Abstract
This study examined age and sexassociated variation in peak oxygen consumption (V˙o _{2}) of young male and female distance runners from an allometric scaling perspective. Subjects were from two separate studies of 9 to 19yrold distance runners from the midMichigan area, one conducted between 1982 and 1986 (Young Runners Study I, YRS I) and the other in 1999–2000 (Young Runners Study II, YRS II). Data from 27 boys and 27 girls from YRS I and 48 boys and 22 girls from the YRS II were included, and a total of 139 and 108 measurements of body size and peak V˙o _{2} in boys and girls, respectively, were available. Subjects were divided into whole year age groups. A 2 × 9 (sex × age group) ANOVA was used to examine differences in peakV˙o _{2}. Intraindividual ontogenetic allometric scaling was determined in 20 boys and 17 girls measured annually for 3–5 yr. Allometric scaling factors were calculated using linear regression of logtransformed data. Results indicated that1) absolute peak V˙o _{2}increases with age in boys and girls, 2) relative peakV˙o _{2}(ml · kg^{−1} · min^{−1}) remains relatively stable in boys and in girls, 3) relative peakV˙o _{2}(ml · kg^{−0.75} · min^{−1}) increases throughout the age range in boys and increases in girls until age 15 yr, and 4) peakV˙o _{2} adjusted for body mass (ml/min) increases with age in boys and girls. The overall mean crosssectional scaling factor was 1.01 ± 0.03 (SE) in boys and 0.85 ± 0.05 (SE) in girls. Significant age × sex interactions and significant scaling factors between sexes identify the progressive divergence of peak V˙o _{2} between adolescent male and female distance runners. Mean ontogenetic allometric scaling factors were 0.81 [0.71–0.92, 95% confidence interval (CI)] and 0.61 (0.50–0.72, 95% CI) in boys and girls, respectively (P = 0.002). There was considerable variation in individual scaling factors (0.51–1.31 and 0.28–0.90 in boys and girls, respectively). The results suggest that the interpretation of growthrelated changes in peak V˙o _{2} of young distance runners is dependent upon the manner of expressing peakV˙o _{2} relative to body size and/or the statistical technique employed.
 aerobic power
 maximal oxygen uptake
 children
 adolescents
during growth andmaturation, absolute peak oxygen consumption (V˙o _{2}, ml/min) increases as a function of body size (1, 21). A major question related to this observation is, Are the growthrelated improvements in physiological capacity a function of increasing body size or qualitative changes in the structural and functional capacity independent of body size or both (30, 40)? To provide answers to this question, the potentially confounding effect of variation in body size must be partitioned appropriately.
Age and sexassociated variation in peakV˙o _{2} has been studied extensively in the general population (1, 21). Several crosssectional studies have characterized the physiological profile of young endurance athletes, but longitudinal studies of the development of peakV˙o _{2} in young athletes, especially girls, are rather limited (7, 9, 12, 22, 24, 27, 34). These studies generally include small sample sizes, are limited to a narrow age range (i.e., 11–15 yr), and therefore do not describe the growthrelated changes in peak V˙o _{2} across the entire adolescent period. Longitudinal studies are important to identify individual and population growth patterns. Thus there is a need for analyses of longitudinal data examining the age and sexassociated variation of peak V˙o _{2} in young athletes from various sports.
Traditionally and conventionally, peakV˙o _{2} is expressed as a ratio standard, or per kilogram of body mass (ml · kg^{−1} · min^{−1}). When expressed as the simple ratio standard, peakV˙o _{2} remains stable in boys and declines in girls during adolescence (21). By expressing peakV˙o _{2} in this manner, it is assumed that peak V˙o _{2} is “normalized” and the influence of body mass is removed. However, the theoretical and statistical limitations of the ratio standard have been widely addressed yet largely ignored (37, 40). Therefore, alternate statistical models, including analysis of covariance (ANCOVA), allometric scaling, and multilevel modeling, have been used to create a “sizefree” expression of peakV˙o _{2}. The mathematical model that is widely used to create a sizefree variable is allometry. Besides the calculation of crosssectional allometric scaling factors, intraindividual, or ontogenetic, scaling factors can be calculated from longitudinal records. Ontogenetic allometry refers to differential growth in the individual growth process (15). Few studies have employed ontogenetic allometry to examine growthrelated changes of peak V˙o _{2} in young athletes (9,27, 34).
