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1 From the Department of Biomedical Kinesiology, Faculty of Kinesiology and Rehabilitation Sciences (MWP, GPB, ALC, and MAT), Department of Human Genetics, Faculty of Medicine (RV), Katholieke Universiteit Leuven, Leuven, Belgium; Virginia Institute for Psychiatric and Behavioral Genetics, Department of Human Genetics, Virginia Commonwealth University, Richmond, VA (HHM); and Medical Research Council (MRC) Epidemiology Unit, Strangeways Research Laboratory, Cambridge, United Kingdom (RJFL)
2 Supported by the Research Fund Katholieke Universiteit Leuven (OT/86/80; PDM/05/260 to MWP), Nationale Bank van België, Fund for Medical Research (Belgium) (3.0038.82, 3.0008.90, 3.0098.91), and North Atlantic Treaty Organisation (860823). 3 Address reprint requests to MW Peeters, Department of Biomedical Kinesiology, Faculty of Kinesiology and Rehabilitation Sciences, Katholieke Universiteit Leuven, Tervuursevest 101, B3001 Leuven, Belgium. E-mail: maarten.peeters{at}faber.kuleuven.be
ABSTRACT
Background: The distribution of fat and adipose tissue is an important predictor of disease risk. Variation in fat distribution during adolescence is correlated with fat distribution in adulthood.
Objective: The objective was to gain insight into the relative contribution of genes and environment to the stability of subcutaneous fat distribution from early adolescence into young adulthood.
Design: Ratio of trunk to extremity skinfold thickness (TER) data from the Leuven Longitudinal Twin Study (n = 105 Belgian twin pairs followed from 10 to 18 y of age) was entered into a longitudinal path analysis.
Results: The best-fitting model included additive genetic sources of variance and nonshared environment. Heritabilities ranged between 84.3% (95% CI: 63.9–92.3%) and 88.6% (95% CI: 76.5–94.1%) in boys and between 78.4% (95% CI: 59.3–88.3%) and 88.3% (95% CI: 77.0–93.8%) in girls. The majority of the phenotypic tracking (boys: 0.40–0.78; girls: 0.38–0.72) could be attributed to the moderate-to-high genetic correlations (rG) (between 0.27–0.84 and 0.38–0.80 for the various age intervals in boys and girls, respectively). This rG could be attributed to both genetic sources of variance, which are the same throughout adolescence, as well as genetic sources of variance that are "switched-on" at a certain age, the effect of which is then transmitted to subsequent observations. Environmental correlations (rE) in boys ranged between 0.51 and 0.70 but contributed relatively little to phenotypic tracking because the amount of variance explained by the environment was low (11.4–15.7%). In girls rE was low to moderate at best (0.09–0.48).
Conclusion: Phenotypic tracking in subcutaneous fat distribution during adolescence is predominantly explained by additive genetic sources of variance.
Key Words: Heritability • stability • subcutaneous adipose tissue distribution • growth • twins
INTRODUCTION
In addition to the degree of overall fatness the distribution of fat and adipose tissue is an important predictor of disease risk (1). Three types of fat distribution are generally distinguished: excess subcutaneous truncal abdominal fat (android obesity), excess abdominal visceral fat, and excess gluteofemoral fat (gynoid obesity). These 3 types of fat distribution have been anatomically identified and are differentially associated with health risks (1). Android obesity is associated with cardiovascular risk factors and disease in adults and with cardiovascular risk factors in children and adolescents (2–5). Rice et al (6) found that among several indicators of body fat and fat distribution upper-body fat had the strongest genetic correlation with blood pressure, particularly for the ratio of trunk to extremity skinfold thickness (TER) with diastolic blood pressure.
Obese and overweight children and adolescents have considerable higher risks of becoming obese or overweight adults (7–9). The stability of fat distribution from childhood to adolescence and into adulthood has been less studied (10, 11). For Canadian males and females aged 7–69 y the 7-y stability coefficients for the TER ranged from 0.23 to 0.73. Furthermore, the average percentage of participants remaining in the upper TER quintiles ranged from 29% to 50% in males and from 29% to 80% in females (10). In the Québec Family Study tracking coefficients of the TER, adjusted for the sum of 6 measurements of skinfold thickness, from childhood and adolescence into adulthood (12-y follow-up, starting at ages between 8 and 18 y) were 0.41 and 0.47 for boys and girls, respectively (11). These tracking coefficients are the outcome of underlying genetic and environmental determinants.
