became increasingly steeper. We suggest that allometric variation underlying evolutionary diversification in metameric organisms may manifest among individuals and also among their repeated structures. Moreover, structures with contrasting patterns of development within metameric organisms can experience different degrees of developmental constraint, and this can in turn affect morphological diversification.

Growth and Mortality as Causes of Variation in Metabolic Scaling Among Taxa and Taxonomic Levels

Metabolic rate (MR) usually changes (scales) out of proportion to body mass (BM) as MR = aBMb, where a is a normalisation constant and b is the scaling exponent that reflects how steep this change is. This scaling relationship is fundamental to biology, but over a century of research has provided little consensus on the value of b, and why it appears to vary among taxa and taxonomic levels. By analysing published data on fish and taking an individual-based approach to metabolic scaling, I show that variation in growth of fish under naturally restricted food availability can explain variation in within-individual (ontogenetic) b for standard (maintenance) metabolic rate (SMR) of brown trout (Salmo trutta), with the fastest growers having the steepest metabolic scaling (b ≈ 1). Moreover, I show that within-individual b can vary much more widely than previously assumed from work on different individuals or different species, from -1 to 1 for SMR among individual brown trout. The negative scaling of SMR for some individuals was caused by reductions in metabolic rate in a food limited environment, likely to maintain positive growth. This resulted in a mean within-individual b for SMR that was significantly lower than the across-individual ("static") b, a difference that also existed for another species, cunner (Tautogolabrus adspersus). Interestingly, the wide variation in ontogenetic b for SMR among individual brown trout did not exist for maximum (active) metabolic rate (MMR) of the same fish, showing that these two key metabolic traits (SMR and MMR) can scale independently of one another. I also show that across-species ("evolutionary") b for SMR of 134 fishes is significantly steeper (b approaching 1) than the mean ontogenetic b for the brown trout and cunner. Based on these interesting findings, I hypothesise that evolutionary and static metabolic scaling can be systematically different from ontogenetic scaling, and that the steeper evolutionary than ontogenetic scaling for fishes arises as a by-product of natural selection for fast-growing individuals with steep metabolic scaling (b ≈ 1) early in life, where size-selective mortality is high for fishes. I support this by showing that b for SMR tends to increase with natural mortality rates of fish larvae within taxa.

Exceptionally Steep Brain-Body Evolutionary Allometry Underlies the Unique Encephalization of Osteoglossiformes

Brain-body static allometry, which is the relationship between brain size and body size within species, is thought to reflect developmental and genetic constraints. Existing evidence suggests that the evolution of large brain size without accompanying changes in body size (that is, encephalization) may occur when this constraint is relaxed. Teleost fish species are generally characterized by having close-fitting brain-body static allometries, leading to strong allometric constraints and small relative brain sizes. However, one order of teleost, Osteoglossiformes, underwent extreme encephalization, and its mechanistic bases are unknown. Here, I used a dataset and phylogeny encompassing 859 teleost species to demonstrate that the encephalization of Osteoglossiformes occurred through an increase in the slope of evolutionary (among-species) brain-body allometry. The slope is virtually isometric (1.03 ± 0.09 SE), making it one of the steepest evolutionary brain-body allometric slopes reported to date, and it deviates significantly from the evolutionary brain-body allometric slopes of other clades of teleost. Examination of the relationship between static allometric parameters (intercepts and slopes) and evolutionary allometry revealed that the dramatic steepening of the evolutionary allometric slope in Osteoglossiformes was a combined result of evolution in the slopes and intercepts of static allometry. These results suggest that the evolution of static allometry, which likely has been driven by evolutionary changes in the rate and timing of brain development, has facilitated the unique encephalization of Osteoglossiformes.