The purpose of this study is to examine age and sexassociated variation of peak V˙o _{2} in competitive young distance runners from an allometric scaling perspective.
METHODS
Design
Subjects are from two separate studies of young distance runners from the midMichigan area conducted at the Institute for the Study of Youth Sports at Michigan State University. The first study (Young Runners Study I, YRS I) was an interdisciplinary, mixedlongitudinal assessment of intensive training and competition on “elite” young distance runners between 1982 and 1986 (33). The second study (Young Runners Study II, YRS II) was a crosssectional design. Data sets were pooled for the crosssectional analysis to create a larger sample for age group comparisons. Differences in subject inclusion criteria, treadmill protocol, and exercise testing systems between the two studies are recognized. However, subjects from both studies were highly trained, as indicated by training history, race performance, and peak V˙o _{2}. Previous studies have also shown that minimal differences in peakV˙o _{2} occur as a result of treadmill protocol (speed and incline, continuous vs. discontinuous; see Refs.26 and 35) and exercise testing systems (automated vs. nonautomated; see Ref. 18). The former has specifically been addressed in adolescent distance runners (28). Only data from the YRS I were used for the ontogenetic allometric analysis.
Subjects
YRS I.
Runners between the ages of 8 and 15 yr, who consistently placed within the top five finishers of road races of 10 km or more by age and sex, were identified and contacted for the study. Race results were obtained from a statewide running publication, Michigan Runner,between May and August 1981. Of the runners contacted (response rate unknown), 27 boys and 27 girls agreed to participate in the study. Subjects entered the study at 8.0–15.7 yr of age and were followed annually. Twenty boys and 17 girls were followed at approximately annual intervals for 3–5 yr. The remaining subjects (7 boys and 10 girls) participated in either one or two annual visits. Each age and sex group included only one observation per subject; thus, the subjects were treated as independent in each age group. Totals of 99 and 84 annual measurements were available for boys and girls, respectively. In a subsample of subjects (16 boys, 19 girls), reported training volumes were 38.9 ± 17.6 and 35.8 ± 15.2 (SD) km/wk in boys and girls, respectively. Parental consent and child assent was obtained before the study. The study was approved by the Michigan State University Committee for Research Involving Human Subjects.
YRS II.
Fortyeight boys and 22 girls, 10–19 yr of age, agreed to participate in the study. Eligible subjects participating on local Michigan junior or senior high school crosscountry teams or local track clubs during fall 1999 and spring 2000 were invited to participate. Subjects who had trained <30–40 wk/yr or nonconsecutively during the past three consecutive months were excluded to ensure a sample engaged in regular participation in longdistance running. Reported training volumes were 47.7 ± 22.8 and 35.2 ± 13.8 (SD) km/wk in boys and girls, respectively. Parental consent and child assent was obtained before the study. The study was approved by the Michigan State University Committee for Research Involving Human Subjects.
Anthropometry
YRS I.
Chronological age was calculated as the difference between observation date and birth date and was expressed as a decimal age. Anthropometry was conducted by two experienced anthropometrists according to standard procedures (38). Stature was measured with a fixed stadiometer. Body mass was measured with the subject attired in gym shorts and Tshirt without shoes on a balance beam scale. Measurements were conduced between early morning and midafternoon. Intra and/or interobserver reliabilities were not reported.
YRS II.
Chronological age was calculated as the difference between observation date and birth date and was expressed as a decimal age. Stature and body mass were measured according to the procedures of the International Biology Program (38). Stature was measured with a fixed stadiometer. Body mass was measured with the subject attired in gym shorts and Tshirt without shoes on a balance beam scale. The stadiometer and scale were calibrated periodically during the study. Intraobserver reliability was conducted on a small subsample by the principal investigator (Eisenmann). The intraclass correlation coefficient was 0.99 for both stature and body mass, whereas the intraobserver technical errors of measurement were 0.42 cm for stature and 0.08 kg for body mass.
