Scale Effects between Body Size and Limb Design in Quadrupedal Mammals

Recently the metabolic cost of swinging the limbs has been found to be much greater than previously thought, raising the possibility that limb rotational inertia influences the energetics of locomotion. Larger mammals have a lower mass-specific cost of transport than smaller mammals. The scaling of the mass-specific cost of transport is partly explained by decreasing stride frequency with increasing body size; however, it is unknown if limb rotational inertia also influences the mass-specific cost of transport. Limb length and inertial properties – limb mass, center of mass (COM) position, moment of inertia, radius of gyration, and natural frequency – were measured in 44 species of terrestrial mammals, spanning eight taxonomic orders. Limb length increases disproportionately with body mass via positive allometry (length ∝ body mass^0.40); the positive allometry of limb length may help explain the scaling of the metabolic cost of transport. When scaled against body mass, forelimb inertial properties, apart from mass, scale with positive allometry. Fore- and hindlimb mass scale according to geometric similarity (limb mass ∝ body mass^1.0), as do the remaining hindlimb inertial properties. The positive allometry of limb length is largely the result of absolute differences in limb inertial properties between mammalian subgroups. Though likely detrimental to locomotor costs in large mammals, scale effects in limb inertial properties appear to be concomitant with scale effects in sensorimotor control and locomotor ability in terrestrial mammals. Across mammals, the forelimb''s potential for angular acceleration scales according to geometric similarity, whereas the hindlimb''s potential for angular acceleration scales with positive allometry.     

Skeletal allometry and interlimb scaling patterns in mustelid carnivorans

To address the effects of an evolutionary increase in body size on long bone skeletal allometry, scaling patterns relating body mass, bone length, limb length, midshaft diameters, and cross-sectional properties of the humerus and femur were analyzed for four species of scansorial mustelids. Humeral and, to a lesser extent, femoral allometry is consistent with expectations of elastic similarity: bone and limb length scale with negative allometry on body mass while bone robusticity (cross-sectional parameters against bone length) scales with strong positive allometry. Differences between fore- and hindlimb scaling patterns, however, are observed, with size-dependent increases in forelimb length and humeral strength and robusticity exceeding those of the hindlimb and femur. It is hypothesized that this greater fore- than hindlimb lengthening results in postural modifications that serve to straighten the hindlimb of larger bodied scansorial mustelids relative to smaller mustelids. Straightening of hindlimb joints would more precisely align the long axis of the femur with peak (vertical) ground reaction forces, thereby accounting for the reduction in relative bending stresses acting on the femur compared to the humerus. J. Morphol. 235:121–134, 1998. © 1998 Wiley-Liss, Inc.     

Energetic benefits and adaptations in mammalian limbs: Scale effects and selective pressures

Differences in limb size and shape are fundamental to mammalian morphological diversity; however, their relevance to locomotor costs has long been subject to debate. In particular, it remains unknown if scale effects in whole limb morphology could partially underlie decreasing mass‐specific locomotor costs with increasing limb length. Whole fore‐ and hindlimb inertial properties reflecting limb size and shape—moment of inertia (MOI), mass, mass distribution, and natural frequency—were regressed against limb length for 44 species of quadrupedal mammals. Limb mass, MOI, and center of mass position are negatively allometric, having a strong potential for lowering mass‐specific locomotor costs in large terrestrial mammals. Negative allometry of limb MOI results in a 40% reduction in MOI relative to isometry's prediction for our largest sampled taxa. However, fitting regression residuals to adaptive diversification models reveals that codiversification of limb mass, limb length, and body mass likely results from selection for differing locomotor modes of running, climbing, digging, and swimming. The observed allometric scaling does not result from selection for energetically beneficial whole limb morphology with increasing size. Instead, our data suggest that it is a consequence of differing morphological adaptations and body size distributions among quadrupedal mammals, highlighting the role of differing limb functions in mammalian evolution.     

The scaling of the size and stiffness of primary flight feathers

Birds encompass a large range of body sizes, yet the importance of body size on feather morphology and mechanical properties has not been characterized. In this study, I examined the scaling relationships of primary flight feathers within a phylogenetically diverse sample of avian species varying in body size by nearly three orders of magnitude. I measured the scaling relationships between body mass and feather linear dimensions as well as feather flexural stiffness. The resnlts of an independent contrasts analysis to test the effects of phylogenetic history on the characters measured had no effect on the scaling relationships observed. There was slight, but not significant, positive allometry in the scaling of shaft diameter with respect to feather length across a range of body masses. The scaling of feather length and diameter against body mass was not significantly different from isometry. Flexural stiffness, however, exhibited strong negative allometry. Therefore, larger birds have relatively more flexible feathers than smaller birds. The more flexible primary feathers of large birds may reduce stresses on the wing skeleton during take-off and landing and also make these feathers less susceptible to mechanical failure. Conversely, the greater flexibility of these feathers may also reduce their capacity to generate aerodynamic lift.     