In a recent review Katzmarzyk and Bouchard (12) concluded that the TER is under genetic control (transmission of 40–50% and heritabilities between 25% and 50%), with higher heritabilities (40–50%) when total body fat was taken into account. Beunen et al (13) showed that for Belgian twins from the Leuven Longitudinal Twin Study (LLTS) from 10 to 14 y of age, the heritability for TER was 85% (95% CI: 79–89%). The remaining variance was explained by unique environmental factors with no evidence for a common environmental factor. Results from a few studies even suggest the influence of major genes on regional fat distribution (12), and in the human obesity gene map (14) genetic association is reported between the ADRA2A gene (10q24–q26) and TER (15, 16), as well as modest linkage with the GYPA gene (4q31.1) (17) and the D7S495 marker (7q34) (18).
Until now it has, to our knowledge, never been investigated whether the tracking or stability during adolescence is caused by genetic or environmental factors or both. Therefore, the main research question of the present study is whether the stability (tracking) of fat distribution during adolescence as measured by TER is caused by a stable environment, by the same genes affecting the fat distribution over that period, or by a combination of both.
SUBJECTS AND METHODS
Sample
Participants are from the LLTS (19). All twins in the LLTS belong to the East Flanders Prospective Twin Survey (EFPTS) (20). The twins (n = 105 pairs, equally divided among 5 zygosity groups, see "Zygosity"), first participated in the testing program at 10 y of age and were followed at semiannual intervals between 10 and 16 y of age and again at 18 y of age. For the present analyses data from observations at 10, 12, 14, 16, and 18 y of age were included. This selection was made to cover the whole adolescent age span and yet not to include too many parameters to be estimated with the relatively modest sample size. All twins were informed about the study, its longitudinal character, and the tests and measurements that were to be taken, after which the parents gave written informed consent for their children's participation. Furthermore, the children gave their assent. The project was approved by the Ethics Committee of the Faculty of Kinesiology and Rehabilitation Sciences of the Katholieke Universiteit Leuven and approved by the Belgian Fund for Medical Research.
Zygosity
In each twin of the EFPTS fetal membranes were examined and placental morphometry was performed. Placental alkaline phosphates were assayed by electrophoresis, and umbilical cord blood was used to determine the ABO, Rh, MNs, Duffy, and Kell blood groups by routine methods. DNA restriction fragment polymorphisms were also studied. Zygosity was determined through sequential analysis (20). Twins of opposite sex were classified as dizygotic opposite-sex (DZO) twins. Same-sexed dichorionic (DC) twins with at least one different marker were classified as dizygotic (DZ) twins. Monochorionic twins were classified as monozygotic (MZ) twins. The probability of monozygosity based on the genetic markers was calculated for all same-sexed DC twins with identical genetic markers. All DC twins of the same sex and same markers, reaching a probability of monozygosity of 0.90, were classified as MZ. The remaining DZ twins in the EFPTS were classified as "unknown" zygosity and are excluded from this study (LLTS).
Measurements
Four measurements of skinfold thickness were included in the analyses: 2 on the extremities (triceps and medial calf) and 2 on the trunk (suprailiac and subscapular). These measurements were all taken on the left side of the body with a Harpenden skinfold caliper (Baty Int, West Sussex, United Kingdom) and followed the procedures as described by Claessens et al (21). The 4 measurements of skinfold thickness were used to calculate the TER as follows: TER = (subscapular + suprailiac)/(triceps + medial calf). This ratio was logarithmically transformed to improve normality of the input data for further analyses.
Statistical analysis
Although some evidence suggests that adiposity and fat distribution are related to biological maturation (22, 23), the TERs in our data were not aligned on age at peak height velocity because the correlations between the TER values at different ages and age at peak height velocity were nonsignificant at most ages and did not exceed r = –0.28 in boys and r = –0.20 in girls. Sex-specific interage correlations (Pearson) were calculated as an index of tracking or stability.
To determine the relative contributions of genetic and environmental factors to the variation in TER and to simultaneously allow for tracking and thus for covariation between the consecutive measurements, longitudinal path models were fitted to the data (24, 25). First, the assumptions for these models were tested, including tests for normality (Shapiro-Wilk test), and for differences between means (t test) and variances (F test) in birth order and zygosity. MX (Medical College of Virginia, Richmond, VA), a structural equation modeling package, was used to compute the goodness of fit and maximum likelihood estimates for the path coefficients (26). The log-transformed raw data were used as input, allowing a maximal use of the available data in MX.