Measurement of maximal V˙o_{2}
YRS I.
An intermittent progressive treadmill protocol consisting of 3min work intervals and 3min rest intervals until volitional exhaustion was used to determine peak V˙o _{2}. The protocol began with a warmup at 6 mph and 0% grade. After the warmup, the grade was increased to 5%. Speed increased 1 mph, and grade increased 1% in each subsequent stage until volitional exhaustion. Expired gases were collected using the Douglas bag method. Gas concentrations were analyzed with Beckman oxygen and carbon dioxide analyzers within 2 min after collection. Gas volumes were measured with a ParkinsonCowan CD2 dry gas meter. Before testing, expired gas volumes were calibrated with a 3liter syringe, and gas concentrations were calibrated with standard gases of known concentrations. Heart rate (HR) was monitored using a commercial electrocardiogram. Endoftest criteria were established by volitional exhaustion, HR ≥90% of agepredicted maximum, respiratory exchange ratio >1.0, and a plateau inV˙o _{2} (defined by an increase inV˙o _{2} of <2.0 ml · kg^{−1} · min^{−1} with increasing workload). Two of the latter three criteria must have been met for a subject to be included in the analysis.
YRS II.
A maximal exercise test was conducted on a motorized treadmill to exhaustion in an airconditioned laboratory (20–22°C, relative humidity 45–60%). The treadmill protocol was determined by the subject's estimated 5km race pace. Subjects walked/jogged at a speed of 3 and 4.5 miles/h for 1 min each. This initial warmup period was followed by 4min stages at 6, 7.5, and 8 miles/h (depending on an estimated 5km race pace) and then increased in grade of 2.5% every minute until exhaustion or test termination. Expired gases were collected for the measurement of V˙o _{2}, carbon dioxide production, and minute ventilation. Expired gases were continually sampled and averaged every 20 s via the opencircuit method using a metabolic cart (model 2900; Gould, Dayton, OH). Expired gas volumes were measured with a flow probe anemometer, and expired gas concentrations were measured by electronic analyzers. Before testing, expired gas volumes were calibrated with a 3liter syringe, and gas concentrations were calibrated with standard gases of known concentrations. HR was monitored continually by pulse telemetry (Polar Advantage). Endoftest criteria were established by volitional exhaustion, HR ≥90% of agepredicted maximum, respiratory exchange ratio >1.0, and a plateau in V˙o _{2}(defined by an increase in V˙o _{2} of <2.0 ml · kg^{−1} · min^{−1} with increasing workload). Two of the latter three criteria must have been met to be included in the analysis.
Statistical Analysis
Subjects were divided into wholeyear age groups (i.e., 11.0–11.99), except for the youngest age group in both sexes, which consisted of subjects 9.0–10.99 yr, and the oldest age group in girls that consisted of subjects 17.0–19.49 yr. Descriptive statistics were calculated by age and sex groups for absolute peakV˙o _{2} and relative peakV˙o _{2} (expressed per kg^{1.0} and per kg^{0.75}). The exponent 0.75 is common in the allometric literature and is based on both theoretical and statistical evidence. A 2 × 9 (sex × age group) ANOVA was used to examine differences in peak V˙o _{2}. Paired post hoc differences were examined by the Scheffé test. The allometric analysis was applied to the entire group for each sex (i.e., scaling factor for all boys and all girls) and to each age and sexspecific group (i.e., scaling factor for 14yrold girls, etc.).
Allometric Scaling
Before allometric analysis, the relationship between body mass and peak V˙o _{2} was initially checked for linearity after Tanner (37). In this procedure, the Pearson correlation coefficient (r) between body mass and absolute peak V˙o _{2} was compared with the ratio of the coefficient of variation (CV) for the two variables [(SD_{x}/X_{x} )/(SD_{y}/X_{y} )]. If r is approximately equal to the CV, a linear relationship is indicated, and the simple ratio standard (ml · kg^{−1} · min^{−1}) is appropriate. Conversely, if these two terms are not similar, a linear relationship does not exist, and the simple ratio standard is inappropriate.