What constrains adaptive radiation? Documentation and explanation of under-evolved morphologies in Anolis lizards

Adaptive radiations fill ecological and morphological space during evolutionary diversification. Why do some trait combinations evolve during such radiations, whereas others do not? 'Required' constraints of pleiotropy and developmental interaction frequently are implicated in explanations for such patterns, but selective forces also may discourage particular trait combinations. Here, we use a dataset of 351 species to demonstrate the dearth of some theoretically plausible trait combinations of limb, toe and tail length in Anolis lizards. For example, disproportionately few Anolis species display long limbs and short toes. We evaluate recovered patterns within three species of Anolis, and find that cladewide patterns are not evident at intraspecific levels. For example, within species, the combination of long limbs and short toes is not significantly rarer than long limbs and long toes. Differences in scale complicate inter- and intraspecific comparisons and disallow concrete conclusions of cause. However, the absence of the interspecific pattern at the intraspecific level is more compatible with selection favouring particular trait combinations than with 'required' forces dictating which trait combinations are available for selection. We also demonstrate the isometry of toe, tail and hindlimb length relative to body length between species but allometry in four of nine trait-body comparisons within species.

Allometric scaling and growth: Evaluation and applications in subadult body mass estimation

OBJECTIVES

Previously developed methods in subadult body mass estimation have not been tested in populations other than European-American or African-American. This study uses a contemporary Taiwanese sample to test these methods. Through evaluating their accuracy and bias, we addressed whether the allometric relationships between body mass and skeletal traits commonly used in subadult body mass estimation are conserved among different populations.

MATERIALS AND METHODS

Computed tomography scans of lower limbs from individuals aged 0-17 years old of both sexes were collected from National Taiwan University Hospital along with documented body weight. Polar second moment of area, distal femoral metaphyseal breadth, and maximum superior/inferior femoral head diameter were collected either directly from the scans or from reconstructed 3D models. Estimated body mass was compared with documented body mass to assess the performance of the equations.

RESULTS

Current methods provided good body mass estimates in Taiwanese individuals, with accuracy and bias similar to those reported in other validation studies. A tendency for increasing error with increasing age was observed for all methods. Reduced major axis regression showed the allometric relationships between different skeletal traits and body mass across different age categories can all be summarized using a common fitted line. A revised, maximum likelihood-based approach was proposed for all skeletal traits.

DISCUSSION

The results suggested that the allometric relationships between body mass and different skeletal traits are largely conserved among populations. The revised method provided improved applicability with strong underlying theoretical justifications, and potential for future improvements.

Feet first: Adaptive growth in magellanic penguin chicks

Growing animals should allocate their limited resources in ways that maximize survival. Seabird chicks must balance the growth of features and fat reserves needed to survive on land with those needed to successfully fledge and survive at sea. We used a large, 34-year dataset to examine energy allocation in Magellanic penguin chicks. Based on the temporal trends in the selective pressures that chicks faced, we developed predictions relating to the timing of skeletal feature growth (Prediction 1), variation in skeletal feature size and shape (Prediction 2), and responses to periods of high energetic constraint (Prediction 3). We tested our predictions using descriptive statistics, generalized additive models, and principal component analysis. Nearly all of our predictions were supported. Chicks grew their feet first, then their flippers. They continued to grow their bill after fledging (Prediction 1). Variance in feature size increased in young chicks but declined before fledging; this variance was largely driven by overall size rather than by shape (Prediction 2). Chicks that died grew slower and varied more in feature size than those that fledged (Prediction 2). Skeletal features grew rapidly prior to thermoregulation and feet and flippers were 90% grown prior to juvenile feather growth; both thermoregulation and feather growth are energetically expensive (Prediction 3). To avoid starvation, chicks prioritized storing mass during the first 10 days after hatching; then, the body condition of chicks began to decline (Prediction 3). In contrast to our prediction of mass prioritization in young chicks, chicks that were relatively light for their age had high skeletal size to mass ratios. Chicks did not show evidence of reaching physiological growth limits (Prediction 3). By examining energy allocation patterns at fine temporal scales and in the context of detailed natural history data, we provide insight into the trade-offs faced by growing animals.

Three-dimensional geometric morphometric studies of modern human occipital variation

Objectives

To investigate three-dimensional morphological variation of the occipital bone between sexes and among populations, to determine how ancestry, sex and size account for occipital shape variation and to describe the exact forms by which the differences are expressed.

Methods

CT data for 214 modern crania of Asian, African and European ancestry were compared using 3D geometric morphometrics and multivariate statistics, including principal component analysis, Hotelling’s T² test, multivariate regression, ANOVA, and MANCOVA.

