The static allometry of sexual and non-sexual traits in vervet monkeys

Sexual traits vary tremendously in static allometry. This variation may be explained in part by body size-related differences in the strength of selection. We tested this hypothesis in two populations of vervet monkeys, using estimates of the level of condition dependence for different morphological traits as a proxy for body size-related variation in the strength of selection. In support of the hypothesis, we found that the steepness of allometric slopes increased with the level of condition dependence. One trait of particular interest, the penis, had shallow allometric slopes and low levels of condition dependence, in agreement with one of the most consistent patterns yet detected in the study of allometry, namely that of genitalia exhibiting shallow allometries.This research was supported by NIH grant R01RR0163009

The scaling of postcranial muscles in cats (Felidae) I: forelimb, cervical, and thoracic muscles

The body masses of cats (Mammalia, Carnivora, Felidae) span a ~300‐fold range from the smallest to largest species. Despite this range, felid musculoskeletal anatomy remains remarkably conservative, including the maintenance of a crouched limb posture at unusually large sizes. The forelimbs in felids are important for body support and other aspects of locomotion, as well as climbing and prey capture, with the assistance of the vertebral (and hindlimb) muscles. Here, we examine the scaling of the anterior postcranial musculature across felids to assess scaling patterns between different species spanning the range of felid body sizes. The muscle architecture (lengths and masses of the muscle‐tendon unit components) for the forelimb, cervical and thoracic muscles was quantified to analyse how the muscles scale with body mass. Our results demonstrate that physiological cross‐sectional areas of the forelimb muscles scale positively with increasing body mass (i.e. becoming relatively larger). Many significantly allometric variables pertain to shoulder support, whereas the rest of the limb muscles become relatively weaker in larger felid species. However, when phylogenetic relationships were corrected for, most of these significant relationships disappeared, leaving no significantly allometric muscle metrics. The majority of cervical and thoracic muscle metrics are not significantly allometric, despite there being many allometric skeletal elements in these regions. When forelimb muscle data were considered in isolation or in combination with those of the vertebral muscles in principal components analyses and MANOVAs, there was no significant discrimination among species by either size or locomotory mode. Our results support the inference that larger felid species have relatively weaker anterior postcranial musculature compared with smaller species, due to an absence of significant positive allometry of forelimb or vertebral muscle architecture. This difference in strength is consistent with behavioural changes in larger felids, such as a reduction of maximal speed and other aspects of locomotor abilities

Range-based techniques for discovering optimality and analyzing scaling relationships in neuromechanical systems

In this paper, a method for decoupling the neuromuscular function of a set of limbs from the role morphology plays in regulating the performance of an activity is introduced. This method is based on two previous methods: the rescaled range analysis specific to time series data, and the use of scaling laws. A review of the literature suggests that limb geometry can either facilitate or constrain performance as measured experimentally. Whether limb geometry is facilitatory or acts as a constraint depends on the size differential between arm morphology and the underlying muscle. "Changes in size and shape" are theoretically extrapolations of morphological geometry to other members of a population or species, to other species, or to technological manipulations of an individual via prosthetic devices. Three datasets are analyzed using the range-based method and a Monte-Carlo simulation, and are used to test the various ways of executing this analysis. It was found that when performance is kept stable but limb size and shape is scaled by a factor of .25, the greatest gain in performance results. It was also found that introducing force-based perturbations results in 'shifts' in the body geometry/performance relationship. While results such as this could be interpreted as a statistical artifact, the non-linear rise within a measurement class and linear decrease between measurement classes suggests an effect of scale in the optimality of this relationship. Overall, range-based techniques allow for the simulation and modeling of myriad changes in phenotype that result from biological and technological manipulation

Limb-Bone Scaling Indicates Diverse Stance and Gait in Quadrupedal Ornithischian Dinosaurs

Background The most primitive ornithischian dinosaurs were small bipeds, but quadrupedality evolved three times independently in the clade. The transition to quadrupedality from bipedal ancestors is rare in the history of terrestrial vertebrate evolution, and extant analogues do not exist. Constraints imposed on quadrupedal ornithischians by their ancestral bipedal bauplan remain unexplored, and consequently, debate continues about their stance and gait. For example, it has been proposed that some ornithischians could run, while others consider that none were cursorial. Methodology/Principal Findings Drawing on biomechanical concepts of limb bone scaling and locomotor theory developed for extant taxa, we use the largest dataset of ornithischian postcranial measurements so far compiled to examine stance and gait in quadrupedal ornithischians. Differences in femoral midshaft eccentricity in hadrosaurs and ceratopsids may indicate that hadrosaurs placed their feet on the midline during locomotion, while ceratopsids placed their feet more laterally, under the hips. More robust humeri in the largest ceratopsids relative to smaller taxa may be due to positive allometry in skull size with body mass in ceratopsids, while slender humeri in the largest stegosaurs may be the result of differences in dermal armor distribution within the clade. Hadrosaurs are found to display the most cursorial morphologies of the quadrupedal ornithischian cades, indicating higher locomotor performance than in ceratopsids and thyreophorans. Conclusions/Significance Limb bone scaling indicates that a previously unrealised diversity of stances and gaits were employed by quadrupedal ornithischians despite apparent convergence in limb morphology. Grouping quadrupedal ornithischians together as a single functional group hides this disparity. Differences in limb proportions and scaling are likely due to the possession of display structures such as horns, frills and dermal armor that may have affected the center of mass of the animal, and differences in locomotor behaviour such as migration, predator escape or home range size

