Genetic Determinants of Bone Mass in Adults A Twin Study

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1 Genetic Determinnts of Bone Mss in Adults A Twin Study Nichols A. Pocock,* John A. ismn,* John L. Hopper,* Michel G. Yetes,1 Philip N. Smbrook,* nd Stefn beri *Grvn Institute ofmedicl Reserch, Sydney, Austrli; IDeprtment ofnucler Medicine, St. Vincent's Hospitl, Sydney, Austrli; nd tpidemiology Unit, Fculty ofmedicine, University ofmelbourne, Melbourne, Austrli Abstrct The reltive importnce of genetic fctors in determining bone mss in different prts of the skeleton is poorly understood. Lumbr spine nd proximl femur bone minerl density nd forerm bone minerl content were mesured by photon bsorptiometry in 38 monozygotic nd 27 dizygotic twin pirs. Bone minerl density ws significntly more highly correlted in monozygotic thn in dizygotic twins for the spine nd proximl femur nd in the forerm of premenopusl twin pirs, which is consistent with significnt genetic contributions to bone mss t ll these sites. The lesser genetic contribution to proximl femur nd distl forerm bone mss compred with the spine suggests tht environmentl fctors re of greter importnce in the etiology of osteopeni of the hip nd wrist. This is the first demonstrtion of genetic contribution to bone mss of the spine nd proximl femur in dults nd confirms similr findings of the forerm. Furthermore, bivrite nlysis suggested tht single gene or set of genes determines bone mss t ll sites. Introduction Osteoporosis is mjor helth problem of Western societies tht ffects up to hlf of the elderly femle popultion (1). Osteoporosis-relted frctures re n incresing problem in ging men nd women. In women, the sudden decline in estrogen production t the menopuse is n importnt etiologicl fctor in the subsequent ccelerted rte of bone minerl loss (2, 3). However, the significnt prevlence ofthe disese in ging men nd its bsence in some postmenopusl women indicte tht other fctors re lso importnt in determining bone mss nd hence the risk of osteoporotic frctures. nvironmentl fctors such s tobcco nd lcohol use, physicl ctivity, nd body weight hve ll been reported to influence bone mss (4-1). A genetic contribution to bone mss hs previously been reported for the bones of the upper limb (1 1-13). One study found genetic component of spinl bone mss in individuls less thn 25 yers old, but not in subjects older thn 25 (11). To our knowledge, no dt hve been published in reltion to possible genetic contribution to bone mss in the cliniclly importnt site of the proximl femur. Address correspondence to Dr. ismn, Grvn Institute of Medicl Reserch, St. Vincent's Hospitl, Sydney, NSW 21, Austrli. Received for publiction 27 August 1986 nd in revised form 3 Mrch J. Clin. Invest. The Americn Society for Clinicl Investigtion, Inc /87/9/76/5 $2. Volume 8, September 1987, The study oftwins provides unique method to investigte the importnce of genetic nd environmentl fctors in determining bone mss. We report here the results of twin study exmining heritbility of bone mss in the lumbr spine, proximl femur, nd distl forerm. Methods The twin pirs studied were volunteers obtined through the Austrlin Ntionl Helth nd Medicl Reserch Council Twin Registry nd from ppels through the medi. Only dult twins ofthe sme sex were studied, nd informed written consent ws obtined from ll prticipnts. Twins were only excluded from nlysis on the bsis of disese, such s rheumtoid rthritis, or use of medictions, such s corticosteroids, which my hve ffected bone density in one or both twins. 65 twin pirs were studied in full. The zygosity ofthe twins ws determined from their own clssifiction. This hs been shown to be ccurte to within 5% nd is comprble with clssifiction by more sophisticted nd extensive investigtion (14). The study group comprised 32 femle nd 6 mle monozygotic (MZ)' twin pirs, s well s 26 femle nd 1 mle dizygotic (DZ) twin pirs. 13 of the MZ nd 4 of the DZ femle twin pirs were postmenopusl. Two other DZ twin pirs were discordnt for menopusl sttus; one twin of ech pir ws premenopusl nd the other postmenopusl (four yers in ech cse). Bone minerl density (BMD, grms per squre centimeter) ws mesured in the lumbr spine (L2-L4) nd right proximl femur using DP3 dul photon bsorptiometer (Lunr Rdition, Mdison, WI). Dul photon bsorptiometry utilizes the reltive