• Are adult physiques geometrically similar? The dangers of allometric scaling using body mass power laws.

      Nevill, Alan M.; Stewart, Arthur D.; Olds, Tim; Holder, Roger L. (Wiley-Liss, 2004)
      Human physique classification by somatotype assumes that adult humans are geometric similar to each other. However, this assumption has yet to be adequately tested in athletic and nonexercising human populations. In this study, we assessed this assumption by comparing the mass exponents associated with girth measurements taken at 13 different sites throughout the body in 478 subjects (279 athletic subjects, and 199 nonexercising controls). Corrected girths which account for subcutaneous adipose tissue at the upper arm, thigh, and calf sites, and which simulate muscle circumference, were also calculated. If subjects are geometrically similar to each other, girth exponents should be approximately proportional to M(1/3), where M is the subjects' body mass. This study confirms that human adult physiques are not geometrically similar to each other. In both athletic subjects and nonexercising controls, body circumferences/limb girths develop at a greater rate than that anticipated by geometric similarity in fleshy sites containing both muscle and fat (upper arms and legs), and less than anticipated in bony sites (head, wrists, and ankles). Interestingly, head girths appear to remain almost constant, irrespective of subjects' body size/mass. The results also suggest that thigh muscle girths of athletes and controls increase at a greater rate than that predicted by geometric similarity, proportional to body mass (M(0.439) and M(0.377), respectively). These systematic deviations from geometric similarity have serious implications for the allometric scaling of variables such as energy expenditure, oxygen uptake, anaerobic power, and thermodynamic or anthropometric studies involving individuals of differing size.
    • Does living in urban or rural settings affect aspects of physical fitness in children? An allometric approach.

      Tsimeas, P.D.; Tsiokanos, A.L.; Koutedakis, Yiannis; Tsigilis, N.; Kellis, S. (BMJ Publishing Group Ltd & British Association of Sport and Exercise Medicine, 2005)
      The aim of this study was to investigate physical fitness in relation to fatness in urban and rural Greek children by means of allometric scaling. METHODS: The sample consisted of 360 (189 urban and 171 rural; age 12.3+/-0.42 years) boys and 247 (125 urban and 122 rural; age 12.3+/-0.43 years) girls. The sample was highly representative (32-64%) of all 12 year old children registered in the prefecture of Trikala, Greece. All volunteers were assessed for BMI and % body fat, as well as sit and reach, basketball throw (BT), vertical jump (VJ), handgrip strength (HG), 40 m sprint, agility run, and 20 m shuttle run. To correct for possible associations between fatness and fitness, a single cause allometric scaling was employed using the natural logarithms (ln) of fitness parameters that were significantly correlated with the ln body fat. RESULTS: Independent-samples t tests revealed that VJ (p<0.05) was significantly higher in boys living in urban settings compared to their rural counterparts. Similarly, BT was found to be significantly better (p<0.05) in urban girls, whereas HG was significantly higher (p<0.05) in rural girls. CONCLUSION: Considering that (a) only three out of the 14 possible cases (seven fitness parameters for boys and seven for girls) were significantly different between urban and rural children, and (b) these differences were not uniformly distributed in children living in either urban or rural environments, it is concluded that the place of residence has no clear impact on physical fitness as studied herein.
    • Scaling children's waist circumference for differences in body size

      Nevill, Alan M; Duncan, Michael J.; Lahart, Ian; Davies, Paul; Ramirez-Velez, Robinson; Sandercock, Gavin; Faculty of Education; Health and Wellbeing, University of Wolverhampton; Walsall Campus Walsall United Kingdom; Faculty of Health and Life Sciences; Coventry University; Coventry United Kingdom; Faculty of Education; Health and Wellbeing, University of Wolverhampton; Walsall Campus Walsall United Kingdom; Faculty of Education; Health and Wellbeing, University of Wolverhampton; Walsall Campus Walsall United Kingdom; et al. (Wiley, 2017-07-12)
      Objectives Both waist circumference (WC) and body size (height) increase with age throughout childhood. Hence, there is a need to scale WC in children to detect differences in adiposity status (eg, between populations and different age groups), independent of body size/height. Methods Using two culturally different samples, 1 English (10–15.9 years n = 9471) and 2 Colombian (14–15 years, n = 37,948), for WC to be independent of height (HT), a body shape index was obtained using the allometric power law WC = a.HTb. The model was linearized using log-transformation, and multiple regression/ANCOVA to estimate the height exponents for WC controlling for age, sex, and any other categorical/population differences. Results In both samples, the power-law height exponent varied systematically with age. In younger children (age 10–11 years), the exponent was approximately unity, suggesting that pre-pubertal children might be geometrically similar. In older children, the height exponent declined monotonically to 0.5 (ie, HT0.5) in 15+ year-olds, similar to the exponent observed in adults. UK children's height-adjusted WC revealed a “u” shaped curve with age that appeared to reach a minimum at peak-height velocity, different for boys and girls. Comparing the WC of two populations (UK versus Colombian 14–15-year-old children) identified that the gap in WC between the countries narrowed considerably after scaling for height. Conclusions Scaling children's WC for differences in height using allometric modeling reveals new insights into the growth and development of children's WC, findings that might well have been be overlooked if body size/height had been ignored.
    • Scaling, normalizing, and per ratio standards: an allometric modeling approach.

      Nevill, Alan M.; Holder, Roger L. (Bethesda, MD: The American Physiological Society, 1995)
      The practice of scaling or normalizing physiological variables (Y) by dividing the variable by an appropriate body size variable (X) to produce what is known as a "per ratio standard" (Y/ X), has come under strong criticism from various authors. These authors propose an alternative regression standard based on the linear regression of (Y) on (X) as the predictor variable. However, if linear regression is to be used to adjust such physiological measurements (Y), the residual errors should have a constant variance and, in order to carry out parametric tests of significance, be normally distributed. Unfortunately, since neither of these assumptions appear to be satisfied for many physiological variables, e.g., maximum oxygen uptake, peak and mean power, an alternative approach is proposed of using allometric modeling where the concept of a ratio is an integral part of the model form. These allometric models naturally help to overcome the heteroscedasticity and skewness observed with per ratio variables. Furthermore, if per ratio standards are to be incorporated in regression models to predict other dependent variables, the allometric or log-linear model form is shown to be more appropriate than linear models. By using multiple regression, simply by taking logarithms of the dependent variable and entering the logarithmic transformed per ratio variables as separate independent variables, the resulting estimated log-linear multiple-regression model will automatically provide the most appropriate per ratio standard to reflect the dependent variable, based on the proposed allometric model.