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).     

Sexual dimorphism in the baboon facial skeleton

Baboons exhibit marked sexual dimorphism in many aspects of their morphology. Dimorphism is especially pronounced in the face. We use finite-element analysis to investigate the ontogeny of sexual dimorphism in a cross-sectional sample of baboon (Papio sp.) faces. This method provides detailed quantitative information about size and shape changes at anatomical landmarks in the face during growth. Allometric results suggest that sexual dimorphism in facial size and shape is produced by ontogenetic scaling: males and females share a common ontogenetic trajectory. Analyses of growth in time, which complement allometric analyses, show that female growth slows much earlier than male growth, accounting for the differences between sexes. Local size and local shape follow similar patterns of growth, but changes in these variables are slower in females. Local and global facial size are much more dimorphic than local and global facial shape.     

干热河谷草本植物生物量分配及其对环境因子的响应

以干热河谷6种草本植物为对象,研究了水分、养分、刈割对生物量在根、茎、叶的分配及异速生长关系的影响.结果表明:刈割处理叶生物量质量分数从25.1%显著增加到31.2%,茎生物量质量分数从43.7%显著降低到34.2%;养分添加处理根生物量质量分数从34.0%显著降低到30.8%;水分处理对生物量分配没有显著影响.物种对根、茎、叶生物量分配有显著影响,适应贫瘠土壤的物种将更多生物量分配给叶和根,对茎生物量的分配相对较低.物种与环境因子存在显著的互作效应,表明环境因子对不同物种的生物量分配影响不同.适应贫瘠土壤的物种叶-茎标度指数和异速生长常数大于其他物种,而茎-根标度指数和异速生长常数小于其他物种.养分显著增加了叶-茎和叶-根的异速生长常数,刈割显著降低了茎-根的标度指数,水分处理则没有显著效应.环境因素对器官间异速生长关系的影响存在种间差异.生物量分配的种间差异及其对环境因素的响应特征可能对植物适应环境变化产生重要影响.     

Scaling of maximal oxygen uptake by lower leg muscle volume in boys and men.

The aim of this study was to critically examine the influence of body size on maximal oxygen uptake (VO2 max) in boys and men using body mass (BM), estimated fat-free mass (FFM), and estimated lower leg muscle volume (Vol) as the separate scaling variables. VO2 max and an in vivo measurement of Vol were assessed in 15 boys and 14 men. The FFM was estimated after percentage body fat had been predicted from population-specific skinfold measurements. By using nonlinear allometric modeling, common body size exponents for BM, FFM, and Vol were calculated. The point estimates for the size exponent (95% confidence interval) from the separate allometric models were: BM 0.79 (0.53-1.06), FFM 1.00 (0.78-1.22), and Vol 0.64 (0.40-0.88). For the boys, substantial residual size correlations were observed for VO2 max/BM0.79 and VO2 max/FFM1.00, indicating that these variables did not correctly partition out the influence of body size. In contrast, scaling by Vol0.64 led to no residual size correlation in boys or men. Scaling by BM is confounded by heterogeneity of body composition and potentially substantial differences in the mass exponent between boys and men. The FFM is precluded as an index of involved musculature because Vol did not represent a constant proportion of FFM [Vol proportional, variantFFM1.45 (95% confidence interval, 1.13-1.77)] in the boys (unlike the men). We conclude that Vol, as an indicator of the involved muscle mass, is the most valid allometric denominator for the scaling of VO2 max in a sample of boys and men heterogeneous for body size and composition.     

Lower-extremity ground reaction forces in collegiate baseball pitchers

The purpose of this study was to investigate ground reaction forces (GRF) in collegiate baseball pitchers and their relationship to pitching mechanics. Fourteen healthy collegiate baseball pitchers participated in this study. High-speed video and force plate data were collected for fastballs from each pitcher. The average ball speed was 35 ± 3 m/sec (78 ± 7 mph). Peak GRFs of 245 ± 20% body weight (BW) were generated in an anterior or braking direction to control descent. Horizontal GRFs tended to occur in a laterally directed fashion, reaching a peak of 45 ± 63% BW. The maximum vertical GRF averaged 202 ± 43% BW approximately 45 milliseconds after stride foot contact. A correlation between braking force and ball velocity was evident. Because of the downward inclination and rotation of the pitching motion, in addition to volume, shear forces may occur in the musculoskeletal tissues of the stride limb leading to many of the lower-extremity injuries seen in this athletic population.     