trnsmission of photons oftwo energies (44 nd 1 kev), emitted from Gdolinium 153 rdition source, to determine bone minerl content (BMC) (15). BMD ws derived by dividing the BMC ofech region by the projected bone re. In the proximl femur three sites were mesured: the femorl neck t trns-cervicl position, the trochnteric region, nd Wrd's tringle within the femorl neck. All femorl scns were checked, without knowledge of zygosity or bone density estimte, to ensure there ws no difference in positioning of region of interest between twin pirs. The rdition dose to the skin nd gonds ws < 2 nd 1 ggy, respectively (1-2 mrd). As we hve described previously the coefficient ofvrition ws 1.4% over 36 determintions (weekly) with cdveric vertebre nd 2.6% on repeted determintions in five norml volunteers (16), consistent with published vlues (17). Forerm BMC (units per centimeter) of the distl rdius nd uln ws mesured using single photon densitometer (Molsgrd Instruments, Copenhgen, Denmrk). Scnning ws commenced t site corresponding to 8 mm seprtion between the rdius nd the uln; five subsequent scns were performed, ech 4 mm more proximl. Forerm BMC ws clculted from the men of the six scns. At the 8-mm site the rdius nd uln re comprised of - 2 nd 12% trbecu- 1. Abbrevitions used in this pper: BMC, bone minerl content; BMD, bone minerl density; DZ, dizygotic; MZ, monozygotic; V2mx, mximum oxygen uptke. 76 Pocock, ismn, Hopper, Yetes, Smbrook, nd berl

2 lr bone, respectively, while t the most proximl site the rdius nd uln re both - 5% trbeculr bone (18). The coefficient of vrition on repeted mesurements in norml volunteers ws 1.5%. Mesurements ofbmd were mde without knowledge s to the zygosity of the twins. Lumbr spine rdiogrphs were obtined in ll subjects older thn 4 yers. Scns ofech twin were nlyzed with reference to relevnt X rys without knowledge of the sibling's results. The lumbr BMD estimtes were excluded from nlysis for six twin pirs becuse of the presence ofspinl osteorthritis, which my flsely elevte estimtes of spinl bone density. Vsculr clcifiction ws not problem in ny subject. No subject in the study hd prior history ofrenl disese nd ll hd norml renl function s ssessed by cretinine clernce (vilble in 1 subjects) nd/or norml serum cretinine. Weight (kilogrm) nd height (meter) were mesured in ll subjects nd body mss index (kilogrm per squred meter) ws clculted. Physicl fitness ws estimted in 26 MZ nd 23 DZ twin pirs by mesurement of predicted mximl oxygen uptke (VO2mx, liters per minute) ccording to the criteri of Astrnd nd Ryhming (19). Subjects were exercised t known work lod on bicycle ergometer. The plteu pulse rte, stedy for t lest 2 min, ws used in conjunction with the lod to estimte the V2mx ccording to the nomogrm of Astrnd nd Ryhming (19). Sttisticl Methods Anlyses of twin studies ssume tht intrpir vrince of MZ nd hence geneticlly identicl twins is due to environmentl fctors nd mesurement error, while intrpir vrince in DZ twins is dditionlly ffected by genetic fctors. It is lso ssumed tht common environmentl fctors re shred to similr extent between MZ nd DZ twins. Comprison of the correltion of BMD in MZ twin pirs with tht in DZ twin pirs cn therefore provide mens ofdetermining the nd O2, respectively. The reltionship of BMD in twin pirs (BMD1,BMD2) s mesured by covrince (Cov) cn therefore be expressed s: Cov(BMD1,BMD2) = Cov(G,,G2) + Cov(C,,C2). For MZ pirs the correltion of GI nd G2 = 1, while for DZ pirs the correltion of GI nd G2 = 1/2 (2). The clssicl twin model ssumes the correltion of Cl nd C2 = 1 independent of zygosity. Hence for MZ pirs: Cov(BMD,,BMD2) = Cov(MZ) = g2 + 2, while for DZ genetic contribution to observed vrition in BMD. Thus, t ny prticulr loction: BMD =, + G + C +, where Mis the men BMD for tht loction (nd my itself be function of mesured vribles such s ge, sex, yers postmenopuse, etc.), G represents genetic determinnts of bone mss, C represents common environmentl fctors ffecting bone mss, nd represents environmentl fctors prticulr to n individul including mesurement error. Furthermore, for ech twin, G, C, nd re ssumed to be independent, normlly distributed rndom vribles with mens equl to zero nd non-negtive vrinces 82, 2, pirs Cov(BMD1,BMD2) = Cov(DZ) = 1/2 g2 + Cf 2, nd therefore Cov(MZ) = Cov(DZ) if nd only if Cfg2 =. In summry, for ny trit (e.g., BMD), demonstrtion of significnt difference in covrince, nd hence in the correltion, between MZ twin pirs nd DZ twin pirs is consistent with significnt genetic determinnt of vrition in tht trit. stimtion ofprmeters. The correltions of BMD nd BMC t different sites in MZ nd DZ twin pirs were clculted by mximum likelihood s outlined below. In the nlyses the men ws fitted independently of zygosity nd s liner function of ge for mles nd premenopusl femles, or liner function of yers postmenopuse for postmenopusl femles. In ll nlyses the men ws llowed to differ between loctions. Tests of fit for outliers were performed fter Hopper nd Mthews (21): In no instnce ws there evidence of poor fit. For ech twin pir, t ech loction, it is ssumed tht BMD hs bivrite norml distribution with covrinces tht cn be expressed s bove in terms of CTg2 nd oct2. Under the restriction tht ll re nonnegtive, the vrince components CT82, C,2, nd,2 re estimted by mximum likelihood (22) using the lgorithm Fisher (23, 24). After convention we define heritbility to be h = Cg2/2, nd similrly define c = oj2/12, nd e = CT2/o2, where or2 = og2 + T2 + C. Tht is, h, c, nd e re the proportions of totl vrition explined by genetic, common environmentl, nd other fctors, respectively. The correltions between twins were estimted by mximum likelihood s rmz = Cov(MZ)/l2, nd rdz = Cov(DZ)/2, with both Cov(MZ) nd Cov(DZ) not constrined. The likelihood rtio criteri is used to test the null hypothesis Org2 =, i.e., heritbility =. The mximum log likelihood ws clculted under two models with Tg2 = nd Cg2 2. Under the null hypothesis, twice the bsolute difference in log likelihood between these models will be symptoticlly distributed s 5:5 mixture of x2 vrite nd point mss t the origin (21). Bivrite nlyses. The similrity between the fctors G, C, nd determining BMD t different skeletl sites ws investigted. This sttisticl nlysis ws crried out in the premenopusl femle twin pirs who constituted the lrgest subgroup. All possible pirs of skeletl sites were nlyzed using bivrite nlysis. Thus, for ech loction (k) nd twin (i) (i = 1, 2), BMDA, = Ak + Gk, + Cki + ki, with corresponding vrince components rgk(2, CT2 nd ek2 s bove. For ech pir of skeletl sites k nd m, we clculted Pg, Pc, nd Pe, the correltions between the G, C, nd components, respectively, t different loctions in the sme individul. Tht is, Pg = Corr(Gkj,Gmj), independent of i, so tht, for two individuls, i nd j, if i # j for MZ pirs, Cov(Gki,Gmj) = pgcgkgm, while for DZ pirs Cov(Gki,Gmj) = ½/2 pgcgkgc,. Also, Cov(CkCmj) = Pcckr, nd Cov(kimj) = PeCekcem independent of zygosity. The correltions p = Cor(Yki,Ymi), between BMD t different sites in the sme individul were lso clculted by mximum likelihood s outlined bove. Results The men ge of the MZ twins ws 47 yr (rnge, 24 to 75 yr), nd for the DZ twins 4 yr (rnge, 24 to 65 yr). The men body mss index of the MZ twins ws 23 kg/m2 (rnge, 17 to 31 kg/m2) nd for the DZ twins, 23 kg/mr2 (rnge, 18 to 36 kg/m2). There ws no significnt difference between the correltion of body mss index in the MZ twins nd in the DZ twins (.39 nd.25, respectively). The men VO2mx of the femle MZ twins ws 34 ml/kg per min (rnge, 18 to 57 ml/kg per min) nd for the DZ twins, 36 ml/kg per min (rnge, 21 to 62 ml/kg per min). There ws no significnt difference between the intrpir correltion of V2mx, in the MZ twins (r =.88) nd in the DZ twins (r =.81). There ws no significnt difference between the men BMD or BMC t ny site in the twins compred with vlues from ge-mtched controls. Also, for no skeletl site were the mens or interpir vrinces different between MZ nd DZ pirs. The correltions of BMD t the different skeletl sites re shown in Tble I (top) for ll MZ nd DZ twin pirs. At ll sites the correltion between MZ twins ws greter thn tht between DZ twins. stimtes of heritbility derived from mximum likelihood nlysis re lso listed. From this nlysis we found tht heritbility ws significntly greter thn zero t ll loctions except the distl forerm. Anlysis excluding the two twin pirs discordnt for yers postmenopuse did not lter the results. However, nlysis ofthe correltions of BMD t the different skeletl sites confined to the premenopusl femle twin pirs (Tble I, bottom) resulted in somewht different estimtes of heritbility. In this subgroup t ll sites the correltion between MZ twins ws greter thn between DZ twins nd heritbility ws significnt for the spine, forerm, Genetic Determinnts ofbone Density 77