The allometric relationship between body size and peakV˙o
_{2} is based on the general allometric equation
Ontogenetic Allometry
Individual (ontogenetic) scaling factors were calculated for individual longitudinal records for subjects who were assessed annually for 3–5 yr. Of the 27 boys and 27 girls enrolled in YRS I, 20 boys and 17 girls were considered in the present analysis. A leastsquares linear regression was carried out for the records of each subject on the doublelogarithmic transformations of peakV˙o _{2} and body mass. Individual regressions were checked for goodness of fit by examining the multiple rvalue and the P value from the ANOVA. Sexspecific means and SD of the ontogenetic allometric scaling factors were calculated. The difference was examined by an independent ttest.
Regression Diagnostics
Residuals (predicted − observed peakV˙o _{2}) were converted to absolute values and correlated with the predictor variable (log body mass) to examine the data for heteroscedasticity. Pearson correlations were also calculated between the simple ratio standard and the common power function ratio (ml · kg^{−0.75} · min^{−1}) as a diagnostic test. In this case, if the influence of body size has been removed, the correlation should not be different from zero (5).
RESULTS
Age and sexspecific anthropometric and peakV˙o _{2} values are reported in Tables1 and 2. Stature reaches a plateau at 17 yr in boys and 15 yr in girls. Body mass progressively increases across age in both sexes. Before 14 yr, girls are taller and heavier than boys; thereafter, boys are taller and heavier than girls. Mean statures for both boys and girls approximate the medians of U.S. reference values (16), and mean body mass for both boys and girls is somewhat below the reference medians. Stature and mass also maintain their position relative to the reference values across age (13).
Means for absolute peak V˙o _{2} (ml/min) increase with age in both sexes (P < 0.05). Absolute differences between the sexes are small (134–186 ml/min) before 14 yr, when the differences increase sharply in each age group and reach a mean difference of 1000–1,500 ml/min in the oldest age groups (P < 0.05).
There is no significant agerelated trend for peakV˙o _{2} expressed as the simple ratio standard (ml · kg^{−1} · min^{−1};P > 0.05). Means of relative peakV˙o _{2} remain stable in boys between 9 and 15 yr (61–63 ml · kg^{−1} · min^{−1}) and are insignificantly higher in the older age groups (65–67 ml · kg^{−1} · min^{−1}). In girls, means for relative peak V˙o _{2} remain stable between 9 and 15 yr of age (55–58 ml · kg^{−1} · min^{−1}) and decrease insignificantly in the oldest age groups (52–53 ml · kg^{−1} · min^{−1}). Sex differences vary between 5 and 7 ml · kg^{−1} · min^{−1} before 16 yr and increase to 12–15 ml · kg^{−1} · min^{−1} in the oldest age groups (P < 0.005). When peakV˙o _{2} is expressed to the theoretical value of body mass 0.75, it increases significantly with age (P < 0.05). Similar to absolute values, sex differences are small before 15 yr and then increase (P< 0.05 at all age groups).
Peak V˙o _{2} adjusted for body mass also shows a significant agerelated increase (P < 0.05). The largest differences in adjusted means occur in the youngest and oldest age groups (600–750 ml/min). Mean differences between 12 and 15 yr of age are 410–475 ml/min, and there is a significant age group × sex interaction in adjusted means (P= 0.001).
Results of the crosssectional allometric analysis are shown in Table3. Overall, body mass exponents are 1.01 ± 0.03 (SE) and 0.85 ± 0.05 (SE) in boys and girls, respectively. The adjusted r ^{2} is 0.89 in boys and 0.75 in girls. Agespecific scaling factors are closer to the theoretical values of 0.67 and 0.75 in boys, but do not fit the model closely, and in two age groups are not significantly different from zero. In girls, three of the eight agespecific models are not significantly different from zero. The significant models have scaling factors between 0.53 and 0.89. In general, the agespecific models fit better in boys than girls. The cumulative effect of multiple age groups on the overall scaling factor is also shown in Table 3. Although agespecific scaling factors differ from those calculated for the entire sample, this may be due to small agespecific sample sizes and a lack of variation in body mass and peakV˙o _{2} within agespecific groups. Scaling factors begin to approximate the overall sexspecific scaling factor when multiple age groups are considered.