BODY AND LIMB SIZE DISSOCIATION AT THE ORIGIN OF BIRDS: UNCOUPLING ALLOMETRIC CONSTRAINTS ACROSS A MACROEVOLUTIONARY TRANSITION

The origin of birds and powered flight is a classic major evolutionary transition. Research on their origin often focuses on the evolution of the wing with trends of forelimb elongation traced back through many nonavian maniraptoran dinosaurs. We present evidence that the relative forelimb elongation within avian antecedents is primarily due to allometry and is instead driven by a reduction in body size. Once body size is factored out, there is no trend of increasing forelimb length until the origin of birds. We report that early birds and nonavian theropods have significantly different scaling relationships within the forelimb and hindlimb skeleton. Ancestral forelimb and hindlimb allometric scaling to body size is rapidly decoupled at the origin of birds, when wings significantly elongate, by evolving a positive allometric relationship with body size from an ancestrally negative allometric pattern and legs significantly shorten by keeping a similar, near isometric relationship but with a reduced intercept. These results have implications for the evolution of powered flight and early diversification of birds. They suggest that their limb lengths first had to be dissociated from general body size scaling before expanding to the wide range of fore and hindlimb shapes and sizes present in today's birds.     

Morphological scaling of body form in four shark species differing in ecology and life history

Body form can change across ontogeny, and can influence how animals of different sizes move and feed. Scaling data on live apex predatory sharks are rare and, therefore, we examined patterns of scaling in ontogenetic series of four sympatric shark species exhibiting a range of sizes, ecologies and life histories (tiger, bull, blacktip, and nurse shark). We evaluated 13 linear morphological variables and two areas (caudal and dorsal) that could influence both animal condition and locomotor performance. These measurements included dimensions of the dorsal, pectoral, and caudal fins, as well as several dimensions of body circumference, and of the head. For all four species, the body axis (eye‐to‐eye, lateral span, frontal span, proximal span) scaled close to isometry (expected slope of 1.0). The two largest sharks (tiger and bull sharks) also showed significant negative allometry for elements of the caudal fin. We found significant negative allometry in the lengths of the upper lobe of the caudal fin (caudal fin 1) and the overall height of the caudal fin (caudal fin 2) in tiger and bull sharks, with slopes ranging from about 0.60 to 0.73. Further, tiger sharks showed negative allometry in caudal fin area. These results suggest that in terms of overall body dimensions, small sharks are roughly geometrically similar to large sharks, at least within the species we examined. However, juvenile tiger (and to a lesser extent bull sharks) are notable in having proportionately larger caudal fins compared to adult sharks. As the caudal fin contributes to generating thrust during forward locomotion, this scaling implies differences among adult and juvenile sharks in locomotor ability. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 114 , 126–135.     

Salient features in the locomotion of proboscideans revealed via the differential scaling of limb long bones

The standard differential scaling of proportions in limb long bones (length against circumference) was applied to a phylogenetically wide sample of the Proboscidea, Elephantidae and the Asian (Elephas maximus) and African (Loxodonta africana) elephants. In order to investigate allometric patterns in proboscideans and terrestrial mammals with parasagittal limb kinematics, the computed slopes between long bone lengths and circumferences (slenderness exponents) were compared with published values for mammals, and studied within a framework of the theoretical models of long bone scaling under gravity and muscle forces. Limb bone allometry in E. maximus and the Elephantidae is congruent with adaptation to bending and/or torsion induced by muscular forces during fast locomotion, as in other mammals, whereas the limb bones in L. africana appear to be adapted for coping with the compressive forces of gravity. Hindlimb bones are therefore more compliant than forelimb bones, and the resultant limb compliance gradient in extinct and extant elephants, contrasting in sign to that of other mammals, is shown to be a new important locomotory constraint preventing elephants from achieving a full‐body aerial phase during fast locomotion. Moreover, the limb bone pattern of African elephants, indicating a noncritical bone stress not increasing with increments in body weight, explains why their mean and maximal body masses are usually above those for Asian elephants. Differences in ecology may be responsible for the subtle differences observed in vivo between African and Asian elephants, but they appear to be more pronounced when revealed via mechanical patterns dictated by limb bone allometry. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 100 , 16–29.     