In structural equation modeling, the structural linear equations can be visually represented in path diagrams (Figure 1). In these diagrams the latent variables are enclosed in circles and the observed variables (TER values) in squares. In the classic twin study, with data of MZ and DZ twins reared together, the latent variables can be additive (A) genetic, dominant (D) genetic, unique (ie, nonshared) environmental (E), and common (ie, shared) environmental (C) factors. These unmeasured, latent factors are the causes of the variation in and covariation between the consecutive observed variables (ie, TER). The causal paths between the latent and observed variables are specified and depicted as single-headed arrows. The correlation paths between the latent variables are depicted by 2-headed arrows. Because MZ twins are genetically identical, the correlation between the A factors equals 1.00. The correlation between their D factors also equals 1.00. For DZ twins the corresponding values are 0.50 for A and 0.25 for D. In addition, the correlation between the C factors is by definition 1.00 both for MZ and DZ twins, because the C factor represents shared environment. There is no correlation between the E factors. In the classic twin study, with the use of data of MZ and DZ twins reared together, models that include both C and D sources of variation are not identified such that the presence of C and D factors cannot be tested in the same model (25).
FIGURE 1.. Visual representation of the full nonscalar model for additive genetic (A) and unique environmental (E) factors with 61 estimated path coefficients (1–60, ). Latent (unmeasured) variables are enclosed in circles. Observed variables are enclosed in squares. Single-headed arrows represent causal paths. Double-headed arrows represent correlational paths. = 1.0 or 0.5 in monozygotic (MZ) and dizygotic (DZ) same-sexed twins, respectively. = estimated freely between 0 and 0.5 in DZ opposite-sex twins to allow nonscalar sex differences, which is also why the model is referred to as nonscalar. T1,1–5 indicates variance of the ratio of trunk to extremity skinfold thicknesses (TER) of twin 1 at measurement occasions 1–5; T2,1–5, variance of TER of twin 2 at measurement occasions 1–5; A1–A5, additive genetic innovation factor (innovation paths 1–5 and 21–25, and transmission paths 6–9 and 26–29); Ac, common additive genetic factor, allowing for covariation between measurement occasions (common paths 41–45 and 51–55); Ec, common unique environmental paths allowing for covariation between measurement occasions (common paths 46–50 and 56–60); Ar, residual additive genetic factor (paths 10 and 30); Er, residual additive genetic factor (paths 20 and 40). Note that the figure represents a DZ opposite-sex twin pair with different path coefficients for each member of the twin pair. In the classic twin study with MZ and DZ twins reared together, this model can also include shared environmental factors (C) or dominant genetic sources of variance (D), yielding a total of 91 estimated path coefficients.
In the longitudinal models tested in the present analysis the respective sources of variance (A, C, D, and E) are further divided into "common" sources of variance (eg, Ac, Cc, Dc, and Ec), "innovation" sources of variance (eg, Ai, Ci, Di, and Ei), "transmission" sources of variance (eg, At, Ct, Dt, and Et), and "residual" sources of variance (eg, Ar, Cr, Dr, and Er). Ac represents additive genetic sources of variance common to all measurement occasions and hence represents a group of genes that causes variation at all measurement occasions and can account for covariation and therefore stability over time. Innovation sources of variance are, in the case of genes (Ai), a group of genes that switches on at a certain measurement occasion and hence can cause discontinuity or instability with previous and subsequent measurement occasions. If innovation sources of variance are combined with transmission sources of variance (eg, At), however, together they can also cause correlations (and hence tracking) with subsequent measurement occasions (but not with previous measurement occasions). More details about the model-fitting procedures can be found in Appendix A.
The percentages of variance in TER values explained by the different latent variables were calculated from the parameter estimates of the best-fitting and most parsimonious model. The 95% maximum likelihood CIs of these percentages were also estimated (27). The phenotypic correlations (tracking) recovered under the best-fitting model were decomposed into their genetic (rG) and environmental (rE) correlations (28).
RESULTS
The average TER values are given in Figure 2. For girls, average values increase almost linearly from 0.59 (±SD: 0.13) at 10 y to 0.84 (±0.23) at 18 y of age. In boys in contrast, average TER values are almost constant from 10 (0.61 ± 0.13) to 12 y (0.59 ± 0.13) with a pronounced increase to 1.19 (±0.28) at 18 y of age. Values differ significantly (P < 0.05) at 12 (TER for girls greater than TER for boys), 16, and 18 y of age, with boys having a higher TER than girls at the latter 2 measurement occasions.