The computation of Tanner's “special circumstance” (37) and other diagnostic results are reported in Table4. Body mass is significantly related to absolute peak V˙o _{2} in boys (r = 0.95) and girls (r = 0.87). As a group, there is a similarity between r (body mass and absolute peak V˙o _{2}) and CV for boys. Agespecific calculations produce divergent ratios, especially in girls, suggesting a nonlinear relationship. As a group, the correlations between the simple ratio standard and body mass are 0.07 and −0.41 in boys and girls, respectively. Correlations between scaled peak V˙o _{2} and body mass are 0.71 and 0.03 in boys and girls, respectively. Correlations between absolute residuals and log body mass are 0.07 and −0.11 in boys and girls, respectively. Agespecific correlations vary between the sexes, with coefficients approaching zero in some age groups when peakV˙o _{2} is expressed per unit body mass 0.75. Correlations do not approach zero in any age group in girls.
In general, the intraindividual (ontogenetic) linear regression shows a better fit in boys than girls. In boys, 4 of 20 scaling factors are not significantly different from zero (P > 0.10). Logarithmically transformed peak V˙o _{2} and mass are highly related (r > 0.85) in all but one male subject. In contrast, scaling factors are significantly different from zero in 6 of 17 girls. The relationship between logarithmically transformed peak V˙o _{2} and mass is high (r > 0.85) in eight girls and moderate (0.40–0.85) in seven others. Based on a combination of the correlation coefficients and leastsquares regression model, one male and two female subjects were eliminated from the analysis.
Ontogenetic scaling factors show considerable variation (range, 0.51–1.31 and 0.29–0.90 in boys and girls, respectively). Five boys exhibit scaling factors ≥0.99. The mean (95% confidence interval) ontogenetic scaling factors are 0.81 (0.71–0.92) and 0.61 (0.50–0.72) in boys and girls, respectively (P = 0.002 betweengroup differences).
DISCUSSION
This study examined age and sexassociated variation in peakV˙o _{2} of 9 to 19yrold distance runners and provides unique information from three perspectives. First, previous studies are generally limited to a relatively narrow age range (i.e., 11–15 yr) and therefore do not describe growthrelated changes in peak V˙o _{2} across the entire adolescent period. Second, only one longitudinal study (7) has included girls across a broad age range in childhood and adolescence. No study has included young distance runners of both sexes 9–19 yr. Third, this study used allometric scaling techniques to interpret the age and sexassociated variation in peakV˙o _{2} of young distance runners.
The observed values for absolute and relative peakV˙o _{2} expressed per unit body mass in this sample of young distance runners are similar to those previously reported in longitudinal studies of young endurance athletes (Figs.1 and2). Limited information is available on the agerelated trend in female athletes. In the general population of normal, healthy girls, relative peakV˙o _{2} decreases during adolescence (21). In the only study that reported age (maturity)specific values, relative peakV˙o _{2} remains stable at ∼52 ml · kg^{−1} · min^{−1} in pre, mid, and latepubertal swimmers (7). More evidence is needed to establish if the agerelated decline of peakV˙o _{2} in adolescent girls is attenuated with exercise training.
Many authors have argued the interpretation of the growthrelated changes in peak V˙o _{2} on the basis of theoretical and statistical limitations of the simple ratio standard (1, 7, 34, 40). Therefore, alternate statistical models, including allometric scaling, ANOVA, and multilevel modeling, have been used in an attempt to create a sizefree expression of peakV˙o _{2}. The use of alternate models has resulted in different interpretations of growthrelated changes in peakV˙o _{2} when expressed per body mass^{0.75}. Previous studies have shown an increase in scaled peak V˙o _{2} in boys (20, 29,32, 34, 39). Armstrong and colleagues (1, 2, 39) have used adjusted means produced from ANCOVA (controlling for body mass) to explore age and growthrelated changes in peakV˙o _{2} of normal, healthy children and adolescents. The results generally indicate an increase in adjusted means across age and maturity groups in boys and an increase in adjusted means from prepuberty to puberty and similar values between puberty and young adulthood in girls. The results suggest that peakV˙o _{2} remains constant from late adolescence into young adulthood in girls.