Postnatal long bone growth in terrestrial placental mammals: Allometry,life history,and organismal traits

The ontogenetic allometry of long bone proportions is poorly understood in Mammalia. It has previously been suggested that during mammalian ontogeny long bone proportions grow more slender (positive allometry; length ∝ circumference^>1.0), although this conclusion was based upon data from a few small‐bodied taxa. It remains unknown how ontogenetic long bone allometry varies across Mammalia in terms of both taxonomy and body size. We collected long bone length and circumference data for ontogenetic samples of 22 species of mammals spanning six major clades and three orders of magnitude in body mass. Using reduced major axis bivariate regressions to compare bone length to circumference, we found that isometry and positive allometry are the most widespread patterns of growth across mammals. Negative allometry (i.e., bones growing more robust during ontogeny) occurs in mammals but is largely restricted to cetartiodactyls. Using regression slope as a proxy for long bone allometry, we compared long bone allometry to life history and organismal traits. Neonatal body mass, adult body mass, and growth rate have a negative relationship with long bone allometry. At an adult mass of roughly 15–20 kg, long bone growth shifts from positive allometry to mainly isometry and negative allometry. There were no significant relationships between ontogenetic long bone allometry and either cursoriality or basal metabolic rate. J. Morphol. © 2012 Wiley Periodicals, Inc.     

The structural mechanics and evolution of aquaflying birds

Mass‐specific bone strength was examined in the forelimb and hindlimb of 64 species of birds to determine if aquaflying birds (which utilize the wings for propulsion underwater) differ in their skeletal strength compared with other avian taxa. Long bone strengths were estimated from cross‐sectional measurements. Compared with the expectation from geometric similarity, humeral section modulus in volant birds scales nearly isometrically, while femoral strength scales with significant positive allometry. Penguin mass‐specific humeral strength is greatly elevated, but the average humeral strength in species that are propelled by the wings in both air and water do not differ from the values calculated in non‐diving taxa. However, amphibious flyers have gracile femora. Comparative analyses using independent contrasts were utilized to examine the impact of phylogenetic signal. The residual measured for the penguin–procellariiform humeral strength contrast was larger in magnitude (residual of 2.14) than at any other node in the phylogeny. The data strongly indicate that the transition from an amphibious flight condition to a fully aquatic condition involves greater changes in mechanical factors than the transition from purely aerial locomotion to amphibious wing use. There remains the possibility that a historical effect, such as ancestral body size, has impacted the mechanical scaling of penguins. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 99 , 687–698.     

Post-hatching growth and development of the pectoral and pelvic limbs in the black noddy, Anous minutus

The black tern (Anous minutus) uses a semi-precocial growth strategy. Terrestrial locomotor capacity occurs soon after hatching, but pectoral limb development is delayed and flight is not possible until about post-hatching day 50. A growth series (hatchlings to fledglings) was used to explore how limb musculoskeletal development varied with body mass. In the pelvic limb, bone lengths scaled isometrically or with negative allometry. Gastrocnemius muscle mass and the failure load and stiffness of the tibiotarsus scaled isometrically. In the pectoral limb, pectoralis and supracoracoideus muscle masses increased with strong positive allometry that was mirrored by increases in wing bone strength and stiffness. Bending strength (sigma(ult)) and modulus (E) remained fairly constant throughout development to fledging for all limb bones. The moment of inertia (I) scaled with negative allometry for the tibiotarsus and with strong positive allometry in the wing bones. Differences in sigma(ult) and E of the tibiotarsus between pre-fledged chicks and adults was due, primarily, to increases in bone density rather than increases in the moment of inertia of the skeletal elements, whereas sigma(ult) of wing bones was a function of increases in both bone density and I. Early development of functional pelvic limbs in tree-nesting birds is relatively unusual, and presumably reflects a familial trait that does not appear to compromise breeding success in this species.     

