Normalizing physical performance tests for body size: a proposal for standardization

There is a lack of standardized methodology for normalizing various indices of muscle strength and movement performance tests for differences in body size in human movement-related disciplines. Most of the data presented in the literature have been body size dependent, which precludes both comparisons between subjects and establishment of standards for specific subject populations. The goal of the present review was to propose standardized tests that normalize physical performance tests to body size. Specifically, we propose (a) using an allometric normalization based on theoretical models that presume geometric similarity, (b) using classification of performance tests based on particular values of the allometric parameters required for normalization, and (c) using a simple "performance index" that represents an individual or group performance relative to a reference population. Correspondences between theory and experimental findings and limitations are discussed.     

The relationship of lean limb volume to performance in the handgrip and standing long jump tests in boys and girls, aged 11.6–13.2 years

Twenty-three girls and 19 boys performed the handgrip and standing long jump (SLJ) tests. Their total forearm and leg volumes were calculated from circumference and length measurements and the lean volumes (bone + muscle) were calculated by making allowance for skinfold thickness. Although the boys were older than the girls (12.8 and 12.4 years), there was no significant difference in their heights or body masses. The absolute performances of the boys were superior to those of the girls in both tests (handgrip 234 and 205 N and SLJ 1.53 and 1.34 m), but when jumping performance was expressed as distance x body mass, there was no significant difference. In both tests, performance in terms of unit lean limb volume showed no significant gender difference. When performance was related to lean limb volume, both boys and girls showed a linear relationship in the two tests, with no significant difference between them. This absence of a gender difference contrasts with the results of a previous study on young adults and comparison shows that the relationships between lean limb volume and performance in the two tests for both boys and girls lie just below those of the young, adult females. The difference between the girls and the young adult females was just significant in the handgrip (p less than 0.05), but not significant in the SLJ (p greater than 0.25), whereas the differences between the boys and young adult males were significant (p less than 0.01) in both tests. Thus it would appear that a gender difference in the performance of skeletal muscle develops during adolescence and possible contributory factors are discussed.     

The ratio and allometric scaling of speed, power, and strength in elite male rugby union players

This study compared the effectiveness of ratio and allometric scaling for normalizing speed, power, and strength in elite male rugby union players. Thirty rugby players (body mass [BM] 107.1 ± 10.1 kg, body height [BH] 187.8 ± 7.1 cm) were assessed for sprinting speed, peak power during countermovement jumps and squat jumps, and horizontal jumping distance. One-repetition maximum strength was assessed during a bench press, chin-up, and back squat. Performance was normalized using ratio and allometric scaling (Y/X), where Y is the performance, X, the body size variable (i.e., BM or BH), and b is the power exponent. An exponent of 1.0 was used during ratio scaling. Allometric scaling was applied using proposed exponents and derived exponents for each data set. The BM and BH variables were significantly related, or close to, performance during the speed, power and/or strength tests (p < 0.001-0.066). Ratio scaling and allometric scaling using proposed exponents were effective in normalizing performance (i.e., no significant correlations) for some of these tests. Allometric scaling with derived exponents normalized performance across all the tests undertaken, thereby removing the confounding effects of BM and BH. In terms of practical applications, allometric scaling with derived exponents may be used to normalize performance between larger rugby forwards and smaller rugby backs, and could provide additional information on rugby players of similar body size. Ratio scaling may provide the best predictive measure of performance (i.e., strongest correlations).     

Adaptation and constraint in the evolution of Drosophila melanogaster wing shape

SUMMARY We have taken advantage of parallel instances of natural selection on body size in Drosophila melanogaster to investigate constraints and adaptation affecting wing shape. Using recently developed techniques for statistical shape analysis, we have examined variation in wing shape in similar body size clines on three continents. Gender-related shape differences were constant among all populations, suggesting that gender differences represent a developmental constraint on wing shape. In contrast, the underlying shape varied significantly between continents and shape change within each cline (i.e., between small and large body size populations) also varied between continents. Therefore, variation at these two levels presumably results from either drift or natural selection. Functional considerations suggest that shape variation between the continents is unlikely to be adaptive. However, cline-related shape change, which we show has a significant allometric component, may be adaptive. The overall range of wing shape variation, across a large range of wing size, is extremely small, and the possibility that wing shape is subject to stabilizing selection (or canalization) is discussed.     

Allometry and prediction in hominoids: a solution to the problem of intervening variables.