Normalization of ground reaction forces

The appropriateness of normalizing data, as one method to reduce the effects of a covariate on a dependent variable, should be evaluated. Using ratio, 0.67-nonlinear, and fitted normalizations, the aim of this study was to investigate the relationship between ground reaction force variables and body mass (BM). Ground reaction forces were recorded for 40 female subjects running at 3.7 +/- 0.18 m x s(-1) (mass = 58 +/- 6 kg). The explained variance for mass to forces (peak-impact-vertical = 70%; propulsive-vertical = 27%; braking = 40%) was reduced to <0.1% for mass to ratio normalized forces (i.e., forces/BM1) with statistically significantly different power exponents (p < 0.05). The smaller covariate effect of mass on loading rate variables of 2-16% was better removed through fitted normalization (e.g., vertical-instantaneous-loading rate/ BM(0.69+/-0.93); +/-95% CI) with nonlinear power exponents ranging from 0.51 to 1.13. Generally, these were similar to 0.67 as predicted through dimensionality theory, but, owing to the large confidence intervals, these power exponents were not statistically significantly different from absolute or ratio normalized data (p > 0.05). Further work is warranted to identify the appropriate method to normalize loading rates either to mass or to another covariate. Ratio normalization of forces to mass, as predicted through Newtonian mechanics, is recommended for comparing subjects of different masses.     

Control of ground reaction forces by hindlimb muscles during cat locomotion

It has been proposed that biarticular muscles are primarily responsible for the control of the direction of external forces, as their activation is closely related and highly sensitive to the direction of external forces. This functional role for biarticular muscles has been supported qualitatively by experimental evidence, but has never been tested quantitatively for lack of a mathematical/mechanical formulation of this theory and the difficulty of measuring individual muscle forces during voluntary movements. The purposes of this study were: (1) to define rules for muscular coordination based on the control of external forces; (2) to develop a model of the cat hindlimb that allows for the calculation of the magnitude and direction of the ground reaction forces (GRFs) produced by individual hindlimb muscles; and (3) to test if the coordination of mono- and biarticular cat hindlimb muscles is related to the control of the resultant GRF. We measured the GRF, hindlimb kinematics, selected muscle forces and activations during cat locomotion. Then, the measured muscle forces were used as input to the hindlimb model to compute the muscle-induced GRF. We assume that if activation (and possibly force) increased as the muscle-induced component of GRF approximated the resultant GRF, then that muscle was used by the central nervous system (CNS) to help control the direction of the external GRF. During cat walking, medial gastrocnemius (MG) and plantaris (PL) forces increased with increasing proximity to the GRF, while soleus (SOL) forces and vastus lateralis (VL) activations did not. SOL and VL activation were most strongly related to the vertical and parallel (braking/accelerating) component of the GRF, respectively. We concluded from these results that MG and PL are primarily responsible for the control of the direction of the GRF, while SOL primarily functions as an anti-gravity muscle, and VL as an acceleration/deceleration muscle.     

The influence of body size on measurements of overall cardiac function

The purpose of this study was to determine the best scaling method to account for the effects of body size on measurements of overall cardiac function and subsequently the interpretation of data based on cardiac power output (CPO). CPO was measured at rest (CPO(rest)) and at maximal exercise (CPO(max)) on 88 and 103 healthy but untrained men and women, respectively, over the age range of 20-70 yr. Cardiac reserve (CR) was calculated as CPO(max) - CPO(rest). CPO(rest), CPO(max), and CR were all significantly related to body mass (BM), body surface area (BSA), and lean body mass (LBM). The linear regression model failed to completely normalize these measurements. In contrast, the allometric model produced size-independent values of CPO. Furthermore, all the assumptions associated with the allometric model were achieved. For CPO(rest), mean body size exponents were BM(0.33), BSA(0.60), and LBM(0.47). For CPO(max), the exponents were BM(0.41), BSA(0.81), and LBM(0.71). For CR, mean body size exponents were BM(0.44), BSA(0.87), and LBM(0.79). LBM was identified (from the root-mean-squares errors of the separate regression models) as the best physiological variable (based on its high metabolic activity) to be scaled in the allometric model. Scaling of CPO to LBM(b) (where b is the scaling exponent) dramatically reduced the between-gender differences with only a 7% difference in CPO(rest) and CPO(max) values. In addition, the gender difference in CR was completely removed. To avoid erroneous interpretations and conclusions being made when comparing data between men and women of different ages, the allometric scaling of CPO to LBM(b) would seem crucial.     

