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Predictive power of individual genetic and environmental factor scores

Martine A Thomis1, Robert F Vlietinck3, Hermine H Maes5, Cameron J Blimkie6, Marc van Leemputte2, A l brecht L Cl aessens1, Guy Marchal4 and Gaston P Beunen 1

1Center for Physi cal Devel opment Research, and 2Exercise Physiology and Biomechanics Laboratory, Faculty of Physical Education and Physiotherapy, Leuven 3Center for Human Genetics, and 4Radiology Unit, Faculty of Medicine, Katholieke Universiteit Leuven, Belgium 5Virginia Institute for Psychiatric and Behavioral Genetics, Department of Human Genetics, Virginia Commonwealth University Virginia, Richmond, VA, USA 6Chi l dren’s Sport and Exerci se Sci ence, The New Chi l dren’s Hospi tal , Westmead, NSW, A ustral i a

This study explores the use of an individual’s genetic (IGFS) and environmental factor score (IEFS), constructed using genetic model ﬁtting of a multivariate strength phenotype. Maximal isometric and dynamic strength measures, one maximal repetition load (1RM) and muscle cross- sectional area (MCSA) were measured in 25 monozygotic and 16 dizygotic twin pairs. The use of I GFS and I EFS i n pr edi cti ng the sensi ti vi ty to envi r onmental str ess w as eval uated by the association of the scores with strength training gains after a 10-week high resistance strength training programme. Results show a high contribution of genetic factors to the covariation between maximal strength and muscle cross-sectional area (84–97%) at pre-training evaluation. Individual factor scor es expl ai ned the l ar gest par t of the var i ati on i n 1RM and other str ength measur es at pr e- training and post-training evaluation respectively. Genes that are switched on due to training str ess (gene–envi r onment i nter acti on) coul d expl ai n the decr ease i n expl ai ned var i ati on over ti me. A negative correlation was found between IGFS and strength training gains (–0.24 to –0.51, P < 0.05); individuals with a high IGFS tend to gain less str ength than i ndi vi dual s w i th l ow I GFS. Individual environmental factor scores have lower differential power. The predictive value of the IGFS has potential utility in identifying an individual’s susceptibility to environmental stress i n a var i ety of mul ti factor i al char acter i sti cs, eg di seases and i mpai r ments, and for sel ecti on of si b pai r s for QTL anal yses. Twi n Research (2000) 3, 99–108.

Keyw or ds: geneti c factor scores, tw i ns, predi cti on, envi ronmental stress, strength trai ni ng, si b pai r selection for QTLs

Introduction Recent developments use the technologies of molec- ular biology to map gene loci explaining variation in quantitative traits (QTL).3 Heritability studies esti- M ost common congeni tal mal formati ons (eg cl efti ng, mate the i mportance of geneti c factors at a popul a- spi na bi fi da, pyl ori c stenosi s, hi p di sl ocati on, cl ub ti on l evel . Stati sti cal procedures are now avai l abl e to feet), adul t di seases (eg i schemi c heart di sease, esti mate i ndi vi dual l evel s of geneti c and envi ron- hypertension), and quantifiable biological traits (eg 4 hei ght, w ei ght, bl ood pressure, i ntel l i gence) are mental determination. In this paper we use a path- multifactorial and are determined by both genetic anal yti c approach to construct i ndi vi dual geneti c and environmental factors. One of the major chal- and environmental factor scores and to test whether l enges i n the fi el d of human geneti cs i s to i denti fy these scores predi ct the suscepti bility to environ- i ndi vi dual s at hi gh ri sk for a gi ven di sease or a mental changes. favourable phenotype, and to predict an individual’s When mul ti vari ate observati ons are avai l abl e from outcome in an efficient prevention, training or geneti cal l y rel ated i ndi vi dual s, hypotheses can be educati onal programme. The i mportance of geneti c tested about w hether the same envi ronmental and and environmental effects in normal variation can be the same geneti c factors have pl ei otropi c i nfl uences studied using data of genetically related subjects.1,2 on phenotypi cal l y correl ated measures.5,6 The parameters of such a geneti c factor anal ysi s can be Correspondence: M Thomi s, Facul ty of Physi cal Educati on and esti mated, and i ndi vi dual genotypi c and envi ron- Physiotherapy, Katholieke Universiteit Leuven, Tervuurse- mental factor scores (IGFS and IEFS) for each subject vest 101, B-3001 Leuven, Belgium. Tel: 32 16 32 90 86; Fax: 4 32 16 32 91 97; E-mail: martine.thomis@flok.kuleuven.ac.be may be constructed by standard methods. The Received 1 February 2000; accepted 9 February 2000 major question in this study is:

Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.126, on 01 Oct 2021 at 04:31:19, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1375/twin.3.2.99 Predictive power of individual genetic scores y MA Thomis et al 100 Can individual genetic or environmental factor Subjects and methods scores predict a subject’s susceptibility to an envi ronmental stress factor, speci fi cal l y i n thi s Subjects study an arm flexo training programme? The sample for this study consisted of twin pairs We hypothesise that, depending on the average from Flemish Brabant, Belgium. Male volunteer heritability of the multivariate phenotype, the IGFS twins 17–30 years of age w ere i ncl uded i f both should predict the value of the individual phenotype members of a twin pair had similar physical activity at l east at the pre-trai ni ng l evel . The hi gher the profiles and had not started, nor recently stopped, heritability of the traits, the smaller the proportion of strength training during the preceding year. Forty- the variance explained by non-shared environmental one tw i n pai rs vol unteered, thei r mean age w as factors, the greater the predictive power of the IGFS. 22.4 ± 3.7years. Subjects were fully informed of the Large vari ati on i n envi ronmental scores, refl ecti ng a measurement protocol before giving their written high environmental determination, will lower the consent. The project was approved by the local medical ethics committee. Zygosity was determined predictive power of the IGFS. by exami nati on of the fol l ow i ng geneti c markers: The predictive power of IGFS depends not only on w A BO, Rhesus (D, C, C , c, E, e), MNSs and Duffy(a,b). the average heri tabl e and envi ronmental determi na- The power to detect dizygotic (DZ) twins with this tion of the traits but also on the switching on of other set of geneti c markers w as 91% . Di fferences i n tw o genes i n response to the envi ronmental stress (geno- geneti c markers w ere used to establ i sh di zygosi ty. type–environment interaction). The estimation of The probability of monozygosity (MZ) of pairs with i ndi vi dual factor scores (IFS) i n the pre-stress condi - the same geneti c markers w as cal cul ated.7 All MZ ti on produces factor scores based on the geneti c and pairs had a probability of monozygosity of at least envi ronmental effects acti ng at thi s pre-stress l evel . 95% . Tw enty-fi ve pai rs w ere cl assi fi ed as M Z and 16 If the stress acti vates new genes, then pre-stress IGFS as DZ. will predict the post-stress phenotypes and changes i n phenotypes l ess w el l . The main purpose of this study is to test the Training protocol predictive power of individual genetic and environmental factor scores i n response to envi ronmental Both members of the twin pair participated in a programme in which mainly the elbow flexors were stress i n an empi ri cal trai ni ng study. Although trai ned. Duri ng 10 w eeks, fi ve sets of bi ceps curl s feasi bl e, i t i s ethi cal l y not desi rabl e to do i nter- w ere performed, 3 ti mes a w eek on a trai ni ng vention studies in more relevant multifactorial dis- apparatus (Kettler Sport type7408-150). Every week, eases such as hypertensi on, obesi ty, cancer of behav- the l oad of each set (w i th a preci si on of 0.5 kg) w as ioural disorders etc, therefore we decided to test the adjusted to each subject’s one repeti ti on maxi mal validity of the individual factor scores on muscular val ue (1RM ). The 1RM w as defi ned as the maxi mal strength. Speci fi c resi stance trai ni ng programmes are resistance that could be lifted a single time through effecti ve i n i ncreasi ng muscl e strength and hyper- the full range of motion. During each supervised trophy, and can, in a standardised manner, be used trai ni ng sessi on, the fi rst set w as performed at 60% as an envi ronmental stress factor i n untrained of 1RM with 14repetitions (reps), the second set at subjects. We constructed i ndi vi dual geneti c and 75% of 1RM with 12 reps, the third set at 80% of environmental factor scores for isometric arm 1RM with 10reps and 8reps at 85% of 1RM for the strength and muscl e mass i n 25 monozygoti c and fourth set. The fifth set at 65% of 1RM was 16dizygotic male, adult twin pairs. The environ- performed until exhaustion. mental stress w as a 10-w eek heavy-resi stance trai n- i ng programme for the el bow fl exors. Responses to Measurement protocol and variables thi s envi ronmental stress factor w ere measured as absolute (post-training minus pre-training values) The esti mati on of IGFS and IEFS i s based on a and rel ati ve i ncreases (gai n i n strength expressed as mul ti vari ate phenotype. M easurements that eval - a percentage of i ni ti al strength) i n stati c and uated maximal isometric strength in the pre-training dynamic arm strength and muscle hypertrophy after condi ti on w ere chosen. These phenotypes consi sted the training programme. We hypothesise that sub- of the maximal static voluntary contraction at 140°, jects w i th hi gher i ndi vi dual geneti c factor scores 110°, and 80° arm flexion (180° is the arm in full will be less responsi ve to the envi ronmental stress extensi on), and mean cross-secti onal arm muscl e (trai ni ng) than subjects w i th smal l er geneti c factor area (cm 2). The eval uati on of maxi mal stati c vol un- scores, and will have correspondingly smaller tary contraction was done after one week of adapta- strength gains following training. tion to the training apparatus using low training

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Fi gur e 1 Path-di agram of the mul ti vari ate geneti c anal ysi s. Phenotypes are encl osed i n squares, and l atent factors are encl osed i n

ci rcl es. A c and Ec are the additive genetic and non-shared environmental factors that are common to all phenotypes. A1–4 and E1–4 are additive genetic and non-shared environmental factors that are speciﬁc to each phenotype. The numbers at each causal uni-directional path indicate path coefﬁcients. Double-headed arrows indicate correlations between latent factors (between additive genetic factors, 1 for MZ twins and 0.5 for DZ twins)