To avoid misinterpretation of allometric exponents determined from interspecific allometric comparisons, specific conditions must be met with respect to the common reference variable. Body weight is considered to be the best general indication of overall size and is hence widely acknowledged to be the most suitable reference variable. However, because of the paucity of recorded body weights for museum specimens, various comparative studies have used other size indicators as intervening variables, although the allometric relationships to body size/weight were often unknown and possibly differed between species. Because of differences in the scaling properties of alternative intervening variables across the species investigated, conflicting conclusions may be drawn if different variables are chosen as substitutes for overall size. This is illustrated with two examples. In this study, series of skeletons with associated body weights of Gorilla, Pan, Pongo, and Homo were investigated. Both ontogenetic and static adult allometric relationships between several widely used reference variables and body weight were determined. Neither these variables nor additional estimators investigated in this study displayed allometric exponents and coefficients similar enough across species to justify direct interspecific comparison. To generate an alternative size estimator for both ontogenetic and static interspecific investigations, equations for combined sexes were derived to predict body weight from various long bone dimensions for individual hominoid species. From a total of 25 predictors, 12 prediction equations per species (six for nonadults and six for adults) were selected according to their relative suitability for reliable prediction of body weight. It is shown that the derived reference variable "predicted body weight" avoids problems of intervening variables, is valid for any interspecific ontogenetic and static allometric comparison, and displays less fluctuation in comparison to actual body weight.     

A functional-morphometric analysis of forelimbs in bipedal and quadrupedal heteromyid rodents

The rodent family Heteromyidae contains bipedal hoppers and quadrupedal runners. The possibility that bipedalism is associated with forelimb specialization for nonlocomotory functions, such as burrowing and seed-gathering, motivated a static functional-morphometric and interspecific allometric analysis of 18 metric characters of the forelimb skeleton. A principal-components analysis, across 28 species in six genera, showed that lengths of proximal (scapula, humerus) and distal (ulna, radius, metacarpal) elements were negatively allometric, and widths were positively allometric. Quadrupedal and bipedal species groups showed qualitatively similar allometric patterns, except that scapula width anterior to the spine was positively allometric in quadrupeds and negatively allometric in bipeds; scapula width posterior to the spine was positively allometric in bipeds and isometric in quadrupeds; and olecranon length was isometric in bipeds and positively allometric in quadrupeds. Most morphometric characters varied significantly among species within genera, even when effects of size variation were reduced by reconstructing all species to a common general size (as indicated by their score on the first principal component). These shape differences caused species to vary in the mechanical advantage of the forelimb, of possible importance for digging and seed-harvesting performance. Relative to quadrupeds, bipedal species tended to have greater mechanical advantage for proximal forelimb elements and smaller mechanical advantage for distal forelimb elements, but only the distal pattern remained in reconstructed forms, and no functional character was significantly different when tested over variation among genera nested within locomotion type. Cluster analysis confirmed that forelimb characters related to digging or seed-harvest are not coincident with mode of locomotion. Forelimb characters were, however, associated with digging or seed-harvest performance. Mechanical advantage of the proximal forelimb was positively related to an index of the compaction of soils with which 26 desert-dwelling species are associated, and also to relative use of heavy vs. light soils by nine species in the laboratory. Across 10 species, deviations in seed-harvest rate from expected allometric values were negatively correlated with mechanical advantage of the distal forelimb.     

Characterizing morphological (co)variation using structural equation models: Body size,allometric relationships and evolvability in a house sparrow metapopulation

Body size plays a key role in the ecology and evolution of all organisms. Therefore, quantifying the sources of morphological (co)variation, dependent and independent of body size, is of key importance when trying to understand and predict responses to selection. We combine structural equation modeling with quantitative genetics analyses to study morphological (co)variation in a meta‐population of house sparrows (Passer domesticus). As expected, we found evidence of a latent variable “body size,” causing genetic and environmental covariation between morphological traits. Estimates of conditional evolvability show that allometric relationships constrain the independent evolution of house sparrow morphology. We also found spatial differences in general body size and its allometric relationships. On islands where birds are more dispersive and mobile, individuals were smaller and had proportionally longer wings for their body size. Although on islands where sparrows are more sedentary and nest in dense colonies, individuals were larger and had proportionally longer tarsi for their body size. We corroborated these results using simulations and show that our analyses produce unbiased allometric slope estimates. This study highlights that in the short term allometric relationships may constrain phenotypic evolution, but that in the long term selection pressures can also shape allometric relationships.     