Recently, multilevel modeling has been applied to investigate the growth, maturity, and trainingrelated changes in peakV˙o _{2} (7, 40). Multilevel modeling attempts to partition the independent and multiplicative effects of age, body size and composition, pubertal status, and exercise training on a dependent variable (e.g., peakV˙o _{2}). Studies using multilevel modeling have demonstrated sizeindependent effects of sex and maturity on peakV˙o _{2} (3, 7). Results from the Training of Young Athletes (TOYA) study indicate that peakV˙o _{2}, controlling for age and body size, increases with pubertal status in male and female athletes, although an increase between mid and postpubescent groups in boys is not evident in girls (7). The results are intriguing, given past assumptions about growthrelated changes in peakV˙o _{2}. However, despite acclaimed usefulness in the analysis of longitudinal data, the biological significance of the results derived from the multilevel modeling approach is difficult to interpret.
Sex differences in peak V˙o _{2} during growth and maturation are well documented in the general population of normal, healthy children and adolescents (1, 21). Less information is available on agespecific differences of young athletes due to the lack of longitudinal studies of female athletes and the narrow age ranges reported in crosssectional studies. A significant age × sex group interaction in the present study indicates a progressive divergence in peak V˙o _{2} that can probably be related to differences in body composition, hematological factors, and perhaps exercise training volume and intensity.
Mean crosssectional scaling factors are similar to those reported for body mass and peak V˙o _{2} in crosssectional analyses of longitudinal data of other male athletes (23,27) and crosssectional analysis of 6 to 17yrold boys and girls (11). However, mean scaling factors reported in the literature show considerable variability (14). Agespecific scaling factors in this study show considerable disparity with estimates for the total sample (Table 4). In both sexes, agespecific scaling models do not represent a good fit, as indicated by adjusted r ^{2} values and nonsignificant loglinear regression models. This observation probably reflects the small range of body size within an age group (10), small agespecific sample sizes, confounding influences of biological maturity status (9), and differences in body composition, especially among girls. Indeed, when multiple age groups were considered, scaling factors began to approximate the overall sexspecific scaling factor.
Table 5 provides a summary of longitudinal studies using ontogenetic scaling. The mean ontogenetic scaling factor of 0.81 in boys is considerably less than previous studies of highly trained adolescent athletes (27,34). In contrast, similar results have been obtained for active boys in the Saskatchewan Growth Study (unpublished observation) and early and latematuring boys training in Polish sports schools (track, wrestling, or basketball; see Ref. 9). The mean scaling factor in the present study is actually higher than that in latematuring boys from the Polish sports schools. The mean ontogenetic scaling factor in female distance runners is higher than maturitygrouped girls from Polish sports schools (track or rowing; see Ref. 9) and lower than recreational sport participants (32). Ontogenetic scaling factors in 10 of 16 female distance runners are not significantly different from zero, indicating that the growth of peak V˙o _{2} is not related to growth in body mass. The lack of fit in female runners also reflects a plateau or decline in peak V˙o _{2}with age (9), as typically observed in female adolescents. Therefore, the higher scaling factor found by Rowland et al. (32) may be due to ageassociated variation, as the mean age at entry in their study was 9.2 yr, whereas most of the female subjects in the present study entered at 12–14 yr of age.