Results

Sex differences in average occipital morphology are only observed in Europeans, with males exhibiting a pronounced inion. Significant ancestral differences are observed among all samples and are shared by males and females. Asian and African crania have smaller biasterionic breadths and flatter clivus angles compared to Europeans. Asian and European crania are similar in their nuchal and occipital plane proportions, nuchal and occipital angles, and lower inion positions compared to Africans. Centroid size significantly differs between sexes and among populations. The overall allometry, while significant, explains little of the shape variation. Larger occipital bones were associated with a more curved occipital plane, a pronounced inion, a narrower biasterionic breadth, a more flexed clivus, and a lower and relatively smaller foramen magnum.

Conclusions

Although significant shape differences were observed among populations, it is not recommended to use occipital morphology in sex or population estimation as both factors explained little of the observed variance. Other factors, relating to function and the environment, are suggested to be greater contributors to occipital variation. For the same reason, it is also not recommended to use the occiput in phylogenetic studies.

Static allometry of a small-bodied omnivore: body size and limb scaling of an island fox and inferences for Homo floresiensis

Island dwarfing is a paraphyletic adaptation across numerous mammalian genera. From mammoths to foxes, extreme body size reduction is shared by diverse organisms that migrate to an island environment. Because it largely occurs owing to ecological variables, not phylogenetic ones, skeletal characters in a dwarfed taxon compared with its ancestor may appear abnormal. As a result, allometric patterns between body size and morphological traits may differ for an island dwarf compared with its ancestor. The diminutive Late Pleistocene hominin, Homo floresiensis, displays a unique character suite that is outside of the normal range of variation for any extinct or extant hominin species. To better explain these as ecological traits due to island dwarfing, this research looks at how dwarfing on islands influences limb scaling and proportions in an organism in a similar ecological niche as H. floresiensis. Here, I analyze absolute limb lengths and static allometry of limb lengths regressed on predicted body mass of dwarfed island foxes and their nondwarfed relatives. Dwarfed island foxes have significantly smaller intercepts but steeper slopes of all limb elements regressed on predicted body mass than the mainland gray fox. These allometric alterations produce limbs in the island fox that are significantly shorter than predicted for a nondwarfed gray fox of similar body mass. In addition, the humerofemoral, intermembral, and brachial indices are significantly different. These results provide a novel model for understanding skeletal variation of island endemic forms. Unique body size and proportions of H. floresiensis are plausible as ecological adaptations and likely not examples of symplesiomorphies with Australopithecus sp. Caution should be exerted when comparing an island dwarf with a closely related species as deviations from allometric expectations may be common.

Ontogenetic and static allometry in the skull and cranial units of nine-banded armadillos (Cingulata: Dasypodidae: Dasypus novemcinctus)

A large part of extant and past mammalian morphological diversity is related to variation in size through allometric effects. Previous studies suggested that craniofacial allometry is the dominant pattern underlying mammalian skull shape variation, but cranial allometries were rarely characterized within cranial units such as individual bones. Here, we used 3D geometric morphometric methods to study allometric patterns of the whole skull (global) and of cranial units (local) in a postnatal developmental series of nine-banded armadillos (Dasypus novemcinctus ssp.). Analyses were conducted at the ontogenetic and static levels, and for successive developmental stages. Our results support craniofacial allometry as the global pattern along with more local allometric trends, such as the relative posterior elongation of the infraorbital canal, the tooth row reduction on the maxillary, and the marked development of nuchal crests on the supraoccipital with increasing skull size. Our study also reports allometric proportions of shape variation varying substantially among cranial units and across ontogenetic stages. The multi-scale approach advocated here allowed unveiling previously unnoticed allometric variations, indicating an untapped complexity of cranial allometric patterns to further explain mammalian morphological evolution.