Allometric trajectories of body and head morphology in three sympatric Arctic charr (Salvelinus alpinus (L.)) morphs

A study of body and head development in three sympatric reproductively isolated Arctic charr (Salvelinus alpinus (L.)) morphs from a subarctic lake (Skogsfjordvatn, northern Norway) revealed allometric trajectories that resulted in morphological differences. The three morphs were ecologically assigned to a littoral omnivore, a profundal benthivore and a profundal piscivore, and this was confirmed by genetic analyses (microsatellites). Principal component analysis was used to identify the variables responsible for most of the morphological variation of the body and head shape. The littoral omnivore and the profundal piscivore morph had convergent allometric trajectories for the most important head shape variables, developing bigger mouths and relatively smaller eyes with increasing head size. The two profundal morphs shared common trajectories for the variables explaining most of the body and head shape variation, namely head size relative to body size, placement of the dorsal and pelvic fins, eye size and mouth size. In contrast, the littoral omnivore and the profundal benthivore morphs were not on common allometric trajectories for any of the examined variables. The findings suggest that different selective pressures could have been working on traits related to their trophic niche such as habitat and diet utilization of the three morphs, with the two profundal morphs experiencing almost identical environmental conditions.     

Diet effects on female reproduction in high growth (hg/hg) mice that are deficient in the Socs-2 gene

The detrimental effect of larger body size on reproductive performance has been well documented in mouse models of overgrowth, such as Growth Hormone (GH) transgenics. This study describes the reproductive performance of the High Growth (HG) mouse model of overgrowth. The HG mouse model exhibits overgrowth due to a partially recessive autosomal mutation that increases growth rate and mature body size. The HG phenotype results from the lack of expression of Socs-2, which negatively regulates GH signaling. C57BL/6J (C57) and congenic C57BL/6J-hg/hg (HG) female mice were fed four diets differing in protein and energy content, starting at 8 weeks of age. A complete reproductive cycle from mating to weaning was evaluated. HG mice were 40% larger than C57 and had a higher feed intake throughout the experiment. Significant genotype x diet interactions were detected for growth, body composition and reproductive traits. HG females showed poor reproductive performance compared to controls as demonstrated by their lower fertility during mating, which was not overcome by changes in the diet. No differences were detected in litter size, but HG animals exhibited a longer gestation length and heavier pup weaning weights compared to controls. Reproductive impairment in HG seems to be the consequence of the lack of Socs-2 independent of the effects of increased body size on reproduction.     

The allometric approach to species differences in brain size

Allometric methods can be used to test quantitative theories of the relationship between brain size and body size across species, and to search for ecological, behavioural, life history, and ontogenetic correlates of brain size. Brain size scales with an allometric exponent of around 0.75 against body size across mammals, but is closer to 0.56 for birds and for reptiles. The slope of the allometric line often varies depending upon the taxonomic level of analysis. However, this phenomenon, at least in mammals, may be a statistical artifact. Brain size for a given body size (relative brain size) varies among orders in birds and mammals, and some dietary associations with relative brain size have been found in particular taxa. Developmental status at birth is the most consistent correlate of relative brain size: precocial neonates have larger brains for a given maternal size than altricial neonates in both birds and mammals. Altricial neonates, however, have more brain growth following birth, and in birds also have larger relative adult brain sizes. Energetic explanations for differences in neonatal brain growth, although attractive on theoretical grounds, have largely failed to stand up to empirical tests.     

Differential long bone growth of children between two months and eleven years of age

Diaphyseal lengths of the humerus, radius, femur and tibia of upper-middle class White children between two months and 11 years of age show positive allometric growth, indicating substantial shape or proportional change. The segments of the lower extremity display greater allometric increase than the humerus and radius; variation in relative growth within each extremity is small and inconsistent. Sex differences are consistent, with slightly greater proportional increases demonstrated for boys. The results suggest that absolute intralimb variation in growth, following a disto-proximo growth or maturity gradient, is due to initial differences in size or scale and not to differences in patterns of growth. Developmental variation between extremities is due to scaling plus variation in relative growth patterns.     

Allometric influence on phenotypic variation in the Song Sparrow (Melospiza melodia)

Song Sparrow ( Melospiza melodia ) populations found along the Pacific Coast of North America, from Baja California to the islands off the coast of Alaska, exhibit extensive morphological variation. With a multivariate analysis of size and shape, I describe a portion of this pattern and examine how it could be maintained despite gene flow among the populations. Because shape differences fall along geographic barriers, I suggest that similarities among Song Sparrow populations in multivariate shape reflect their pattern of genetic relatedness. A general pattern of Song Sparrow post-nestling growth allometry has been discovered: bill characteristics are positively allometric and all other characteristics are negatively allometric. In contrast to shape, multivariate patterns of body size variation do not correspond to geographic relationships. In combination with evidence of Song Sparrow phenotypic plasticity, it is proposed that multivariate body size is an environmentally plastic trait and that specific traits exhibit levels of phenotypic plasticity in proportion to their rate of growth with respect to body size. In this way local environmental factors which alter body size may change an entire suite of allometrically related traits and thus create striking patterns of morphological variation.     