Height-diameter allometry of tropical forest trees

Tropical tree height-diameter (H:D) relationships may vary by forest type and region making large-scale estimates of above-ground biomass subject to bias if they ignore these differences in stem allometry. We have therefore developed a new global tropical forest database consisting of 39 955 concurrent H and D measurements encompassing 283 sites in 22 tropical countries. Utilising this database, our objectives were: 1. to determine if H:D relationships differ by geographic region and forest type (wet to dry forests, including zones of tension where forest and savanna overlap). 2. to ascertain if the H:D relationship is modulated by climate and/or forest structural characteristics (e.g. stand-level basal area, A). 3. to develop H:D allometric equations and evaluate biases to reduce error in future local-to-global estimates of tropical forest biomass. Annual precipitation coefficient of variation (PV), dry season length (SD), and mean annual air temperature (TA) emerged as key drivers of variation in H:D relationships at the pantropical and region scales. Vegetation structure also played a role with trees in forests of a high A being, on average, taller at any given D. After the effects of environment and forest structure are taken into account, two main regional groups can be identified. Forests in Asia, Africa and the Guyana Shield all have, on average, similar H:D relationships, but with trees in the forests of much of the Amazon Basin and tropical Australia typically being shorter at any given D than their counterparts elsewhere. The region-environment-structure model with the lowest Akaike\u27s information criterion and lowest deviation estimated stand-level H across all plots to within amedian −2.7 to 0.9% of the true value. Some of the plot-to-plot variability in H:D relationships not accounted for by this model could be attributed to variations in soil physical conditions. Other things being equal, trees tend to be more slender in the absence of soil physical constraints, especially at smaller D. Pantropical and continental-level models provided less robust estimates of H, especially when the roles of climate and stand structure in modulating H:D allometry were not simultaneously taken into account

Observation of Mammalian Similarity Through Allometric Scaling Laws

We discuss the problem of observation of natural similarity in skeletal evolution of terrestrial mammals. Analysis is given by means of testing of the power scaling laws established in long bone allometry, which describe development of bones (of length $L$ and diameter $D$) with body mass in terms of the growth exponents, \QTR{it}{e.g.} $\lambda =d\log L/d\log D$. The bone-size evolution scenario given three decades ago by McMahon was quiet explicit on the geometrical-shape and mechanical-force constraints that predicted $\lambda =2/3$. This remains too far from the mammalian allometric exponent $\lambda ^{(\exp)}=0.80\pm 0.2$, recently revised by Christiansen, that is a chief puzzle in long bone allometry. We give therefore new insights into McMahon's constraints and report on the first observation of the critical-elastic-force, bending-deformation, muscle-induced mechanism that underlies the allometric law with estimated $\lambda =0.80\pm 0.3$. This mechanism governs the bone-size evolution with avoiding skeletal fracture caused by muscle-induced peak stresses and is expected to be unique for small and large mammals.Comment: Keywords: allometric scaling, long bones, muscles, mammals 21 pages, 1 Table, 2 Figure

Ontogenetic scaling patterns and functional anatomy of the pelvic limb musculature in emus (Dromaius novaehollandiae)

Emus (Dromaius novaehollandiae) are exclusively terrestrial, bipedal and cursorial ratites with some similar biomechanical characteristics to humans. Their growth rates are impressive, as their body mass increases eighty-fold from hatching to adulthood whilst maintaining the same mode of locomotion throughout life. These ontogenetic characteristics stimulate biomechanical questions about the strategies that allow emus to cope with their rapid growth and locomotion, which can be partly addressed via scaling (allometric) analysis of morphology. In this study we have collected pelvic limb anatomical data (muscle architecture, tendon length, tendon mass and bone lengths) and calculated muscle physiological cross sectional area (PCSA) and average tendon cross sectional area from emus across three ontogenetic stages (n = 17, body masses from 3.6 to 42 kg). The data were analysed by reduced major axis regression to determine how these biomechanically relevant aspects of morphology scaled with body mass. Muscle mass and PCSA showed a marked trend towards positive allometry (26 and 27 out of 34 muscles respectively) and fascicle length showed a more mixed scaling pattern. The long tendons of the main digital flexors scaled with positive allometry for all characteristics whilst other tendons demonstrated a less clear scaling pattern. Finally, the two longer bones of the limb (tibiotarsus and tarsometatarsus) also exhibited positive allometry for length, and two others (femur and first phalanx of digit III) had trends towards isometry. These results indicate that emus experience a relative increase in their muscle force-generating capacities, as well as potentially increasing the force-sustaining capacities of their tendons, as they grow. Furthermore, we have clarified anatomical descriptions and provided illustrations of the pelvic limb muscle–tendon units in emus