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and muscl e cross-secti onal area. These associ ati ons (A c) expl ai ned the l argest part of the vari ati on i n were tested by correlation coefficients. The distribu- each phenotype (64–76%), while phenotype-specific ti ons of al l vari abl es w ere tested for Gaussi an geneti c and envi ronmental factors w ere l ess i mpor- normality using the Shapiro-Wilk test. We fur- tant (0 to 20%). The common environmental factor thermore tested for birth order effects and differ- only contributed 1% to 16% of the variation in each ences i n mean and vari ances betw een tw i n types phenotype (Table1A). However, leaving out this w i th t tests and F tests, respecti vel y. In al l tests, the common factor worsened the fit of the model stati sti cal si gni fi cance l evel w as chosen at si gni fi cantl y. The hi gh geneti c correl ati ons among P < 0.05. the four phenotypes (> 0.85) indicated that the same genes i nfl uenced strength at di fferent el bow angl es as w el l as the muscl e cross-secti onal area. Non- Resul ts shared envi ronmental correl ati ons w ere hi ghest betw een the strength measures, but l ow betw een Univariate and multivariate genetic analysis muscl e mass and i sometri c strength (Tabl e 1B).

All data were normally distributed. Univariate genetic model fitting on pre-training phenotypes Construction of genetic and environmental factor indicated that a model with additive genetic factors scores and unique environmental factors was the most parsi moni ous. For the mean muscl e cross-secti onal The di stri buti on of IGFS and IEFS w as Gaussi an. area (M CSA ), there w as evi dence for a phenotypi c The mean val ue of al l factor scores (Tabl e 2) w as not interaction factor (one twin’s larger MCSA going significantly different from zero, but the variation in together with a smaller MCSA in his co-twin); both geneti c and especi al l y envi ronmental factor however, this was due to a smaller total variance in scores w as si gni fi cantl y smal l er than the expected MZ twins than in DZ twins. Univariate heritabilities (1.0). Confidence intervals around the IGFS were were 0.92, 0.75, 0.78 and 0.66 for MCSA, and static smaller than those around the IEFS, and the con- moments at 140°, 110° and 80°, respectively.11 The fidence intervals around the factor scores tended to genetic contributions in this study correspond to be larger in DZ than in MZ twins.

Table 1 (A) Proportion of explained variance in each phenotype by genetic and environmental factors. Legend and abbreviations as in Figure 1 (numbers in superscript give path coefficients as in Figure 1). (B) Bi-variate genetic and environmental correlations (above di agonal ) and percentage of expl ai ned covari ati on expl ai ned by geneti c and envi ronmental factors (bel ow di agonal ) A Proportion of explained variance by genetic and environmental factors Genetic variation Environmental variation Ac A1 A2 A3 A4 Ec E1 E2 E3 E4 MCSAa 0.64(1) 0.18(5) 0.01(9) 0.16(13) 140°b 0.76(2) 0.00(6) 0.07(10) 0.17(14) 110°c 0.72(3) 0.00(7) 0.16(11) 0.13(15) 80°d 0.64(4) 0.05(8) 0.11(12) 0.20(16)

B Genetic factors Environmental factors MCSAa 140°b 110°c 80°d MCSAa 140°b 110°c 80°d MCSAa – 0.88 0.88 0.85 – 0.12 0.17 0.13 140°b 97 – 0.97 0.96 3 – 0.40 0.31 110°c 95 88 – 0.96 5 12 – 0.44 80°d 95 89 84 – 4 11 16 – aM CSA : muscl e cross-secti onal area; b140°: maximal static moment at 140° of elbow flexion; c110°: maximal static moment at 110° of elbow flexion; d80°: maximal static moment at 80° of elbow flexion.

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Strength training effects rel ati ve strength as show n by the si gni fi cant negati ve correlations with 1RM (–0.45––0.51), and relative The effect of strength trai ni ng w as fi rst tested by change in isometric and concentric strength (–0.24). anal ysi s of vari ance for repeated measurements. The No significant correlation was found for the training one repeti ti on maxi mal strength i ncreased si gni fi - effects on muscl e mass (0.01, and –0.12). IEFS cantl y by 45.4% on average, maxi mal i sometri c correlated moderately with pre-training isometric strength by 23.3%, and maximal concentric strength and concentric strength (0.44 and 0.30, respectively). by 24.9%. Hypertrophy of arm muscle area was No significant association was found between IEFS smal l er but si gni fi cant (5.3% , P < 0.01). There w as a and training effects in the different phenotypes, si gni fi cantl y l arger i ncrease i n M CSA i n DZ tw i ns except for a si gni fi cant but l ow negati ve correl ati on than in MZ twins (F = 4.7, P < 0.05); however, no w i th the i ncrease i n i sometri c strength (–0.24). other zygosity interaction effects were found, indi- Fi gure 2 show s the pow er of how w el l a subject’s cating no difference in the muscular strength basel i ne IFS predi cts hi s observed basel i ne 1RM response to training between MZ and DZ twins. The strength and his future strength gain after training. In variation in response to training between individ- this figure, both IFS and 1RM scores were cate- uals was very large: the coefficient of variation gorised into quartile groups. Non-overlapping error varied between 34% and 142% for the absolute, and bars indicate significant differences in number of between 45% and 136% for relative changes i n 1RM individuals positioned in the phenotypical quartile and maximal concentric strength respectively. groups by contrasting the individuals according to Changes i n 1RM scores, maxi mal i sometri c strength, tw o IFS quarti l e groups (A , B: IGFS < P25 agai nst and muscle hypertrophy were comparable to train- IGFS P75; and C, D: IEFS < P25 agai nst ing effects in other strength training IEFS P75). Before training, subjects in either the programmes.24–28 lower or upper IGFS quartiles also had a high or low 1RM strength score (Figure2A), while the extreme Predictability and differential power of individual IEFS did not differentiate the subjects except some- geneti c and envi ronmental factor scores what in the middle ( P25– < P50) 1RM quartile (Fi gure 2C). For trai ni ng responses, an i nverse rel a- Table3 shows the correlations of IGFS and IEFS with tionship was found. Subjects in the higher IGFS the pre- and post-training and absolute and relative quarti l e gai ned the l east strength (Fi gure 2B), trai ni ng responses i n the four dependent pheno- w hereas subjects i n the l ow est IGFS quarti l e w ere i n types. IGFS w as hi ghl y posi ti vel y associ ated w i th the hi ghest quarti l es for thei r 1RM response. Con- both pre- and post-training phenotypes (0.67–0.86). trasting the extremes of IEFS (Figure2D) indicated Subjects w i th a hi gh IGFS gai ned l ess absol ute and that individuals with a low IEFS at baseline tended