3 Tble I. Twin Correltion nd Heritbility ofbone Mss Prmeter rmz rdz Heritbility All twin pirs Lumbr BMD (P <.1) Proximl femur BMD Femorl neck (P <.5) Wrd's tringle (P <.1) Trochnteric (P <.2) Forerm BMC (P <.8) Premenopusl twin pirs Lumbr BMD (P <.1) Proximl femur BMD Femorl neck (P <.8) Wrd's tringle (P <.1) Trochnteric (P <.5) Forerm BMC (P <.1) Intrpir correltion coefficients for MZ (rmz) nd DZ (rdz) twins nd heritbility for the five skeletl sites, determined from nlysis of ll twin pirs (top) nd from nlysis of only premenopusl twin pirs (bottom). Heritbility ws clculted using mximum log likelihood with the constrint tht ol, c2, nd el were ll greter thn zero. nd two sites in the proximl femur (i.e., Wrd's tringle nd the trochnteric region). However, heritbility did not rech significnce t the femorl neck. Forerm BMC, on the other hnd, showed significnt heritbility in the premenopusl women. The correltions of lumbr spine nd femorl neck BMD s well s forerm BMC in ll the MZ nd DZ twins re shown in Figs. 1-3, respectively. The rnge of BMD observed S 16" 1.6 cs C~ co 1.2- Zz.8- IL.4 Ne 1.6- N S z 8.8 S U.L A ȯ o p. o Femorl Neck BMD Twin 1 - g/cm Figure 2. Correltion of femorl neck BMD between (A) MZ twins nd (B) DZ twins showing mle (m) nd femle (o) twin pirs. The line of identity is shown. in the twins studied ws the sme s we hve observed in norml popultion. The close correltion between the twin pirs occurs throughout the rnge of BMD. Tble II shows the cross-correltions of BMD in premenopusl women t different sites in the sme individul nd the estimted cross correltions Pg, Pc, nd Pe for ech pir of loctions. The estimtes of pg re positive between ll sites but U I- m U. 2.1 A m N 2.1 B c m 3.2 m c U Lumbr BMD Twin 1 - g/cm Figure 1. Correltion of lumbr spine BMD between (A) MZ twins nd (B) DZ twins showing mle (-) nd femle (u) twin pirs. The line of identity is shown Forerm BMC Twin 1 - U/cm Figure 3. Correltion of forerm BMC between (A) MZ twins nd (B) DZ twins showing mle (i) nd femle (o) twin pirs. The line of identity is shown Pocock, ismn, Hopper, Yetes, Smbrook, nd berl

4 Tble II. Correltions between Determinnts ofskeletl Mss t Different Skeletl Sites Femorl Wrd's neck tringle Trochnteric Forerm Lumbr P Ps Pc Pc Femorl neck p Pg Pc Pe Wrd's tringle p.8.38 PS.8.64 Pc Pe Trochnteric P.44 PS.48 Pc.55 Pe -.21 Correltions (p) between BMD t different skeletl sites. The correltions between genetic (p), common environmentl (Pc), nd individul environmentl (Pe) components of bone mss t different skeletl sites in the sme individul re shown. re greter between the three proximl femur sites thn between these sites nd the lumbr spine nd forerm. The estimtes ofpe re positive between femorl neck, Wrd's tringle, nd trochnteric, nd between lumbr nd forerm, but re negtive between the former three loctions nd the ltter two. stimtes ofheritbility from bivrite nlyses, which impose greter structure on the cross-covrinces, re lower thn those estimted from univrite nlysis but nevertheless re consistently between.4 nd.6. Discussion These dt demonstrte for the first time in dults strong genetic component to the determintion of bone mss in the spine nd proximl femur. They lso confirm the previously reported genetic contribution to bone mss in the ppendiculr skeleton of the upper limb ( 11, 13). Anlysis of ll twin pirs studied, s well s seprte nlysis ofthe premenopusl twins, suggests greter genetic determinnt of BMD in the lumbr spine thn in either the proximl femur or the distl forerm. The pprent greter contribution of genetic fctors in determining forerm bone mss in premenopusl women compred with the group s whole suggests tht environmentl fctors re of incresing importnce fter the menopuse nd/or with dvncing ge t this site. The bivrite nlysis of BMD in the premenopusl women, demonstrting significnt correltion between the genetic components of BMD t different loctions, is consistent with one gene or single set of genes determining bone mss t ll skeletl sites mesured. There were lso strong correltions between common environmentl components cross the different loctions. However, there ws negtive ssocition between individul environmentl components of the sites in the