Stem and wood allometric relationships in Cacteae (Cactaceae)

Allometric relationships in organisms are considered a universal phenomenon. A positive scaling has been reported between stem size and cellular size of tracheary elements in wood of different vascular plants, but few studies have been carried out in slow-growing succulent plants. The aim of this study was to evaluate if a relationship exists between size, growth form and wood cell size among individual species of Cacteae. Forty-four species belonging to 16 genera of the tribe Cacteae with differing growth forms and sizes were studied. When analyzing plant size, we found a positive allometric scaling and the larger-sized species showing a higher percentage of succulent tissue and less accumulation of wood tissue. The positive scaling found between plant size (height and diameter) and vessel elements and fiber length support the universality of the allometric relationship proposed for other vascular plants with non-succulent stems. Notably, wide-band tracheids do not scale with plant size or growth form. Succulence associated with narrow vessel elements with distinctive helical secondary walls and wide-band tracheids suggest they are the key adaptations to tolerate drought and provide support to the stems of most taxa in Cacteae. Fibers do not have the primary role of giving mechanical support; therefore, we assume the scarce fibers in clusters represent reaction wood that, along with the fundamental tissue, maintains the vertical position and shape of those species growing in rocky cracks. Our results with species having short succulent stems support the universal theory of positive allometric scaling of vascular plants.     

Functional assessment in the rat by ground reaction forces

Although the rat sciatic nerve model is used extensively in the investigation of repair techniques, and a variety of evaluation methods utilized to assess the results, a means to measure directly and accurately the return of function in these animals is absent. Histologic, histomorphometric, and electrophysiologic methods can be reliable indicators of nerve regeneration but do not correlate to functional recovery. The purposes of this study were to develop apparatus to continuously measure ground reaction forces (GRF) and use GRF parameters in the assessment of gait parameters in normal rats preoperatively and following peripheral nerve severance and repair. Three neurorrhaphy methods: direct sciatic nerve repair, direct tibial nerve repair and double sciatic nerve repair simulating autograft, as well as a non-repaired tibial nerve transection were evaluated. The testing apparatus was designed to measure the spontaneous and voluntary effort of the rat with objective data. Three orthogonal components - vertical, craniocaudal (braking and propulsion), and mediolateral - of the ground reaction force were measured. Preoperative data showed that vertical forces were comparable among the four limbs but propulsion and braking forces displayed significant differences. At 12 weeks, functional recovery was most evident in the direct tibial nerve repair group and absent in the non-repaired tibial defect group. Direct sciatic nerve repairs and sciatic nerve grafts resulted in lesser degrees of improvement. Results indicated that the propulsive force is the optimal GRF parameter for evaluating recovery of useful function.     

A simple method for computing sprint acceleration kinetics from running velocity data: Replication study with improved design

Measuring the ground reaction forces (GRF) underlying sprint acceleration is important to understanding the performance of such a common task. Until recently direct measurements of GRF during sprinting were limited to a few steps per trial, but a simple method (SM) was developed to estimate GRF across an entire acceleration. The SM utilizes displacement- or velocity-time data and basic computations applied to the runner’s center of mass and was validated against compiled force plate (FP) measurements; however, this validation used multiple-trials to generate a single acceleration profile, and consequently fatigue and error may have introduced noise into the analyses. In this study, we replicated the original validation by comparing the main sprint kinetics and force-velocity-power variables (e.g. GRF and its horizontal and vertical components, mechanical power output, ratio of horizontal component to resultant GRF) between synchronized FP data from a single sprinting acceleration and SM data derived from running velocity measured with a 100 Hz laser. These analyses were made possible thanks to a newly developed 50-m FP system providing seamless GRF data during a single sprint acceleration. Sixteen trained male sprinters performed two all-out 60-m sprints. We observed good agreement between the two methods for kinetic variables (e.g. grand average bias of 4.71%, range 0.696 ± 0.540–8.26 ± 5.51%), and high inter-trial reliability (grand average standard error of measurement of 2.50% for FP and 2.36% for the SM). This replication study clearly shows that when implemented correctly, this method accurately estimates sprint acceleration kinetics.     