Gill surface area provides a clue for the respiratory basis of brain size in the blacktip shark (Carcharhinus limbatus)

Brain size varies dramatically, both within and across species, and this variation is often believed to be the result of trade-offs between the cognitive benefits of having a large brain for a given body size and the energetic cost of sustaining neural tissue. One potential consequence of having a large brain is that organisms must also meet the associated high energetic demands. Thus, a key question is whether metabolic rate correlates with brain size. However, using metabolic rate to measure energetic demand yields a relatively instantaneous and dynamic measure of energy turnover, which is incompatible with the longer evolutionary timescale of changes in brain size within and across species. Morphological traits associated with oxygen consumption, specifically gill surface area, have been shown to be correlates of oxygen demand and energy use, and thus may serve as integrated correlates of these processes, allowing us to assess whether evolutionary changes in brain size correlate with changes in longer-term oxygen demand and energy use. We tested how brain size relates to gill surface area in the blacktip shark Carcharhinus limbatus. First, we examined whether the allometric slope of brain mass (i.e., the rate that brain mass changes with body mass) is lower than the allometric slope of gill surface area across ontogeny. Second, we tested whether gill surface area explains variation in brain mass, after accounting for the effects of body mass on brain mass. We found that brain mass and gill surface area both had positive allometric slopes, with larger individuals having both larger brains and larger gill surface areas compared to smaller individuals. However, the allometric slope of brain mass was lower than the allometric slope of gill surface area, consistent with our prediction that the allometric slope of gill surface area could pose an upper limit to the allometric slope of brain mass. Finally, after accounting for body mass, individuals with larger brains tended to have larger gill surface areas. Together, our results provide clues as to how fishes may evolve and maintain large brains despite their high energetic cost, suggesting that C. limbatus individuals with a large gill surface area for their body mass may be able to support a higher energetic turnover, and, in turn, a larger brain for their body mass.     

Modeling the influence of body size on weightlifting and powerlifting performance

The purpose of this study was to examine 1) if lifting performance in both the weightlifting (WL) and powerlifting (PL) scale with body mass (M) in line with theory of geometric similarity, and 2) whether there are any gender differences in the allometric relationship between lifting performance and body size. This was performed by analyzing ten best WL and PL total results for each weight class, except for super heavyweight, achieved during 2000-2003. Data were analysed with the allometric and second-order polynomial model, and detailed regression diagnostics was applied in order to examine appropriateness of the models used. Results of the data analyses indicate that 1) women's WL and men's PL scale for M in line with theory of geometric similarity, 2) both WL and PL mass exponents are gender-specific, probably due to gender differences in body composition, 3) WL and PL results scale differently for M possibly due to their structural and functional differences. However, the obtained mass exponents does not provide size-independent indices of lifting performances since the allometric model exhibit a favourable bias toward middleweight lifters in most lifting data analyzed. Due to possible deviations from presumption of geometric similarity among lifters, future studies on scaling lifting performance should use fat-free mass and height as indices of body size.     

Sexual dimorphism and allometry in primate ossa coxae

Five measurements were taken on the ossa coxae of 454 adult primates representing Ceboidea, Cercopithecoidea and Hominoidea. Sex differences in these variables and their relationships to overall body size and sexual dimorphism were tested by means of Student's t-test and regression analysis. The study attempts to clarify the nature of primate pelvic sexual dimorphism, including allometric effects, and more specifically, test the assertion made by Mobb and Wood (1977) that sexual dimorphism in body size in not an important determinant in pelvic sex differences. Variables that contribute to the size of the birth canal tend to be larger in females than males in all taxa studied except two. In these, Hylobates and Alouatta, there were no significant differences between the sexes for any of the five variables. In general, sexual dimorphism in variables contributing to the size of the birth canal was correlated (r ? 0.8) with sexual dimorphism in body size. Furthermore, the coefficients of allometry underlying pelvic sex differences were shown to be moderately correlated (r ? 0.5) with sexual dimorphism in size. The influence of other adaptive factors on primate pelvic sexual dimorphism are also briefly discussed.     