FIGURE 2.. Ratio of trunk to extremity skinfold thicknesses (TER) of Belgian twins in the Leuven Longitudinal Twin Study. Error bars represent ±1 SD. Overall age effects, sex effects, and age x sex interaction effects are significant (P < 0.05). The * indicates post hoc age-specific sex effects significant at P < 0.05. n = 210, 206, 204, 182, and 184 persons at ages 10, 12,14,16, and 18 y, respectively. At 10 y of age TER values of drop outs did not differ significantly from those of twins continuing their participation in the study (P > 0.05, t test).
With the exception of the distribution for boys at 16 y of age, all log-transformed TER distributions were normally distributed (P > 0.10, Shapiro-Wilk). In same-sexed twins no differences in means and variances were found for birth order or zygosity categories (except for mean TER differences of MZ and DZ twins in boys at 10 y of age and in girls at 10 and 18 y of age between MZ and DZ; P < 0.05). For this longitudinal analysis it was deemed that the basic assumptions for structural equation modeling were sufficiently met.
Tracking coefficients (Pearson interage correlations) for 2-y periods varied between r = 0.65 and r = 0.78 in boys and between r = 0.52 and r = 0.72 in girls (Table 1). With increasing intervals (4, 6, and 8 y) correlations tended to be lower, but no clear simplex structure was present. The intrapair twin correlations at the different ages varied between r = 0.79 and r = 0.89 for MZ boys, between r = 0.82 and r = 0.91 for MZ girls, between r = 0.30 and r = 0.60 for DZ boys, between r = 0.49 and r = 0.66 for DZ girls, and between r = 0.13 and r = 0.47 for the DZO twins. These intrapair correlations indicate a strong genetic effect, possible sex specificity, and the possibility of a C effect.
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TABLE 1. Interage correlations (tracking coefficients) for ratio of trunk to extremity skinfold thicknesses in boys (above diagonal) and girls (below diagonal) in the Leuven Longitudinal Twin Study1
The best-fitting and most parsimonious model is represented in Figure 3. This is the model that explains the covariance between subsequent measurement occasions in both boys and girls with the fewest number of parameters without significantly worsening the fit of the model. Parameter estimates could not be constrained to be equal in boys and girls (for details, see Appendix A and Table A1). Only A and E factors were required to explain the variation in TER values at the different ages. Moreover, At paths were present, and also Ai paths at each age and an Ar path, constrained to be equal across ages, were retained in this model. Finally, an Ac factor completed the genetic part of the model. Besides age-specific Ei factors, only an Ec (to all ages) factor was incorporated in the model. In Figure 4 the contributions to the explained variance in the TER values of each of these factors are given. Total heritabilities, including Ai, At, Ar, and Ac, varied between h2 = 0.84 (95% CI: 0.64–0.92) and h2 = 0.89 (95% CI: 0.77–0.94) in boys and between h2 = 0.78 (95% CI: 0.59–0.88) and h2 = 0.88 (95% CI: 0.77–0.93) in girls. In boys, the genetic innovation paths explained between 12% and 43% of the total variance. It should be noted that the Ai at 10 y of age includes an unknown amount of At variance from previous unmeasured occasions. The At variance explained between 14% and 66%. The variance explained by the Ac factors varied between 0.04% and 42%. The Ar variance was estimated to be 0. There were no clear age trends in these different genetic factors. The proportion of the variance explained by Ec and Ei factors ranged between 6% and 12% and between 3% and 7%, respectively. In girls, the relative contributions of the different genetic factors included Ai paths, ranging from 14% to 61%, again including an unknown amount of transmitted variance from previous (unmeasured) ages at age 10 y, At paths, ranging from 18% to 49%, and Ac factors, ranging from 8% to 52%. The Ec and Ei factors ranged between 1% and 17% and between 4% and 14%, respectively, with low contributions for the Ec factor for girls aged 12–18 y.