Allometric scaling in two bushcricket species (Orthoptera: Tettigoniidae) suggests sexual selection on song-generating structures

In acoustically communicating bushcrickets (Orthoptera: Tettigoniidae), most signal properties are influenced by the dimensions of the stridulatory apparatus, which in turn reflects body size and condition of the signaller. Females can assess male quality based on acoustic signals, suggesting that male stridulatory structures may be under sexual selection. We investigated scaling relationships between stridulatory structures, body size and body mass in males of the bushcricket Poecilimon veluchianus veluchianus, in comparison to the congeneric Poecilimon ampliatus. Stridulatory structures in P. v. veluchianus exhibited strong left–right correlation and coupling with body size and mass, indicating stabilizing selection for functional integration. In addition, sound-generating (the width of stridulatory teeth) and sound-radiating (mirror area on the right tegmen) structures scaled hyperallometrically to tegmen area, suggesting that both are under sexual selection. Finally, interspecies comparison revealed a steeper slope in tegmen area and stridulatory file length in relation to body size in P. ampliatus than in P. v. veluchianus, implying stronger sexual selection in the former, smaller species. Our study emphasizes the significance of a comparative allometric approach in elucidating evolutionary patterns of sound-generating and -radiating structures.

Network-regulated organ allometry: The developmental regulation of morphological scaling

Morphological scaling relationships, or allometries, describe how traits grow coordinately and covary among individuals in a population. The developmental regulation of scaling is essential to generate correctly proportioned adults across a range of body sizes, while the mis-regulation of scaling may result in congenital birth defects. Research over several decades has identified the developmental mechanisms that regulate the size of individual traits. Nevertheless, we still have poor understanding of how these mechanisms work together to generate correlated size variation among traits in response to environmental and genetic variation. Conceptually, morphological scaling can be generated by size-regulatory factors that act directly on multiple growing traits (trait-autonomous scaling), or indirectly via hormones produced by central endocrine organs (systemically regulated scaling), and there are a number of well-established examples of such mechanisms. There is much less evidence, however, that genetic and environmental variation actually acts on these mechanisms to generate morphological scaling in natural populations. More recent studies indicate that growing organs can themselves regulate the growth of other organs in the body. This suggests that covariation in trait size can be generated by network-regulated scaling mechanisms that respond to changes in the growth of individual traits. Testing this hypothesis, and one of the main challenges of understanding morphological scaling, requires connecting mechanisms elucidated in the laboratory with patterns of scaling observed in the natural world. This article is categorized under: Establishment of Spatial and Temporal Patterns > Regulation of Size, Proportion, and Timing Comparative Development and Evolution > Organ System Comparisons Between Species.

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.

The genetic control of leaf allometry in the common bean, Phaseolus vulgaris

BACKGROUND

To maximize photosynthetic efficiency, plants have evolved a capacity by which leaf area scales allometrically with leaf mass through interactions with the environment. However, our understanding of genetic control of this allometric relationship remains limited.

RESULTS

We integrated allometric scaling laws expressed at static and ontogenetic levels into genetic mapping to identify the quantitative trait loci (QTLs) that mediate how leaf area scales with leaf mass and how such leaf allometry, under the control of these QTLs, varies as a response to environment change. A major QTL detected by the static model constantly affects the allometric growth of leaf area vs. leaf mass for the common bean (Phaseolus vulgaris) in two different environments. The ontogenetic model identified this QTL plus a few other QTLs that determine developmental trajectories of leaf allometry, whose expression is contingent heavily upon the environment.

CONCLUSIONS

Our results gain new insight into the genetic mechanisms of how plants program their leaf morphogenesis to adapt to environmental perturbations.

The longer the better: evidence that narwhal tusks are sexually selected

Once thought to be the magical horn of a unicorn, narwhal tusks are one of the most charismatic structures in biology. Despite years of speculation, little is known about the tusk's function, because narwhals spend most of their lives hidden underneath the Arctic ice. Some hypotheses propose that the tusk has sexual functions as a weapon or as a signal. By contrast, other hypotheses propose that the tusk functions as an environmental sensor. Since assessing the tusks function in nature is difficult, we can use the morphological relationships of tusk size with body size to understand this mysterious trait. To do so, we collected morphology data on 245 adult male narwhals over the course of 35 years. Based on the disproportional growth and large variation in tusk length we found, we provide the best evidence to date that narwhal tusks are indeed sexually selected. By combining our results on tusk scaling with known material properties of the tusk, we suggest that the narwhal tusk is a sexually selected signal that is used during male-male contests.