The Morphometry of Solenopsis Fire Ants

Size-related changes of body shape were explored in 15 polymorphic species of Solenopsis fire ants by analyzing body weight along with linear measurements of 24 body parts. Log regression slopes were used to detect changes of shape with increasing size. Within species, the largest workers weighed from about 5 to 30-fold as much as the smallest. The range of within-species body lengths varied from 1.6 mm to 4 mm. As worker size increased, the gaster tended to make up a larger proportion of body length, usually at the cost of the petiole, and rarely at the cost of head length or mesosoma length. In most, the relative volume of the gaster increased and that of the head and mesosoma decreased. Most also showed an increasingly “humped” mesosoma. For all species, head shape changed from barrel-shaped to heart-shaped as worker size increased. Antennae became relatively shorter as the relative size of the club decreased. Shape changes of the legs were more variable. S. geminata was exceptional in the extreme nature of its head shape change, and was the only species in which relative head volume increased and gaster volume decreased with increasing body size. With the exception of S. geminata, the allometric rules governing shape are remarkably similar across species, suggesting a genus-level developmental scheme that is not easily modified by evolution. It also suggests that the evolution of shape is highly constrained by these conserved growth rules, and that it acts primarily (perhaps only) through allometric growth. The results are discussed in light of the growth of imaginal discs in a resource-limited body (the pupa). The substantial variation of allometries within species and across localities is also discussed in relation to using allometric patterns to identify species or to construct phylogenies.     

Morphological caste and sex differences in the Taiwanese stingless bee Trigona ventralis hoozana (Hymenoptera: Apidae)

To examine morphological differences among queens, workers and males, 14 external body characters were measured in two colonies of the Taiwanese stingless bee Trigona ventralis hoozana. Queens were largest in all of the body parts measured except eye width and mesoscutum length, and values for most variables in queens did not overlap with those of workers and males. In contrast, the worker : male size ratios for 11 variables were close to 1.0, showing that overall body size and shape of workers resembled that of males rather than of queens. Males had the largest eyes and their mesoscutum length was comparable to that of queens. ancova between 14 morphometric variables and mesoscutum width chosen as standard body size showed that allometric growth in most variables was not linear. Plotting of some variables on mesoscutum width showed that queens had a proportionally wider first metasomal tergum and longer antennal scape, but a proportionally narrower head and eye than workers and males. These tests suggest that the morphological caste differences in this species belong to a category of complete dimorphism.     

Sexual differences in locomotor performance in Tropidurus catalanensis lizards (Squamata: Tropiduridae) – body shape,size and limb musculature explain variation between males and females

Sexual dimorphism (SD) is the evolutionary outcome of selection acting differently on males and females. Several studies describe sexual differences in body size, although other morphological traits might be allometric between sexes and imply functional consequences. Here we test whether morphological differences between sexes in size and shape in the lizard Tropidurus catalanensis explain variation in performance of four locomotor traits. Our results show that males are larger than females and also exhibit longer limbs, longer muscles and larger muscle cross‐sectional areas, while females have longer trunks and more sharped anterior claws; males outperform females in all locomotor performances measured. Sexual differences in sprinting and climbing is related with body size, and climbing performance is also explained by limb lengths, by differences in lengths and cross‐sectional areas of specific muscles, and by interlimb distances. Between‐sex differences in exertion are also related to SD, despite associations with sharper posterior claws that are independent of sex. Grasping performance, however, is associated with some muscle and morphological parameters that are not sexually dimorphic. Together our results suggest that morphology might be under sexual selection in T. catalanensis, given that better locomotor performance likely favours male lizards in typical activities of this polygenic species, such as territory defence and female acquisition. Moreover, the longer trunks that characterize females may confer more space to accommodate eggs. On the other hand, territory defence by males probably increases their exposure to predators, resulting in a synergistic effect of sexual and natural selection in the evolution of SD in T. catalanensis.     

Morphological Diversity Despite Isometric Scaling of Lever Arms

In the absence of a substantial functional shift, morphological evolution is usually expected to follow an allometric trajectory, however, studies of tree squirrel jaws have found isometry across most of their size range. This isometry appears to reflect the integration of a small number of lever arm lengths that are critical for generating bite force. To test whether this integration constrains only the ratios of these lengths, or jaw shape in general, we analyzed jaw shapes and a set of lengths comparable to those used in previous studies for 23 species of sciurine tree squirrels (Sciurus, Tamiasciurus and Microsciurus), a lineage that is both functionally uniform and spans a large size range. We found that the measured lengths were highly correlated and isometric with respect to each other, but negatively allometric with respect to jaw size. Shape differences are generally small, but shape diversity was still greater than the diversity of mechanical advantages (input lever lengths scaled by output lever length). In addition, phylogenetic analyses demonstrated that only a minute fraction of shape evolution is correlated with size evolution. This contrast between the diversity of shape and the stability of proportions among a suite of functionally relevant lengths suggests that constraints on those lengths and the associated mechanical parameters have little or no ability to restrict changes in other aspects of jaw form.