FIGURE 3.. Visual representation of the specific scalar-AitcrEic model. Best-fitting and most parsimonious model with 50 estimated path coefficients. Latent (unmeasured) variables are enclosed in circles. Observed variables are enclosed in squares. Single-headed arrows represent causal paths. Double-headed arrows represent correlational paths. Aitcr indicates additive genetic sources of variance (A) including innovation (i), transmission (t), common (c), and residual (r) paths; Eic, unique environmental sources of variance including i and c paths; = 1.0 or 0.5 in monozygotic (MZ) and dizygotic (DZ) twins, respectively; T1,1–5, variance of the ratio of trunk to extremity skinfold thicknesses (TER) of twin 1 at measurement occasions 1–5; T2,1–5, variance of TER of twin 2 at measurement occasions 1–5; A1–A5, additive genetic innovation factor; Ac, common additive genetic factor; Ec, common unique environmental paths; Ar, residual additive genetic factor (equated over all measurement occasions).
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TABLE A1. Overview of tested models and their fit indexes1
FIGURE 4.. Percentages of variance in ratio of trunk to extremity skinfold thicknesses explained by different sources of variance under the specific scalar Aitcr-Eic model for boys (A) and girls (B). Ai indicates additive genetic innovation variance; Ac, common additive genetic variance; Ar, additive genetic residual variance (estimated at or near 0.0); At, additive genetic transmitted variance; Ec, common unique environmental variance; Ei, unique environmental innovation variance. Note that Ai at 10 y of age includes an unknown amount of additive genetic variance transmitted from previous unmeasured time points. Also note that At in this figure is the sum variance transmitted from all previous occasions, eg, at 14 y. At represents the sum of the additive genetic variance transmitted from 10 y of age plus additive genetic variance transmitted from 12 y of age. Error bars represent 95% CIs on the total heritability (Ai + Ac + At + Ar).
The genetic and environmental correlations recovered under the best-fitting model are represented in Table 2. rG results from both At and Ac factors, whereas rE is solely based on a unique environmental source of variance shared by all measurement occasions (Ec). rG is moderate to high in both boys (0.37–0.84) and girls (0.37–0.80). rE is also moderate to high in boys (0.51–0.70) but low to moderate at best in girls (0.09–0.48).
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TABLE 2. Genetic correlations (rG, above diagonal) and environmental correlations (rE, below diagonal) based on the best-fitting model1
DISCUSSION
This longitudinal study of 105 twin pairs who were followed between 10 and 18 y of age, over the entire adolescent growth period, shows that phenotypic tracking in the TER values is to a large extent explained by genetic sources of variation. These genetic sources include both sets of genes that are the same for each measurement occasion (Ac) and sets of genes that are activated at a specific measurement occasion (Ai), the effects of which are subsequently (in part) transmitted to all subsequent observations (At). The modest contribution of environmental factors to the tracking in TER is limited to environmental factors that are the same for each measurement occasion (Ec). In both boys and girls, the heritabilities are high (>78%) with rather small 95% CIs, which however overlap between sexes and measurement occasions. No Et or C (familial) factors are identified in the most parsimonious model.
The growth curve for TER values corresponds quite closely to the curve reported by Malina and Bouchard (29) for the ratio between measurements of 5 trunk (pectoral, subscapular, midaxillary, paraumbilical, and suprailliac) and 5 extremity (triceps, biceps, forearm, medial thigh, and medial calf) skinfold thicknesses. The steep increase between 12 and 18 y of age in boys marks the typical male adipose tissue distribution. It starts from around the onset of the growth spurt in height and tapers off in approaching adulthood.
The heritabilities found for this sample of Belgian twins are rather high compared with what is reported in the literature (12). Estimates in the latter report vary between 30% and 50%. But in most of the studies TER values are adjusted for total fat mass or body mass index. It can be questioned whether this adjustment is the most appropriate procedure to deal with the association between adipose tissue distribution and fat mass. In a previous analysis based on the same sample of twins, Beunen et al (13) showed that there is good evidence that skinfold thicknesses at different sites of the body are under control of the same set of genes with an additional extremity skinfold genetic factor. Katzmarzyk and Bouchard (12) also report a maximal heritability of h2 = 0.68 for abdominal adipose tissue assessed by computed tomography and of h2 = 0.42 after adjustment for fat mass. The unadjusted heritability corresponds more closely to the values reported herein. Note also that in the LLTS a sample of adolescents is investigated and age-specific heritabilities are estimated, whereas in most other studies adult samples are considered with a wide age range, which is adjusted for in the analyses. As indicated earlier, genetic pleiotropy for body fat phenotypes was shown with data from the Quebec family study (30) and the LLTS (13). Furthermore Rice et al (6) found that among several indicators of body fat and fat distribution upper-body fat (TER) had the strongest genetic correlation with blood pressure, particularly diastolic blood pressure.