Molar scaling in strepsirrhine primates

We examined how maxillary molar dimensions change with body and skull size estimates among 54 species of living and subfossil strepsirrhine primates. Strepsirrhine maxillary molar areas tend to scale with negative allometry, or possibly isometry, relative to body mass. This observation supports several previous scaling analyses showing that primate molar areas scale at or slightly below geometric similarity relative to body mass. Strepsirrhine molar areas do not change relative to body mass(0.75), as predicted by the metabolic scaling hypothesis. Relative to basicranial length, maxillary molar areas tend to scale with positive allometry. Previous claims that primate molar areas scale with positive allometry relative to body mass appear to rest on the incorrect assumption that skull dimensions scale isometrically with body mass. We identified specific factors that help us to better understand these observed scaling patterns. Lorisiform and lemuriform maxillary molar scaling patterns did not differ significantly, suggesting that the two infraorders had little independent influence on strepsirrhine scaling patterns. Contrary to many previous studies of primate dental allometry, we found little evidence for significant differences in molar area scaling patterns among frugivorous, folivorous, and insectivorous groups. We were able to distinguish folivorous species from frugivorous and insectivorous taxa by comparing M1 lengths and widths. Folivores tend to have a mesiodistally elongated M1 for a given buccolingual M1 width when compared to the other two dietary groups. It has recently been shown that brain mass has a strong influence on primate dental eruption rates. We extended this comparison to relative maxillary molar sizes, but found that brain mass appears to have little influence on the size of strepsirrhine molars. Alternatively, we observed a strong correlation between the relative size of the facial skull and relative molar areas among strepsirrhines. We hypothesize that this association may be underlain by a partial sharing of the patterning of development between molar and facial skull elements.     

Post-hatching growth and development of the pectoral and pelvic limbs in the black noddy, Anous minutus.

The black tern (Anous minutus) uses a semi-precocial growth strategy. Terrestrial locomotor capacity occurs soon after hatching, but pectoral limb development is delayed and flight is not possible until about post-hatching day 50. A growth series (hatchlings to fledglings) was used to explore how limb musculoskeletal development varied with body mass. In the pelvic limb, bone lengths scaled isometrically or with negative allometry. Gastrocnemius muscle mass and the failure load and stiffness of the tibiotarsus scaled isometrically. In the pectoral limb, pectoralis and supracoracoideus muscle masses increased with strong positive allometry that was mirrored by increases in wing bone strength and stiffness. Bending strength (sigma(ult)) and modulus (E) remained fairly constant throughout development to fledging for all limb bones. The moment of inertia (I) scaled with negative allometry for the tibiotarsus and with strong positive allometry in the wing bones. Differences in sigma(ult) and E of the tibiotarsus between pre-fledged chicks and adults was due, primarily, to increases in bone density rather than increases in the moment of inertia of the skeletal elements, whereas sigma(ult) of wing bones was a function of increases in both bone density and I. Early development of functional pelvic limbs in tree-nesting birds is relatively unusual, and presumably reflects a familial trait that does not appear to compromise breeding success in this species.     

The scaling of tongue projection in the veiled chameleon,Chamaeleo calyptratus

Within a year of hatching, chameleons can grow by up to two orders of magnitude in body mass. Rapid growth of the feeding mechanism means that bones, muscles, and movements change as chameleons grow while needing to maintain function. A previous morphological study showed that the musculoskeletal components of the feeding apparatus grow with negative allometry relative to snout–vent length (SVL) in chameleons. Here, we investigate the scaling of prey capture kinematics and muscle physiological cross-sectional area in the veiled chameleon, Chamaeleo calyptratus. The chameleons used in this study varied in size from approximately 3 to 18 cm SVL (1–200 g). Feeding sequences of 12 chameleons of different sizes were filmed and the timing of movements and the displacements and velocities of the jaws, tongue, and the hyolingual apparatus were quantified. Our results show that most muscle cross-sectional areas as well as tongue and hyoid mass scaled with isometry relative to mandible length, yet with negative allometry relative to SVL. Durations of movement also scaled with negative allometry relative to SVL and mandible length. Distances and angles generally scaled as predicted under geometric similarity (slopes of 1 and 0, respectively), while velocities generally scaled with slopes greater than 0 relative to SVL and mandible length. These data indicate that the velocity of jaw and tongue movements is generally greater in adults compared to juveniles. The discrepancy between the scaling of cross-sectional areas versus movements suggests changes in the energy storage and release mechanisms implicated in tongue projection.     