Table 3 Correlations of IGFS and IEFS with the pre-, and post-training and training response phenotypes Phenotypes 1 RMa isometric 110° conc. 140° MCSA b 60°/sec IGFS with pre-training –0.79d –0.86d –0.78d –0.84d post-training –0.72d –0.71d –0.67d –0.83d absolute change –0.45d –0.03 –0.15 –0.01 relative change –0.51d –0.24c –0.24c –0.12

IEFS with pre-training –0.05 –0.44d –0.30c –0.11 post-training –0.15 –0.28c –0.22 –0.10 absol ute change –0.09 –0.14 –0.08 –0.01 relative change –0.07 –0.24c –0.18 –0.03 a1RM: one repetition maximal (kg); bM CSA : muscl e cross-secti onal area (cm 2); cP < 0.05; dP < 0.001.

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Figure2 Differentiation in 1RM phenotype by IGFS and IEFS. Both IFS and 1RM scores are categorized in four quartile groups. Non- overlapping error bars indicate signiﬁcant differences (* : P < 0.05) in number of individuals positioned in the phenotypical quartile group by contrasting two IFS percentile groups. A and B compare the extreme quartiles IGFS < P25 vs IGFS P75, and C and D the extreme quarti l es IEFS < P25 vs IEFS P75. The Y-axi s gi ves the number (n) of i ndi vi dual s i n a gi ven basel i ne IGFS or IEFS quarti l e w ho have 1RM strength scores i n a certai n quarti l e (X-axi s)

to have a lower impact from the training than Di scussi on individuals with higher baseline IEFS scores. Expressed as a rel ati ve ri sk, i ndi vi dual s havi ng a To our knowledge, this is the first study that has l ow IGFS, had a 4.1 ti mes i ncreased chance of havi ng i nvesti gated the use of i ndi vi dual geneti c and envi - a l ow basel i ne strength (RR = 4.1, CI : 1.9 to 8.79), 95 ronmental factor scores to predict the sensitivity of w hi l e havi ng a hi gh IGFS i ncreased the chance of an i ndi vi dual to an envi ronmental stress. Individual havi ng a hi gh 1RM performance seven-fol d geneti c and envi ronmental factor scores w ere con- (RR = 7.0, CI95: 3.1 to 15.76). The relative risk in structed from a mul ti vari ate common geneti c factor individuals with a low IEFS of a low strength model . Thi s model gave a good expl anati on of the performance was not significantly different from observed covariation (low 2); however, a more one, but having a high IEFS gave a two-fold parsimonious model could be developed.29 i ncreased chance of havi ng a hi gh basel i ne strength Individual genotypic and environmental scores score (RR = 2.0, CI93: 1.006 to 4.0). Individuals with explained 60–74% of the variation in pre-training a hi gh IGFS had a si x-fol d si gni fi cantl y decreased phenotypes (r2 from Table3). The proportion of chance (RR = 0.16, CI93: 0.02 to 0.99) of a high expl ai ned vari ance decreased w hen post-trai ni ng trai ni ng response; a si mi l ar rel ati ve ri sk w as phenotypes and training effects were predicted. A observed for individuals with a low IGFS to have a fi rst possi bl e cause of thi s decrease coul d be envi ron- l ow trai ni ng response. Rel ati ve ri sks to predi ct mental factors, other than the training programme, strength gai ns after trai ni ng based on the IEFS scores influencing the phenotypes during training. were not significantly different from 1. Although subjects were asked to maintain pre-