Little if any role of male gonadal androgens in ontogeny of sexual dimorphism in body size and cranial casque in chameleons

Proximate control of the development of sexual dimorphism is still hotly debated in reptiles. In some squamates, many male-typical exaggerated traits including body size were assumed to be controlled by masculinization by male gonadal androgens. We performed a manipulative experiment to test the importance of this mechanism in the development of pronounced sexual differences in body size and size of head casque in the chameleon Chamaeleo calyptratus. Castrated males attained male-typical body size highly deviating from the body size of control females. Ontogenetic allometries of casque size on head length revealed that sexes depart considerably in casque growth later in the ontogeny; however, castrated males still follow male-typical casque growth. Paradoxically, exogenous testosterone led in females to slight increase of casque size, which might reflect interference with the feminizing effects of female gonadal hormones. The results in males strongly suggest that masculinization by male gonadal androgens during growth is not required for the development of sexual dimorphism in body size and casque size in the chameleon. The ontogeny of sexually dimorphic body size and exaggerated traits in at least some squamates is likely controlled by other proximate mechanism, possibly by feminization by ovarian hormones.

Allometric growth in meiofaunal invertebrates: do all kinorhynchs show homogeneous trends?

Allometry determines relevant modifications in metazoan morphology and biology and is affected by many different factors, such as ontogenetic constraints and natural selection. A linear mixed model approach and reduced major axis regression were used to explore evolutionary interspecific allometric trends between the total trunk length and the lengths of the segments and spines in the phylum Kinorhyncha at three taxonomic levels: the whole phylum, the class and the family. Statistically significant results were found in all the trunk segments, meaning that these body units grow proportionally correlated with the body, contrary to the results obtained for the spines. Developmental and morphophysiological constraints could lead to negative allometry in the first and last segments, because these body regions in kinorhynchs are essential to the implementation of some of the main biological functions, such as feeding and locomotion. The differential arrangement of cuticular appendages between the taxonomic groups considered seems to cause different evolutionary trends, because positive allometry may appear if a segment requires more space to accommodate a large number of organs and appendages, and vice versa. The presence of sexual dimorphism could also define positive allometry of a segment, owing to the need to harbour the sexually dimorphic appendages and their associated structures.

Allometry, Scaling, and Ontogeny of Form-An Introduction to the Symposium

Until recently, the study of allometry has been mostly descriptive, and consisted of a diversity of methods for fitting regressions to bivariate or multivariate morphometric data. During the past decade, researchers have been developing methods to extract biological information from allometric data that could be used to deduce the underlying mechanisms that gave rise to the allometry. In addition, an increasing effort has gone into understanding the kinetics of growth and the regulatory mechanisms that control growth of the body and its component parts. The study of allometry and scaling has now become an exceptionally diverse field, with different investigators applying state of the art methods and concepts in evolution, developmental biology, cell biology, and genetics. Diversity has caused divergence, and we felt that although there is general agreement about the new goals for the study of allometry (understanding underlying mechanisms and how those evolve to produce different morphologies), progress is hindered by lack of coordination among the different approaches. We felt the time was right to bring these diverse practitioners together in a symposium to discuss their most recent work in the hope of forging new functional, conceptual, and collaborative connections among established and novice practitioners.

Which Line to Follow? The Utility of Different Line-Fitting Methods to Capture the Mechanism of Morphological Scaling

Bivariate morphological scaling relationships describe how the sizes of two traits co-vary among adults in a population. In as much as body shape is reflected by the relative size of various traits within the body, morphological scaling relationships capture how body shape varies with size, and therefore have been used widely as descriptors of morphological variation within and among species. Despite their extensive use, there is continuing discussion over which line-fitting method should be used to describe linear morphological scaling relationships. Here I argue that the "best" line-fitting method is the one that most accurately captures the proximate developmental mechanisms that generate scaling relationships. Using mathematical modeling, I show that the "best" line-fitting method depends on the pattern of variation among individuals in the developmental mechanisms that regulate trait size. For Drosophila traits, this pattern of variation indicates that major axis regression is the best line-fitting method. For morphological traits in other animals, however, other line-fitting methods may be more accurate. I provide a simple web-based application for researchers to explore how different line-fitting methods perform on their own morphological data.