The relationships among jaw‐muscle fiber architecture,jaw morphology,and feeding behavior in extant apes and modern humans

The jaw‐closing muscles are responsible for generating many of the forces and movements associated with feeding. Muscle physiologic cross‐sectional area (PCSA) and fiber length are two architectural parameters that heavily influence muscle function. While there have been numerous comparative studies of hominoid and hominin craniodental and mandibular morphology, little is known about hominoid jaw‐muscle fiber architecture. We present novel data on masseter and temporalis internal muscle architecture for small‐ and large‐bodied hominoids. Hominoid scaling patterns are evaluated and compared with representative New‐ (Cebus) and Old‐World (Macaca) monkeys. Variation in hominoid jaw‐muscle fiber architecture is related to both absolute size and allometry. PCSAs scale close to isometry relative to jaw length in anthropoids, but likely with positive allometry in hominoids. Thus, large‐bodied apes may be capable of generating both absolutely and relatively greater muscle forces compared with smaller‐bodied apes and monkeys. Compared with extant apes, modern humans exhibit a reduction in masseter PCSA relative to condyle‐M₁ length but retain relatively long fibers, suggesting humans may have sacrificed relative masseter muscle force during chewing without appreciably altering muscle excursion/contraction velocity. Lastly, craniometric estimates of PCSAs underestimate hominoid masseter and temporalis PCSAs by more than 50% in gorillas, and overestimate masseter PCSA by as much as 30% in humans. These findings underscore the difficulty of accurately estimating jaw‐muscle fiber architecture from craniometric measures and suggest models of fossil hominin and hominoid bite forces will be improved by incorporating architectural data in estimating jaw‐muscle forces. Am J Phys Anthropol 151:120–134, 2013. © 2013 Wiley Periodicals, Inc.     

Scaling of the ballistic tongue apparatus in chameleons

Body dimensions of organisms can have a profound impact on their functional and structural properties. We examined the morphological proportions of the feeding apparatus of 105 chameleon specimens representing 23 species in seven genera, spanning a 1,000‐fold range in body mass to test whether the feeding apparatus conforms to the null hypotheses of geometric similarity that is based on the prevalence of geometric similarity in other ectothermic vertebrates. We used a phylogenetically corrected regression analysis based on a composite phylogenetic hypothesis to determine the interspecific scaling patterns of the feeding apparatus. We also determined the intraspecific (ontogenetic) scaling patterns for the feeding apparatus in three species. We found that both intraspecifically and interspecifically, the musculoskeletal components of the feeding apparatus scale isometrically among themselves, independent of body length. The feeding apparatus is thus of conserved proportions regardless of overall body length. In contrast, we found that the tongue apparatus as a whole and its musculoskeletal components scale with negative allometry with respect to snout‐vent length—smaller individuals have a proportionately larger feeding apparatus than larger individuals, both within and among species. Finally, the tongue apparatus as a whole scales with negative allometry with respect to body mass through ontogeny, but with isometry interspecifically. We suggest that the observed allometry may be maintained by natural selection because an enlarged feeding apparatus at small body size may maximize projection distance and the size of prey that smaller animals with higher mass‐specific metabolic rates can capture. J. Morphol. 2012. © 2012 Wiley Periodicals, Inc.     

Relations between microhabitat use and limb shape in phrynosomatid lizards

With the exception of the well-documented case for anoline lizards, recent studies have found few evolutionary relationships between morphology and habitat use in lizards despite clear-cut biomechanical predictions. One of the factors typically hampering these analyses is the clustering of habitat use within evolutionary lineages. In the present study, body shape was quantified for male and female lizards of 30 species of phrynosomatid lizards. This group was selected as little clustering of ecological variables seemed to be present. The results of traditional analyses indicate that evolutionary correlates of habitat use were prominent in the hindlimbs of both sexes. Species living in open habitats are characterized by longer femurs, and longer hindlimbs relative to the forelimb. Moreover, males from ground-dwelling species utilizing open habitats have longer toes on the hind foot than males from climbing species. Phylogenetic analyses indicated strong evolutionary associations between habitat use and the relative length of front and hindlimbs, with species from open terrestrial habitats having significantly shorter frontlimbs relative to their hindlimb than rock or tree climbing species. Evolutionary associations between morphology and habitat use were generally stronger for male lizards, indicating a potentially important contribution of sexual selection to the evolution of differences in limb proportions.  © 2002 The Linnean Society of London, Biological Journal of the Linnean Society , 2002, 77 , 149–163.     