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w as moni tored by a 7-day recal l questi onnai re every unique for each phenotype (E1–E4), was more impor- w eek,30 changes i n physi cal acti vi ty, di et and other tant. The predictive value of the IGFS and IEFS was, environmental factors could not be entirely con- however, not significantly improved compared with trolled during the 10-week study period. Another the predictive values of the raw phenotypic scores important possibility, however, is that other, ‘new’ (eg pre-M CSA scores predi cti ng post-M CSA scores). genetic factors, that do not contribute to the genetic Probably the high heritabilities of the phenotypes variation in the pre-training strength, may be coul d expl ai n these observati ons. In phenotypes sw i tched on duri ng trai ni ng (gene–envi ronment with lower heritabilities like complex diseases or interaction). The proportion of explained genetic behavioural traits, the gain in predictive value of the vari ance by ‘new ’ geneti c factors i n the post-trai ni ng IFS could be larger compared with the raw scores of phenotype could not be explained by IGFS that are the phenotypes. constructed from pre-training phenotypes. The This study demonstrated the feasi bility of using i mportance of ‘new ’ geneti c factors affecti ng the multivariate genetic model fitting in the construction post-training phenotype can be tested in a longitudi- of individual genetic and environmental factor nal model in which a specific genetic factor that only scores, and the use of model fitting in predicting the causes vari ati on i n the post-trai ni ng phenotype but response to strength trai ni ng. The same approach, not in the pre-training phenotype is included. This however, has potential for applications in multi- speci fi c gene–envi ronment i nteracti on w as si gni fi - factori al di seases, such as hypertensi on or obesi ty. cant for the 1RM and maximal static moment at 110° Quantifying the IGFS and IEFS of an individual with flexion, and explained 19–21% of the variation in a hi gh-ri sk phenotype (eg di astol i c bl ood pressure post-training strength but not for maximal torque in above 90mmHg or a systolic value above 140mmHg) eccentric muscle work or concentric muscle work at could indicate whether the cause of a high risk lower velocities (30° and 60°/s).31 Usi ng a tw o-w ay phenotype is mainly a genetic predisposition (high analysis of variance method Thibault et al32 found IGFS) or an environmental deviation (high IEFS).4 no evi dence for a si gni fi cant genotype–trai ni ng Consequently therapeutic strategies may more effi- interaction in peak torque output after 10weeks of ciently concentrate on concrete actions on the isokinetic knee flexion/extension training in five MZ regul atory mechani sms of hypertensi on i n the case tw i ns. There w as no evi dence for speci fi c geneti c of a hi gh geneti c predi sposi ti on, or di mi ni sh the factors in our data to influence post-training muscle negati ve envi ronmental stress factors, i f subjects cross-secti onal area.31 w i th hypertensi on express hi gh envi ronmental fac- We are not aware of any method in the training tor scores. Besi des eti ol ogi cal cl assi fi cati on, thi s l i terature that predi cts i ndi vi dual responses to approach might also predict the therapeutic out- strength training. The prediction of individual train- come, and even gui de the progress by moni tori ng the i ng effects, based on the i ndi vi dual geneti c factor evolution of the IEFS. The weight matrix A (see scores in this study was more accurate for pheno- A ppendi x 1, equati on 3) can be cal cul ated based on types w i th l arger average trai ni ng effects (1RM and multivariate data from twins, or an extended twin rel ati ve changes). The observed negati ve rel ati on- and family design. This weight matrix is then shi p betw een pre-trai ni ng genotype (IGFS) and multiplied by individual screening data to obtain strength i ncrease, someti mes referred to as the l aw of IGFS and IEFS for each individual. initial values,33 has al so been reported i n earl y The results of this study should be interpreted in strength training studies.34 Stronger subjects gai n the context of the following limitations. Although l ess strength w i th a resi stance-trai ni ng programme the sampl e i s one of the l argest i n an experi mental than i ndi vi dual s w i th l ess strength. strength-trai ni ng desi gn, geneti c anal yses usual l y The results indicated that IGFS not only classified require larger samples. The power of this study is subjects into high and low strength groups, but also, sufficient to test for the significant contribution of in spite of the large variability in training responses, geneti c factors agai nst a model w i th sol el y uni que predicted their low or high strength gain: of two environmental contributions to the observed varia- individuals with similar strength at baseline, the one tion. The detection of a small proportion of addi- with the highest IGFS will gain less from trai ni ng tional familial environmental factors or genetic than the one with the lowest IGFS. The individual dominance would require much larger samples. In environmental factor scores, however, did not have the mul ti vari ate case, how ever, pow er i ncreases due the same pow er to categori se subjects, or to predi ct to additional information, although the power to their future training gains. Environmental factors discriminate between different hypothesised models unique to individuals with a common effect on all is still small. Further, results only apply to young

measured phenotypes (Ec), such as previous training adult men, who may not be representative of the status or diet, only explained a small part of the general popul ati on.