Allometric escape from acoustic constraints is rare for frog calls

Allometric constraint is a product of natural selection and physical laws, particularly with respect to body size and traits constrained by properties thereof, such as metabolism, longevity, and vocal frequency. Allometric relationships are often conserved across lineages, indicating that physical constraints dictate scaling patterns in deep time, despite substantial genetic and ecological divergence among organisms. In particular, acoustic allometry (sound frequency ~ body size) is conserved across frogs, in defiance of massive variation in both body size and frequency. Here, we ask how many instances of allometric escape have occurred across the frog tree of life using a Bayesian framework that estimates the location, number, and magnitude of shifts in the adaptive landscape of acoustic allometry. Moreover, we test whether ecology in terms of calling site could affect these relationships. We find that calling site has a major influence on acoustic allometry. Despite this, we identify only four major instances of allometric escape, potentially deriving from ecomorphological adaptations to new signal modalities. In these instances of allometric escape, the optima and strength of the scaling relationship are different than expected for most other frog species, representing new adaptive regimes of body size ~ call frequency. Allometric constraints on frog calls are highly conserved and have rarely allowed escape, despite frequent invasions of new adaptive regimes and dramatic ecomorphological divergence. Our results highlight the rare instances in which natural and sexual selection combined can overcome physical constraints on sound production.     

Testing the allometric scaling laws

Allometric scaling laws have received increasing attention due to the recent theoretical advancements. However, existing evidence suggests that the scaling relationships may vary a lot without much consistency, which poses a challenge to the applicability of general theories. In this report, I demonstrate that much of the discrepancy may be an artefact caused by the limited use of methods for estimating the parameters in the allometric scaling equations. I suggest alternative procedures that can be utilized to avoid biased interpretations. The comments are largely applicable to any research that involves parameterization of equations.     

Is there an influence of body mass on digesta mean retention time in herbivores? A comparative study on ungulates

The relation between body mass (BM) and digesta mean retention time (MRT) in herbivores was the focus of several studies in recent years. It was assumed that MRT scaled with BM(0.25) based on the isometric scaling of gut capacity (BM(1.0)) and allometric scaling of energy intake (BM(0.75)). Literature studies that tested this hypothesis produced conflicting results, arriving sometimes at higher or lower exponents than the postulated 0.25. This study was conducted with 8 ruminants (n=2-6 per species) and 6 hindgut fermenting species/breeds (n=2-6, warthog n=1) with a BM range of 60-4000 kg. All animals received a ration of 100% grass hay with ad libitum access. Dry matter intake was measured and the MRT was estimated by the use of a solute and a particle (1-2 mm) marker. No significant scaling of MRT(particle) with BM was observed for all herbivores (32 BM(0.04), p=0.518) and hindgut fermenters (32 BM(0.00), p=1.00). The scaling exponent for ruminants only showed a tendency towards significance (29 BM(0.12), p=0.071). Ruminants on average had an MRT(particle) 1.61-fold longer than hindgut fermenters. Whereas an exponent of 0.25 is reasonable from theoretical considerations, much lower exponents were found in this and other studies. The energetic benefit of increasing MRT is by no means continuous, since the energy released from a given food unit via digestion decreases over time. The low and non-significant scaling factors for both digestion types suggest that in ungulates, MRT is less influenced by BM (maximal allometric exponent ≤0.1) than often reported.     

The influence of different playing surfaces on the biomechanics of a tennis running forehand foot plant

Research suggests that heightened impacts, altered joint movement patterns, and changes in friction coefficient from the use of artificial surfaces in sport increase the prevalence of overuse injuries. The purposes of this study were to (a) develop procedures to assess a tennis-specific movement, (b) characterize the ground reaction force (GRF) impact phases of the movement, and (c) assess human response during impact with changes in common playing surfaces. In relation to the third purpose it was hypothesized that surfaces with greatest mechanical cushioning would yield lower impact forces (PkFz) and rates of loading. Six shod volunteers performed 8 running forehand trials on each surface condition: baseline, carpet, acrylic, and artificial turf. Force plate (960 Hz) and kinematic data (120 Hz) were collected simultaneously for each trial. Running forehand foot plants are typically characterized by 3 peaks in vertical GRF prior to a foot-off peak. Group mean PkFz was significantly lower and peak braking force was significantly higher on the baseline surface compared with the other three test surfaces (p<0.05). No significant changes in initial kinematics were found to explain unexpected PkFz results. The baseline surface yielded a significantly higher coefficient of friction compared with the other three test surfaces (p<0.05). While the hypothesis is rejected, biomechanical analysis has revealed changes in surface type with regard to GRF variables.     