Reduced phenotypic covariation in marsupial limbs and the implications for mammalian evolution

As serially homologous structures, mammalian fore‐ and hindlimbs ancestrally share a common developmental and genetic architecture. As a result, mammalian fore‐ and hindlimbs are predicted to be highly integrated in the absence of selective pressures to form divergent limb morphologies. Marsupials experience such a divergent selective pressure to form a robust forelimb to power a post‐natal crawl to the teat. In this study, phenotypic covariation in marsupials was assessed to determine if specialization for the crawl did indeed reduce integration between their fore‐ and hindlimbs. To explore the evolution of mammalian limb integration, phenotypic covariation in representative eutherians and monotremes was also examined. Phenotypic covariation in limbs was quantified morphometrically, and analysed with correlational and phylogenetic methods. Results indicate that marsupials generally have relatively high levels of within‐limb phenotypic covariation, and low levels between limbs, in contrast to the pattern reconstructed for the mammalian ancestor. Our findings support the hypothesis that pressure to specialize in one limb (either the fore‐ or the hindlimb) can reduce phenotypic covariation between limbs, and that reduced limb phenotypic covariation is derived in marsupials. Further research is needed to test the effect that these differences in limb phenotypic covariation had on the evolution of the major mammalian groups. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 102 , 22–36.     

Ecological consequences of scaling of chew cycle duration and daily feeding time in Primates

Feeding systems and behaviors must evolve to satisfy the metabolic needs of organisms. This includes modifications to feeding systems as body size and metabolic needs change. Using our own data and data from the literature, we examine how size-related changes in metabolic needs are met by size-related changes in daily feeding time, chew cycle duration, volume of food processed per chew, and daily food volume intake in primates. Increases in chew cycle duration with body mass in haplorhine primates are described by a simple power function (cycle time α body mass^0.181). Daily feeding time increases with body mass when analyzed using raw data from the “tips” of the primate phylogenetic tree, but not when using phylogenetically independent contrasts. Whether or not daily feeding time remains constant or increases with body mass, isometry of ingested bite size and the slow rate of increase in chew cycle time with body size combine to allow daily ingested food volume to scale faster than predicted by metabolic rate. This positive allometry of daily ingested food volume may compensate for negative allometry of nutrient concentration in primate foods. Food material properties such as toughness and hardness have little impact on scaling of chew cycle durations, sequence durations, or numbers of chews in a sequence. Size-related changes in food processing abilities appear to accommodate size-related changes in food material properties, and primates may alter ingested bite sizes in order to minimize the impacts of food material properties on temporal variables such as chew cycle duration and chew sequence duration.     

Fabricational morphology of oblique ribs in bivalves

Most analyses on allometry of long bones in terrestrial mammals have focused on dimensional allometry, relating external bone measurements either to each other or to body mass. In this article, an analysis of long bone mass to body mass in 64 different species of mammals, spanning three orders of magnitude in body mass, is presented. As previously reported from analyses on total skeletal mass to body mass in terrestrial vertebrates, the masses of most appendicular bones scale with significant positive allometry. These include the pectoral and pelvic girdles, humerus, radius+ulna, and forelimb. Total hindlimb mass and the masses of individual hindlimb bones (femur, tibia, and metatarsus) scale isometrically. Metapodial mass correlates more poorly with body mass than the girdles or any of the long bones. Metapodial mass probably reflects locomotor behavior to a greater extent than do the long bones. Long bone mass in small mammals (<50 kg) scales with significantly greater positive allometry than bone mass in large (>50 kg) mammals, probably because of the proportionally shorter long bones of large mammals as a means of preserving resistance to bending forces at large body sizes. The positive allometric scaling of the skeleton in terrestrial animals has implications for the maximal size attainable, and it is possible that the largest sauropod dinosaurs approached this limit.     

Understanding reproductive allometry in turtles: A slippery “slope”

Measures of reproductive output in turtles are generally positively correlated with female body size. However, a full understanding of reproductive allometry in turtles requires logarithmic transformation of reproductive and body size variables prior to regression analyses. This allows for slope comparisons with expected linear or cubic relationships for linear to linear and linear to volumetric variables, respectively. We compiled scaling data using this approach from published and unpublished turtle studies (46 populations of 25 species from eight families) to quantify patterns among taxa. Our results suggest that for log–log comparisons of clutch size, egg width, egg mass, clutch mass, and pelvic aperture width to shell length, all scale hypoallometrically despite theoretical predictions of isometry. Clutch size generally scaled at ~1.7 to 2.0 (compared to an isometric expectation of 3.0), egg width at ~0.5 (compared to an expectation of 1.0), egg mass at ~1.1 to 1.3 (3.0), clutch mass at ~2.5 to 2.8 (3.0), and pelvic aperture width at 0.8–0.9 (1.0). We also found preliminary evidence that scaling may differ across years and clutches even in the same population, as well as across populations of the same species. Future investigators should aspire to collect data on all these reproductive parameters and to report log–log allometric analyses to test our preliminary conclusions regarding reproductive allometry in turtles.