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Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.126, on 01 Oct 2021 at 04:31:19, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1375/twin.3.2.99 Predictive power of individual genetic scores y MA Thomis et al 106 IGFS and IEFS also improve the power of mapping Leuven. At the time of the study MAT was supported Quanti tati ve Trai t Loci (QTL). Present strategi es are by the Fund for Scientific Research, Fl anders (Bel - based on i denti fyi ng pol ymorphi c marker al l el es gi um), as a Research A ssi stant, at present a Post- that are inherited identically by descent (IBD).35 To doctoral Fel l ow. Dr H M aes i s supported by the i ncrease the pow er of mappi ng QTLs, three strategi es Carman Trust and grantsHL48148 and MH45268. are suggested by Lander and Botstei n:36 1) genotypi ng of si bs w i th extreme phenotypes; 2) multipoint interval mapping; and References 3) reducing environmental variation and genetic 1 Eaves L, Last K, Young P, Martin N. Model-fitting approaches variation not associated with the QTL. to the analysis of human behavior. Heredity 1978; 41: Recent simulation studies have dealt with these 249–320. 37–42 3 41 2 Neale MC, Cardon LR. Methodology for Genetic Studies of i ssues or with actual data. Boomsma reports a Twins and Families. Kluwer Academic: Dordrecht, 1992. tw o-fol d i ncrease i n pow er to detect l i nkage betw een 3 Cardon LR, Smith SD, Fulker DW, Kimberling WJ, Pennington a two-allele quantitative trait locus and a fully BF, DeFries JC. Quantitative trait locus for reading disability i nformati ve marker usi ng the Haseman-El ston on chromosome6. Science 1994; 266: 276–279. 4 Boomsma DI, Molenaar PCM, Orlebeke JF. Estimation of regressi on approach w hen usi ng squared di fferences i ndi vi dual geneti c and envi ronmental factor scores. Genet of i ndi vi dual geneti c factor scores (based on a Epidemiol 1990; 7: 83–91. multivariate MZ and DZ twin analysis, including 5 M arti n N, Eaves L. The geneti cal anal ysi s of covari ance genetic variance that is not accounted for by the QTL structure. Heredity 1977; 38: 79–95. and environmental variation) compared with 6 McArdle JJ, Goldsmith HH. Alternative common-factor model s for mul ti vari ate bi ometri c anal yses. Behav Genet 1990; 20: squared differences of phenotypic scores between 42 569–608. sibs. In a recent paper Boomsma and Dolan 7 Meulepas, E, Vlietinck R, Van den Berghe H. The probability performed power calculations (number of sib pairs of dizygosity of phenotypically concordant twins. Am J Hum to be studied to detect linkage) i n w hi ch both si b pai r Genet 1988; 43: 817–826. 8 Van Leemputte M, Willems EJ. EMG quantification and its sel ecti on and QTL anal ysi s w as based on an i ndi vi d- application to the analysis of human movements. Med Sports ual genetic factor score approach. The use of factor Sci 1987; 25: 177–194. scores was shown to be universally more powerful 9 Vande Broek G, Van Leemputte M, Andries R, Willems EJ. than the use of just a multivariate or mean pheno- Mechanical muscle properties after two types of plyometric typi c data approach to detect l i nkage. The l oss i n training. In: Barabas A, Fabian GY (eds). Biometric in Sports XII. Uni versi ty Press: Sjokof, ´ 1995, pp 98–101. power of using the same sample to both calculate the 10 Thomi s M , Cl aessens A L, Vl i eti nck R, M archal G, Beunen G. factor score regressi on matri x and to carry out the Accuracy of anthropometric estimation of muscle-cross-sec- QTL analysis, outweighed the gain in power attribut- tional area of the arm in males. Am J Hum Biol 1997; 9: able to the use of factor scores. 73–86. 11 Thomis M, Beunen G, Van Leemputte M, Maes H, Bl i mki e CJ, In summary, this study explored the use of Cl aessens A L, M archal G, Willems E, Vlietinck R. Inheritance individual genetic and environmental factor scores of static and dynamic arm strength and some of its determi- in predicting an individual’s susceptibility to envi- nants. Acta Physiol Scand 1998; 163: 59–72. ronmental stress. The l arge proporti on of expl ai ned 12 Neale MC. Mx: Statistical Modeling, 4th edn., Department of vari ance i n pre- and post-trai ni ng strength as w el l as Psychiatry: Richmond, VA, 1997. 13 Thurstone LL. The Vectors of the Mi nd. Uni versi ty of Chi cago i n strength i ncreases by IGFS and IEFS l eads to Press: Chi cago, 1935. appl i cati on of these scores i n the devel opment of 14 Sari s WE, De Pi jper M , M ul der J. Opti mal procedures for individual strength training programmes, revalida- estimation of factor scores. Sociol Meth Res 1978; 7: 85–106. ti on programmes and screeni ng for el i te athl etes. 15 Bartlett MS. The statistical conception of mental factors. Br J Psychol 1937; 28: 97–104. Furthermore, the identification of genetic and envi- 16 Weiss V. Die Heritabilitäten sportl i cher Tests, berechnet aus ronmental sources of deviation in individuals, has a den Leistungen zehnjährlichen Zwillingspaare. Leistungssport major field of application in differentiating high-risk 1977; 9: 58–61. phenotypes i n several mul ti factori al di seases. A l so, 17 Pirnay F, Crielaard JM. Influence de l’héredi ´ te ´ sur l es perform- sel ecti on of i ndi vi dual s based on di scordant IGFS ances physi ques. Medic ´ du Sport 1983; 57: 221–225. 18 Jones B, Kl i ssouras V. Geneti c vari ati on i n the strength– coul d i ncrease the pow er to map quanti tati ve trai t velocity relation of human muscle. In: Malina RM, Bouchard C loci. (eds). Sport and Human Genetics. Human Kinetics: Cham- paign, IL, 1986, pp 155–163. 19 Reed T, Fabsitz R, Selby J, Carmelli D. Genetic influences and hand grip strength norms in the NLBI twin study male Acknowledgements aged 59–69. Ann Hum Biol 1991; 18: 425–432. 20 M aes HHM , Beunen GP, Vl i eti nck RF, Neal e M C, Thomi s M , Vanden Eynde B, Lysens R, Simons J, Derom C, Derom R. This study was supported by grant OT/92/27 from Inheritance of physical fitness i n 10-year-old twins and their the Research Fund of the Katholieke Universiteit parents. Med Sci Sports Exerc 1996; 28: 1479–1491.