Allometric relationships to assess ontogenetic adaptative changes in three NE Atlantic commercial sea cucumbers (Echinodermata,Holothuroidea)

Holothuria arguinensis, Holothuria mammata and Holothuria forskali are three common sea cucumber species found in the NE Atlantic, traded in international markets and susceptible to capture. Allometric relationships reveal if the scaling relationships between biometric characters are proportional with growth, being a useful tool to understand species growth strategies. Allometric relationships of the three species were estimated and compared between them and with populations from different regions. These allometric relationships revealed that the three species have negative allometric growth. However, they have different growth strategies between them and reveal different regional intra-specific growth strategies when compared to other populations, suggesting ontogenetic adaptation as a consequence of external factors.

     

Ground reaction forces and impulses during a transient turning maneuver

Understanding the kinetic strategies of turning as expressed in ground reaction forces (GRFs) and impulses (GRIs) is necessary to design therapies and technologies to enable patients with ambulatory difficulties perform daily activities. Previous studies have reported data only for one step of the turn and expressed the data in terms of a global reference frame making it difficult to understand how the forces act on the body to cause a change in heading and orientation during a turn. This study is the first to report GRF and GRI data for three steps of a turn and express that data in terms of a body reference frame. Motion and GRF data were collected from 10 subjects walking at self-selected speeds along a straight path and performing 90 degrees left and right turns. During the left turn, turn initiation and apex steps were collected. During the right turn, turn termination steps were collected. GRF data were rotated to a reference frame whose origin was the body center of mass (COM) and aligned to the COM trajectory and then integrated to find the GRIs. In the medial-lateral direction, straight steps were characterized by a brief medial impulse at heel strike followed by a prolonged lateral impulse. Turn initiation and termination steps were both characterized by medial impulses spanning the entire stance phase while apex steps were characterized by a large lateral impulse. In the anterior-posterior direction, initiation steps had larger braking and smaller propulsive impulses than straight steps. Apex steps had larger propulsive impulses than straight steps, and termination steps had smaller braking and larger propulsive impulses than straight steps.     

Predicting trophic relations in ecological networks: A test of the Allometric Diet Breadth Model

Few food web theory hypotheses/predictions can be readily tested using likelihoods of reproducing the data. Simple probabilistic models for food web structure, however, are an exception as their likelihoods were recently derived. Here I test the performance of a more complex model for food web structure that is grounded in the allometric scaling of interactions with body size and the theory of optimal foraging (Allometric Diet Breadth Model—ADBM). This deterministic model has been evaluated by measuring the fraction of trophic relations it correctly predicts. I contrasted this value with that produced by simpler models based on body sizes and found that the quantitative information on allometric scaling and optimal foraging does not significantly increase model fit. Also, I present a method to compute the p-value for the fraction of trophic interactions correctly predicted by the ADBM, or any other model, with respect to three probabilistic models. I find that the ADBM predicts significantly more links than random graphs, but other models can outperform it. Although optimal foraging and allometric scaling may improve our understanding of food webs, the ADBM needs to be modified or replaced to find support in the data.     

Craniometric allometry in the thicktailed bushbabyOtolemur Crassicaudatus

Static adult craniometric allometry was evaluated in a sample of 66Otolemur crassicaudatus skulls (34 males, 32 females). Although cranial measures were equally well correlated to skull length in males and females, there were noteworthy differences in the exponential values between the sexes. These results underlined the need for caution when allometric analyses are based on pooled data. From the cranial allometric analyses it is concluded that the longer the skull, the shorter and the narrower the maxilla, and the broader the bizygomatic distance. Although cranial length increased proportionately to the increase in skull length, the cranial width in females was positively allometric whilst in males it was negatively allometric. Allometric analyses of mandibular dimensions suggest that larger animals will have proportionately longer mandibulae, which will, in turn, be relatively wider across the gonia, yet shallower behind the first molars. It is postulated that the disproportionate widening of the zygomata might be related to the widening across the gonia.