Because heritabilities are high, the environmental sources of variance (Ei and Ec) only explain a small amount of variance in both boys and girls (between 11% and 22%; Figure 4) with no evidence for transmission. The most parsimonious model did not include a C (familial) effect. The absence of a C effect, which may include growing up in the same household with similar nutritional habits, may seem surprising. However, these effects can only be identified if the effect is rather large or if the sample size is large to identify small effects. Statistical power to detect these effects is, however, increased in multivariate analyses of correlated variables (31), of which the longitudinal study is a special case. Simulations with the current sample size and interage correlations show a statistical power of 65% to detect a shared environmental variation that explains 30% of the total variation. If smaller Ec effects are present and go undetected because of insufficient power, this will result in a somewhat lesser fit of the model (albeit not significant) and an overestimation of the total heritability because variance shared by both members will be included in the additive genetic variance rather than the unique environmental variance.
The TER tracking coefficients over a period of 6 or 8 y (r = 0.40–0.62 in boys and r = 0.38–0.51 in girls; Table 1) are generally somewhat higher than the 7-y interage correlations reported by Katzmarzyk et al (10) for 9–10-y-old Canadians. This discrepancy might be attributed to the adjustment for body mass index in the Canadian data. An advantage of the longitudinal analysis on genetically related persons as presented in the present study is that the phenotypic tracking (interage correlations) can be decomposed into its genetic (rG) and its environmental (rE) parts (Table 2). According to the criteria proposed by Malina (32), environmental interage correlations in boys are moderate to high for all 2-, 4-, 6- and 8-y time intervals, suggesting rather stable unique environmental influences on TER during adolescence in boys. In girls, however, these environmental correlations are low to moderate at best, suggesting that their unique environmental influences are less stable during adolescence as is also evidenced by the somewhat larger relative contribution (compared with boys) of time-specific Ei variance, which is not correlated between measurement occasions (Figure 4). One may speculate on the nature of this latent time-specific Ei variance in terms of a culturally inspired preoccupation with weight and nutrition in girls; however, no data on food intake are available in the LLTS data to support this suggestion. Because the total variance explained by unique environmental sources of variance is rather small (compared with the heritabilities), the contribution of the environmental correlations to the total phenotypic correlations is rather small, even in boys. The genetic correlations under the best-fitting model (Table 2, above diagonal) are moderate to high in both boys and girls for all lengths of age intervals. In combination with the high heritabilities, these results suggest that stable genetic influences are the main cause of the phenotypic tracking in TER during adolescence. This biological stability arises from 2 different sources of genetic variance, Ac and At, neither of which could be dropped from the full model without significantly worsening the fit (Table A1, Appendix A). Thus, the present data suggest that there is a set of genes which plays a role in explaining variation at all ages between 10 and 18 y (Ac) and that there are sets of genes that are possibly switched on at a certain age (Ai), potentially causing discontinuity from previous measurement occasions but the effects of which are subsequently (in part) transmitted (At) to the following occasions and hence also contribute to the tracking of the TER during adolescence. These results therefore suggest that the subcutaneous fat distribution with its potential associated negative health outcomes in adulthood is relatively stable from early adolescence into young adulthood and that this stability is mainly due to a person's genetic makeup.
In summary, distribution of trunk to extremity adipose tissue is under strong genetic control (>75%) in adolescent boys and girls, and the tracking in TER during the adolescent period is principally caused by genetic sources of variation. In males there is also a modest contribution of stable environmental causes of variance to the phenotypic stability in TER during adolescence. There is no evidence for a common environmental effect on the interindividual variation in TER and no indication for significant transmission of environmental factors.