Male Horn Lack of Allometry May be Tied to Food Relocation Behaviour in Lifting Dung Beetles (Coleoptera, Scarabaeidae, Eucraniini)

The small dung beetle tribe Eucraniini includes extremely specialized species that have been defined as "lifters" according to their food relocation behaviour. They are characterized by the presence of well-developed expansions on the head and pronotum, which can be included in the large and varied group of horns, whose presence is usually related to complex reproductive tactics. In this study, two closely related species, Anomiopsoides cavifrons and A. heteroclyta, were examined employing traditional and geometric morphometrics to test whether the Eucraniini has polymorphic males that might exhibit different reproductive tactics, as in the sister tribe Phanaeini, for which a male trimorphism was demonstrated. If also present in Eucraniini polyphenism could be considered a plesiomorphy common to the two clades. The inter- and intraspecific shape variation and object symmetry of the head and the scaling relationships between body size and traits were evaluated. Marked interspecific and small intraspecific differences in shape variation, high symmetry, and similar isometric growth patterns were shown in both species. The hypothesis of male polymorphism in Anomiopsoides was thus rejected. Instead, the results supported the alternative hypothesis that Eucraniini lacks male polymorphism, perhaps due to functional constraints affecting the shape of the structures involved in their peculiar food relocating behaviour.

Diet-Induced Plasticity of Linear Static Allometry Is Not So Simple for Grasshoppers: Genotype–Environment Interaction in Ontogeny Is Masked by Convergent Growth

Grasshoppers, Melanoplus sanguinipes (Orthoptera: Acrididae), develop larger head width (HW) and shorter leg length, relative to body size, when fed low nutrient, lignin-rich grasses compared to sibs fed a diet of high nutrient grasses. To elucidate how underlying genetic variation and plasticity of growth generate plasticity of this linear static allometry within coarse-grained environments, I measured head and leg size of three nymphal instars and adult grasshoppers raised on either a low or high nutrient diet within a half-sib quantitative genetic experiment. Doubly-multivariate repeated measures multiple analysis of variance (MANOVA) of head, mandible, and hind leg size and their rate of growth (mm/period) and growth period (days) through ontogeny were used to analyze how the ontogeny of diet-induced plasticity for these variables and additive genetic variation for plasticity (genotype × environment interaction [G×E]) contribute to plasticity in functional linear static allometry. Genetic variation for diet-induced plasticity (G×E) of head and leg size varied through ontogeny, as did genetic variation for plasticity of growth in third and fourth instar nymphs. Despite extensive genetic variation in plasticity of HW and leg length in fourth instar nymphs, the static allometry between head and leg was stable within each diet because the patterns of G×E were similar for HW, leg length and their coordinated growth. Nutrient sensitive plasticity in growth shifted the intercept but not the slope of static allometry, a result consistent with one outcome of a graphical model of the relationships between G× E and plasticity of within environment static allometry. In addition, G×E of fourth instar head and leg size was reduced in adults by negatively size-dependent, convergent growth in the last period of ontogeny. Consequently, the bivariate reaction norms of head and leg size for adults exhibited no G×E and, again, plasticity in the intercept but not in the slope of static allometry. The ontogeny of seemingly simple diet-induced linear static allometry between functional body parts in grasshoppers arises from a complex combination of differing patterns of nutrient-sensitive growth, duration of growth, convergent growth, and G×E, all relevant to understanding the development and evolution of functional allometry in hemimetabolous insects.