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21 Hoshi H, Ashizawa K, Kouchi M, Koyama C. On the intrapair 41 Boomsma DI. Using multivariate genetic modeling to detect si mi l ari ty of Japanese monozygoti c tw i ns i n some somato- pleiotropic quantitative trait loci. Behav Genet 1996; 26: logical traits. Okajimas Folia Anatomica Japonica 1982; 58: 161–166. 675–686. 42 Boomsma DI, Dolan CV. A comparison of power to detect a 22 M aes HH, Beunen G, Vl i eti nck R. Heri tability of health- and QTL in sib-pair data using multivariate phenotypes, mean performance-rel ated fi tness. Data from the Leuven Longi tudi- phenotypes, and factor scores. Behav Genet 1998; 28: nal Twin Study. In: Duquet W, Day J (eds). Kinanthropometry 329–340. IV. E & FN Spon: London, 1993, pp 140–149. 43 Sage A P, M el sa JP. Esti mati on Theory wi th A ppl i cati on to 23 Loos R, Thomi s M , M aes HH, Beunen G, Feys E, Derom C, Communications and Control. McGraw-Hill: New York, Vl i eti nck R. Geneti c anal ysi s of muscul ari ty i n earl y adol es- 1971. cence: sex-speci fi c regi onal changes of the geneti c structure w i th age. J Appl Physi ol 1997; 82: 1802–1810. 24 Davies J, Parker DF, Rutherford OM, Jones DA. Changes i n strength and cross secti onal area of the el bow fl exors as a Appendix A result of isometric strength training. Eur J Appl Physiol 1988; 57: 667–670. 25 Narci MV, Roi GS, Landoni L, Minetti AE, Cerretelli P. Changes The mul ti vari ate phenotype (P) (see Fi gure 1) can be i n force, cross-secti onal area and neural acti vati on duri ng strength training and detraining of the human quadriceps. Eur expressed by the fol l ow i ng equati on: J Appl Physiol 1989; 59: 310–319. 26 Sale DG. Neural adaptation to strength training. In: Komi (ed.). P(ij) = hc A c(j) + ec Ec(j) + hs A (ij) + es E (ij) (1), Strength and Power in Sport: The Encyclopaedia of Sports w here i represents the four di fferent measured Medicine. Blackwell Scientific Publications: Oxford, 1992, pp 249–265. phenotypes (MCSA, STAT.MOMENT 140°, STAT. 27 Kraemer WJ, Fl eck SJ, Evans WJ. Strength and pow er trai ni ng: MOMENT 110°, STAT. MOMENT 80°) and j the physiological mechanisms of adaptation. In: Holloszy (ed.). examined individuals (j = 1,…82). The phenotype P Exercise and Sport Science Reviews, vol24. Williams and of each individual is a function of his underlying Wilkins: Baltimore, 1996, pp 363–397. genotype (A ) that pleitropically influences all four 28 Chambers RL, M cDermott JC. M ol ecul ar basi s of skel etal c muscl e regenerati on. Can J Appl Physi ol 1996; 21: 155–184. phenotypes, and environmental factors (Ec) that are 29 Thomis M, Van Leemputte M, Maes H, Bl i mki e CJ, Cl aessens not shared in families, and therefore unique to each AL, Marchal G, Willems E, Vlietinck R, Beunen G. Multi- individual, but also influence all four phenotypes. vari ate geneti c anal ysi s of maxi mal i sometri c muscl e force at The factor l oadi ngs of the measured phenotypes on different angles. J Appl Physiol 1997; 82: 959–967. 30 Bl ai r SN, Haskel l WL, Ho P et al . A ssessment of habi tual the latent factor Ac and Ec are indicated by hc and ec. physi cal acti vi ty by a seven-day recal l i n a communi ty survey The resi dual vari abl e-speci fi c vari ance i s al so parti - and controlled experiments. Am J Epidemiol 1985; 122: ti oned i n geneti c factors (A 1 and A4) and unique 794–804. environmental factors (E1 to E4), path coefficients are 31 Thomi s M , Beunen G, M aes H, Bl i mki e CJ, Van Leemputte M, indicated by h and e . Cl aessens A L, M archal G, Willems E, Vlietinck R. Strength s s trai ni ng: i mportance of geneti c factors. Med Sci Sports Exerc The l oadi ng of each common and speci fi c factor i s 1998; 30: 724–731. estimated by maximum likelihood (ML) in Mx 32 Thibault MC, Simoneau J-A, Côte ´ C, Boul ay M R, Lagassé P, (Neal e12). The fol l ow i ng structural equati on i s Marcotte M, Bouchard C. Inheritance of human muscle sol ved: enzyme adaptation to isokinetic strength training. Hum Hered 1986; 36: 341–347. S % Σ = ΛΨΛ' + Θ (2), 33 Schutz RW. Analyzing change. In: Safrit MJ, Wood TM (eds). Measurement Concepts in Physical Education and Exercise where Science. Human Kinetics: Champaign, IL, 1989; pp 207–228. 34 Hettinger TL, Muller EA. Muscular performance and training. S = observed 2p ϫ 2p (p = number of pheno- In: Brown RC, Kenyon GS (eds). Classical Studies on Physical types = 4) covariance matrix of observations in Activity. Prentice-Hall: New Jersey, 1968, pp 262–276. tw i n 1 and tw i n 2 (expressed i n devi ati ons from 35 Haseman JK, El son RC. The i nvesti gati on of l i nkage betw een a the group mean); quantitative trait and a marker locus. Behav Genet 1972; 2: 3–19. Σ =predicted 2pϫ 2p covariance matrix of 36 Lander ES, Botstein D. Mapping mendalian factors underlying quanti tati ve trai ts usi ng RFLP l i nkage maps. Genet 1989; 121: twin1 and twin2; 185–199. Λ =2pϫ 2m matrix, where m = 2 is the num- 37 Eaves L, Meyer J. Locating human quantitative trait loci: gui del i nes for the sel ecti on of si bl i ng pai rs for genotypi ng. ber of common latent factors, containing the Behav Genet 1994; 24: 443–455. esti mated l oadi ngs of the common l atent fac- 38 Risch N, Zhang H. Extreme discordant sib pairs for mapping tors on the four phenotypes of both twins (path quantitative trait loci in humans. Science 1995; 268: coefficients 1–4 and 9–12 in Figure1); the 1584–1589. l oadi ngs are constrai ned to be equal for tw i n 1 39 Risch N, Zhang H. Mapping quantitative trait loci with extreme di scordant si b pai rs: sampl i ng consi derati ons. A m J and twin 2 and for MZ and DZ twins; Hum Genet 1995; 58: 836–843. Ψ ϫ 40 Eaves L, Neal e M C, M aes H. M ul ti vari ate mul ti poi nt l i nkage =2m 2m matrix of correlations between analysis of quantitative trait loci. Behav Genet 1996; 26: the latent factors; the correlation between Ac is 519–525. 1 in MZ twins, 0.5 in DZ twins, the correlation