APPENDIX A
Description of the models and model-fitting procedures
Longitudinal path models were fitted to the data by following a strictly predetermined strategy. The full model (Figure 1) allows for tracking and hence stability by combining an independent pathway (IP) model (25) and a (quasi) simplex structure (24). The IP structure, represented in the lower part of Figure 1 (ie, Ac and Ec), explains covariation by a single set of genes (Ac) which causes variation in the trait at each age without imposing a specific structure on the correlation matrix because the magnitude of these sources of variance (Ac, Ec, Cc, or Dc) may differ for each time point. The simplex model imposes a stricter pattern on the correlational structure which cannot be modeled by an IP structure. It implies that the further 2 measurement occasions are separated in time, the lower the correlations (tracking) will be. It includes both innovation (sources of variance; eg, Ai) and transmission paths (eg, At). The innovation models a new set of genes which starts causing variation at a specific age, thus causing some instability (lowering the tracking) with the previous measurements. However, the variation of the innovation may then subsequently be, totally or in part, transmitted to the next measurement occasion through the transmission paths which cause the tracking in the trait over time. The higher the amount of transmitted variance from one occasion to the next, the higher the interage correlations are and, hence, the higher the stability or tracking of the TER. Residual, time-specific variance is modeled in the full models as well (time-specific sources of variation Ar, Er, Cr, or Dr). These sources of variation need to be constrained to be equal across time to be distinguishable from the innovation sources of variance.
In the present analyses, the fit of all tested models is compared with that of the saturated model which imposes no specific structure on the data and provides a baseline fit. The fit of these models is evaluated by the likelihood ratio test and a parsimony-based index: Akaike's information criterion [AIC = (diff. –2lnL) – (2diff.df), where diff. –2lnL is the difference in the –2 times log likelihoods between the tested and the saturated model, and diff.df is the difference in the df of the 2 models]. AIC favors a simpler model that has fewer estimated parameters and hence more df and a lower value of AIC over a more complex model.
The strategy used in model fitting and dropping of the parameters was as follows. First, a set of nonscalar (NS) sex-limitation models, which are the most general type of sex-limitation models, was tested to determine what combination of general sources of variance (A, E, C, D) were needed to explain variation in TER. Subsequently, nested models of the favored NS model, including the appropriate general sources of variance (eg, C and E), were tested to determine, if present, the nature of sex differences [NS, specific scalar (SS), or general scalar (GS), and models without sex-specific parameter estimates].
The NS sex-limitation models allow nonidentical sets of genes (A differs between sexes; Figure 1: < 0.5 in DZO twins) to cause variation in TER values in boys and girls. In this model the C and E factors are assumed to be the same for both sexes, but their magnitude may differ. This allows the absolute and relative contributions of A, E, and C or D to differ between sexes. In the SS sex-limitation models, it is assumed that the same set of genes influences the trait in both sexes. The magnitude of the effects of A, E, and C or D, however, does not have to be the same across both sexes. In the general scalar models all parameters are set equal across sexes. Only a general scalar difference is allowed to accommodate a difference in total variance between both sexes. In the most stringent models, all parameters are constrained to be equal across sexes (25). Subsequently, from the model that included the appropriate general sources of variance and the favored type of sex differences, the sources of variation needed to explain the covariation (eg, At or Et, Ac or Ec) between the subsequent observations were tested. Note that when transmission paths are dropped from the model, the residual paths (eg, Ar) become redundant and hence are dropped as well because the innovation paths then strictly become time-specific residual paths, only contributing to the variation at one measurement occasion and not to the covariation between successive measurement occasions.
Model-fitting results
The results of the model fitting are shown in Table A1. The fit of all tested models was significantly worse than the fit of the saturated model (P < 0.05) in which no structure is imposed on the data. This is probably due to the relatively small sample size and the multivariate structure of the data. On the basis of likelihood ratio test both C and D could be dropped from the NS-ACE and NS-ADE models, respectively. Furthermore, there was no evidence for a NS sex effect because the genetic correlation between DZO twins could be constrained to 0.5 in the SS-AE model. However, constraining all parameters for boys and girls to be equal significantly worsened the fit (AE model) even when differences in total variance between boys and girls at each time point were allowed (GS-AE model). This implies that, although the same genes and environmental factors cause variation in TER in boys and girls, their absolute and relative contribution to this variation differs significantly between sexes. In the last step the importance of different sources of covariation (transmission compared with common paths) were tested for A and E, respectively. Only Et and Er variance could be dropped from the full SS-AE model without significantly worsening the fit leading to the selection of the SSAitrc-Eic model (Figure 3) as the best-fitting and most parsimonious model.
ACKNOWLEDGMENTS
The author's responsibilities were as follows—MWP and GPB: performed the data analysis, interpreted the results, and wrote the first draft of the manuscript; GPB, RV, and HHM: designed the Leuven Longitudinal Twin Study; HHM, RJFL, ALC, and MAT: were responsible for the data collection; all coauthors provided constructive, critical review of the data analysis and the manuscript. None of authors had personal or financial conflicts of interest.
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