Postmetamorphic ontogenetic allometry and the evolution of skull shape in Nest-building frogs Leptodactylus (Anura: Leptodactylidae)

Allometry constitutes an important source of morphological variation. However, its influence in head development in anurans has been poorly explored. By using geometric morphometrics followed by statistical and comparative methods we analyzed patterns of allometric change during cranial postmetamorphic ontogeny in species of Nest-building frogs Leptodactylus (Leptodactylidae). We found that the anuran skull is not a static structure, and allometry plays an important role in defining its shape in this group. Similar to other groups with biphasic life-cycle, and following a general trend in vertebrates, ontogenetic changes mostly involve rearrangement in rostral, otoccipital, and suspensorium regions. Ontogenetic transformations are paralleled by shape changes associated with evolutionary change in size, such that the skulls of species of different intrageneric groups are scaled to each other, and small and large species show patterns of paedomorphic/peramorphic features, respectively. Allometric trajectories producing those phenotypes are highly evolvable though, with shape change direction and magnitude varying widely among clades, and irrespective of changes in absolute body size. These results reinforce the importance of large-scale comparisons of growth patterns to understand the plasticity, evolution, and polarity of morphological changes in different clades.

The fallacy of biphasic growth allometry for the vertebrate brain

The concept of biphasic, loglinear growth of the vertebrate brain is based on graphical displays of logarithmic transformations of the original measurements. Such displays commonly give the appearance of two distinct mathematical distributions – one set of observations following a steep trajectory at the low end of the size range and another set following a shallow trajectory at the high end. However, the appearance of two distributions is an artefact resulting from the logarithmic transformations. Observations of brain mass vs. body mass in each of the eight vertebrate species examined in the current investigation conform to a single mathematical distribution that is well described by a single equation fitted to the original, untransformed data by non-linear regression. Data for carp, chickens, kangaroos and rabbits are described by three-parameter power equations whereas those for dolphins and primates are described by exponential functions that rise rapidly to a maximum. The brain continues to grow throughout life in carp, chickens, kangaroos and rabbits but not in dolphins and primates. Future investigations of relative growth of the brain should be based on graphical and analytical study of observations expressed on the native mathematical scale.

Scaling of claw sharpness: mechanical constraints reduce attachment performance in larger insects

Claws are the most widespread attachment devices in animals, but comparatively little is known about the mechanics of claw attachment. A key morphological parameter in determining attachment ability is claw sharpness; however, there is a conflict between sharpness and fracture resistance. Sharper claws can interlock on more surfaces but are more likely to break. Body size interacts with this conflict such that larger animals should have much blunter claws and consequently poorer attachment ability than smaller animals. This expected size-induced reduction in attachment performance has not previously been investigated, and it is unclear how animals deal with this effect, and whether it indeed exists. We explored the scaling of claw sharpness with body size using four insect species (Nauphoeta cinerea, Gromphadorhina portentosa, Atta cephalotes and Carausius morosus) each covering a large size range. The scaling of claw sharpness varied significantly between species, suggesting that they face different pressures regarding claw function. Attachment forces were measured for A. cephalotes and G. portentosa (which had different scaling of claw sharpness) on several rough surfaces using a centrifuge setup. As expected, attachment performance was poorer in larger animals. Firstly, larger animals were more likely to slip, although this effect depended on the scaling of claw sharpness. Secondly, when they gripped, they attached with smaller forces relative to their weight. This size-induced reduction in attachment performance has significant implications for the attachment ability of larger animals on rough surfaces.

Why the long face? Static allometry in the sexually dimorphic phenotypes of Neotropical electric fishes

The evolution of sexually dimorphic traits is thought to have marked effects on underlying patterns of static allometry. These traits can negatively affect organismal survivability by creating trade-offs between trait size and performance. Here we use three-dimensional geometric morphometrics to study the static allometry of two species of sexually dimorphic electric fishes (Apteronotus rostratus and Compsaraia samueli) in which mature males grow elongate jaws used in agonistic male–male interactions. We also estimate jaw-closing performance between the sexes of both species to track changes in kinematic transmission associated with the development of sexual weaponry. We find significantly different patterns of static allometry between the sexes of both species, with males exhibiting more positive allometric slopes relative to females. We also find a negative relationship between skull shape and mandibular kinematic transmission in C. samueli, suggesting a trade-off where males with longer faces exhibit lower mechanical advantages, suggesting weaker jaw leverage. In contrast, males and females of A. rostratus exhibit no difference between sexes in mechanical advantage associated with facial elongation.