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between the Ec factors is 0 for both MZ and DZ FSC = AP' (4), twins; where Θ =2pϫ 2p symmetric matrix of estimates of Fsc = [IGFS , IEFS , IGFS , IEFS ], is the vector variable-specific unique environmental and 1 1 2 2 of individual factor scores, IGFS = individual geneti c vari ances that are equated for both genetic factor score, IEFS = individual envi- members of the twin pair and between MZ and ronmental factor score, subscripts1 and 2 indi- DZ twins (path coefficients 5–8 and 13–16 in cate twin 1 and twin 2; Figure1). Within twin pairs, the unique genetic factors are correlated 1.0 in MZ twins and 0.5 P = the measured mul ti vari ate phenotype of in DZ twins. observati ons of tw i n 1 and tw i n 2, expressed i n Z-scores (n ϫ 2p); The constructi on of i ndi vi dual geneti c and envi - ronmental factor scores in the multivariate genetic A=(2mϫ 2p) weight matrix, derived from anal ysi s w as performed by the Thurstone regressi on equation (3). technique.4 The fol l ow i ng l i near expressi on w as Two-sided, 95% confidence intervals of the factor used to obtain the weight matrix A, by minimising ϫ scores w ere cal cul ated as IGFS ± 1.96 SEIGFS and the sum of squares of the difference between esti- IEFS ± 1.96 ϫ SE for both MZ and DZ twins. mated and true factor scores: IEFS SEIGFS and SEIEFS are the square root of the diagonal A = ΨΛ' (ΛΨΛ' + Θ)–1 (3), elements of the matrix from equation 5, which is a 2m ϫ 2m matrix of the sampling distribution of where constructed factor scores. Matrix V is calculated Λ = matrix of loadings from multivariate phe- based on the factor l oadi ngs i n matri x Λ, the notypes on common factor A and E ; correlations between the common factors in matrix c c Ψ, and the esti mated covari ance matri x Σ of respec- Ψ = matrix of correlations between latent tively MZ and DZ twins. This follows from standard factors; Kal man fi l teri ng techni ques:43 Θ = di agonal matri x of uni que geneti c and V = Ψ[Ψ–1 – Λ' Σ–1Λ]Ψ (5). environmental variation. The confidence intervals only depend on the This weight matrix was used to compute factor factor loadings and the amount of variable-specific scores for each subject by mul ti pl yi ng the w ei ght unique variance (in Σ) and will increase i f the matrix by both the subject’s multivariate phenotypic proporti on of uni que vari ance i ncreases. scores and his co-twin’s phenotypic scores.

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