Previous studies also show considerable variability in individual scaling factors (Table 5). It has been suggested that variability in scaling exponents is due to factors other than body mass, including individual variation in geometric similarity, changes in the ratio of leg muscle mass to body mass, differences in physical activity and/or training level, and individual differences in rates of development of sizeindependent factors such as skeletal muscle oxidative enzyme capacity or myocardial contractility (32). The lastmentioned factors would suggest that qualitative changes in the functional capacity of specific subcomponents of the oxygen transport system also contribute to the growthrelated changes in peakV˙o _{2}. The observed variability in the ontogenetic scaling factors may be related to a maturityassociated variation in body mass and peak V˙o _{2}. Given the individuality of timing and tempo of maturation, yeartoyear changes in body mass and peak V˙o _{2} may have been masked by maturity effects. Maturityassociated variation in peak V˙o _{2} has been estimated recently using various statistical models (2, 79). PeakV˙o _{2} increases at a slightly higher rate in early and averagematuring boys than expected from the increase in body mass (unpublished observation; see Ref. 9). In one study, the increase is smaller than expected in latermaturing boys (9). In the present sample of distance runners, differences in biological maturity were evident, as determined by skeletal age estimated from the handwrist Xray obtained on the first visit. The mean difference between chronological age and skeletal age was −0.52 in 12 boys and −0.57 in 10 girls. Unfortunately, an insufficient number of subjects was available for the analysis of skeletal maturity. Future studies should consider maturityassociated variation in peak V˙o _{2}.
Most important to this study is the identification of an appropriate model to interpret growthrelated changes in peakV˙o _{2} of young distance runners, and children and adolescents in general. Several authors argue that peakV˙o _{2} should be expressed in accordance with theoretical values according to the dimensionality theory (i.e., ml · kg^{−0.67} · min^{−1} or ml · kg^{0.75} · min^{−1}; see Refs.1, 17, 19, 25,29, 36). The first step in the investigation of appropriate scaling procedures should involve the calculation of Tanner's special circumstances (5). If r is equal, or approximately equal, to the ratio of the CVs, a linear relationship is evident, and the simple ratio standard (ml · kg^{−1} · min^{−1}) is appropriate. Conversely, if these two terms are not similar, a linear relationship does not exist, and the appropriate power function ratio should be calculated. Other regression diagnostics used in this study (i.e., correlations between residuals, simple and power function ratios, and body mass) were used to examine if the influence of body mass was removed (i.e., the correlation should not be different from 0 if the influence of body mass has been removed; see Refs.5 and 39). On the basis of these criteria, the simple ratio standard could be empirically justified in boys, whereas the power function ratio could be empirically justified in girls (Table 3). Other authors (4, 6) have also concluded that the mass exponent for peak V˙o _{2} is close to unity.
In conclusion, the results of this study suggest that the interpretation of growthrelated changes in peakV˙o _{2} of young distance runners is dependent on the expression of peak V˙o _{2}relative to body size and/or the statistical technique employed. Considerable variability in individual growth patterns in scaled peakV˙o _{2} points to the fact that determining a single scaling factor is difficult and may actually be problematic given the genetic, environmental, and geneticenvironmental interactions that influence peak V˙o _{2}. The most appropriate means of normalizing peakV˙o _{2} for body size still remains problematic (31, 32). Exercise scientists have been criticized for not recognizing the imperfections of ratio standards and being unaware of alternative methods for partitioning the effects of body size in human studies (40). However, it remains to be demonstrated if allometric scaling among a small magnitude of variation in body size warrants such statistical manipulation. According to Calder (10), small size ranges within a species obscure overall trends, patterns, and constraints of size. Thus scaling differences in body size among a small range of body sizes to understand variation in biological function may be of limited value. In contrast, others argue that scaling body size helps us to understand the growth and maturation of the oxygen transport system and its response to submaximal and maximal exercise (1). To solve the problem of the structural and functional consequences of changes in size or scale among growing and maturing children and adolescents, pediatric exercise scientists should perhaps collaborate with comparative mammalian physiologists for whom the statistical tool of allometry has been central for many years.
Acknowledgments
Special thanks to Vern Seefeldt, Wayne Van Huss, Bill Heusner, and other members of the Human Energy Research Laboratory for data collection in Young Runners Study (YRS) I and YRS II.
Footnotes

This study was supported in part by the William Wohlgamuth Memorial Fellowship and the Institute for the Study of Youth Sports at Michigan State University.

Address for reprint requests and other correspondence: J. C. Eisenmann, 118 Corbett, Div. of Kinesiology and Health, Univ. of Wyoming, Laramie, WY 82070 (Email: eisenman{at}uwyo.edu).

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 Copyright © 2001 the American Physiological Society