Ontogenetic allometry conservatism across five teleost orders

Geometric morphometrics were used to analyse ontogenetic trajectories in representatives of the Characiformes, Cichliformes, Cyprinodontiformes, Siluriformes, and Tetraodontiformes. It was not possible to differentiate any allometric growth patterns across groups, indicating that a phylogenetically conserved developmental pattern is widespread throughout Teleostei.

The evolution of ontogenetic allometric trajectories in mammalian domestication

Morphological divergence of domesticated as compared to wild forms must result from changes in the ontogenetic process. Species-specific tests for heterochrony have rejected a single explanation of domestic forms representing juveniles of their wild relatives. Ontogenetic allometric trajectories for 12 pairs of wild and domestic mammals were examined using skull growth data for 1070 specimens, including representatives from all lineages in which domestication has occurred. A suite of tests were performed to quantify allometric disparity in wild and domestic forms and assess the extent and patterning of modification to allometric trajectories. Domestication has modified postnatal ontogenetic allometric trajectories in mammals, and has generated disparity, achieved through lengthening of trajectory slopes and alteration to slope angles. Allometric disparity was similar for domestic forms compared to their wild relatives, whereas the magnitude of dispersion along allometric vectors differed between precocial mammals and altricial mammals, underscoring the importance of life history and shared evolutionary history in patterns of ontogenetic variation. The results verify the importance of scaling in the morphological changes associated with domestication. The response to domestication for all measured trajectory parameters was variable across species, suggesting multiple pathways of change.

The (ongoing) problem of relative growth

Differential growth, the phenomenon where parts of the body grow at different rates, is necessary to generate the complex morphologies of most multicellular organisms. Despite this central importance, how differential growth is regulated remains largely unknown. Recent discoveries, particularly in insects, have started to uncover the molecular-genetic and physiological mechanisms that coordinate growth among different tissues throughout the body and regulate relative growth. These discoveries suggest that growth is coordinated by a network of signals that emanate from growing tissues and central endocrine organs. Here we review these findings and discuss their implications for understanding the regulation of relative growth and the evolution of morphology.

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson-Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date - repeatedly described as more evolutionarily stable than expected - so this skewness should be accounted for when investigating evolutionary dynamics in the wild.

Conservative whole-organ scaling contrasts with highly labile suborgan scaling differences among compound eyes of closely related Formica ants

Static allometries determine how organ size scales in relation to body mass. The extent to which these allometric relationships are free to evolve, and how they differ among closely related species, has been debated extensively and remains unclear; changes in intercept appear common, but changes in slope are far rarer. Here, we compare the scaling relationships that govern the structure of compound eyes of four closely related ant species from the genus Formica. Comparison among these species revealed changes in intercept but not slope in the allometric scaling relationships governing eye area, facet number, and mean facet diameter. Moreover, the scaling between facet diameter and number was conserved across all four species. In contrast, facet diameters from distinct regions of the compound eye differed in both intercept and slope within a single species and when comparing homologous regions among species. Thus, even when species are conservative in the scaling of whole organs, they can differ substantially in regional scaling within organs. This, at least partly, explains how species can produce organs that adhere to genus wide scaling relationships while still being able to invest differentially in particular regions of organs to produce specific features that match their ecology.

Why does offspring size affect performance? Integrating metabolic scaling with life-history theory

Within species, larger offspring typically outperform smaller offspring. While the relationship between offspring size and performance is ubiquitous, the cause of this relationship remains elusive. By linking metabolic and life-history theory, we provide a general explanation for why larger offspring perform better than smaller offspring. Using high-throughput respirometry arrays, we link metabolic rate to offspring size in two species of marine bryozoan. We found that metabolism scales allometrically with offspring size in both species: while larger offspring use absolutely more energy than smaller offspring, larger offspring use proportionally less of their maternally derived energy throughout the dependent, non-feeding phase. The increased metabolic efficiency of larger offspring while dependent on maternal investment may explain offspring size effects-larger offspring reach nutritional independence (feed for themselves) with a higher proportion of energy relative to structure than smaller offspring. These findings offer a potentially universal explanation for why larger offspring tend to perform better than smaller offspring but studies on other taxa are needed.