proximl femur nd both the lumbr nd the forerm loctions. This suggests tht lthough there re genetic nd environmentl components common for bone density t ll loctions, there re some environmentl fctors specific for bone density t the hip compred with the lumbr spine or forerm. A genetic contribution to bone mss in the upper limb hs been previously suggested by single photon bsorptiometry (11, 13) nd by metcrpl morphometry (12). Dequeker et l. (11) hve shown, by bsorptiometry, genetic contribution to spinl bone mss in individuls younger thn 25 yr, s well s to distl rdius BMC in individuls > 25 yr. The vlues for heritbility reported by tht study, i.e.,.88 nd.75, respectively, were clculted s described by Holzinger (25): H = (DZ intrpir vrince - MZ intrpir vrince)/dz intrpir vrince. Similr vlues derived from our dt re.85 for the lumbr spine, nd in the premenopusl femles,.78 for the distl forerm, which is virtully identicl to those reported by Dequeker et l. (1 1). To our knowledge, there re no previous studies tht hve exmined the role of genetic fctors in determining bone mss of the proximl femur, the site of the most cliniclly severe osteoporosis-relted frctures. Tht our dt suggest smller genetic contribution to bone mss of the proximl femur nd forerm compred with the lumbr spine imply tht environmentl fctors ply more dominnt role in determining vrition of bone mss t these sites. This is consistent with the observtion tht skeletl sites in the forerm nd proximl femur re exposed to lrge individul vritions in mechnicl loding; e.g., the lod on the upper nd lower limbs re highly vrible between occuptions. However, the spine bers the weight of the upper hlf of the body with reltively little vrition during wking hours except in occuptions involving hevy lbor. ven the trnsition from sitting position to wlk does not result in lrge chnge in mechnicl lod on the spine, but results in mjor chnge in mechnicl stress exerted on the hip. We hve previously demonstrted (9) tht physicl fitness (VO2mx), nd by impliction hbitul physicl ctivity (26, 27), is importnt in determining BMD in the femorl neck. The high correltion of VO2mx between MZ twins ws similr to tht between DZ twins. This suggests tht both MZ nd DZ twin pirs re concordnt for hbitul physicl ctivity. This concordnce could contribute to the reltive similrity of intrpir correltion of proximl femur BMD in MZ nd DZ twins. In summry, this study hs demonstrted for the first time significnt genetic contribution to bone mss in the spine nd proximl femur in dults nd confirms the previously reported genetic contribution to upper limb bone mss. The smller genetic determinnt of bone density in the hip nd forerm compred with the lumbr spine, nd by impliction the importnce of environmentl fctors, supports the findings of our previous study (9) nd suggests greter potentil for lifestyle intervention in chieving reduction in the incidence of hip nd forerm frctures. The dt emphsize the importnce of fmily history nd suggest the potentil for DNA Genetic Determinnts ofbone Density 79

5 studies (e.g., restriction frgment length polymorphism studies of pproprite genes) to identify individuls t risk. Identifiction of such individuls would llow erly life style (e.g., exercise, diet) nd other therpeutic interventions nd possibly prevent the development of clinicl disese. Acknowledments We re indebted to the Austrlin Ntionl Helth nd Medicl Reserch Council Twin Registry for ssistnce in recruiting volunteers for this study nd to Dr. Brry Wren nd The Center for the Mngement of the Menopuse for the use of the single photon bone densitometer. The work ws supported by Sndoz Austrli, the Austrlin nd New South Wles Diry Corps., the Ntionl Helth nd Medicl Reserch Council, nd by the Grvn Reserch Foundtion. References 1. Stevenson, J. C., nd M. I. Whitehed Postmenopusl osteoporosis. Br. Med. J. 282: Gennt, H. K., C.. Cnn, B. ttinger, nd G. S. Gordn Quntittive computed tomogrphy of vertebrl spongios: sensitive method for detecting erly bone loss fter oophorectomy. Ann. Intern. Med. 97: Krolner, B., nd S. Pors Nielsen Bone minerl content of the lumbr spine in norml nd osteoporotic women: cross sectionl nd longitudinl studies. Clin. Sci. 62: Aloi, J. F., S. H. Cohn, A. Vswni, J. K. Yeh, K. Yuen, nd K. llis Risk fctors for postmenopusl osteoporosis. Am. J. Med. 78: Brewer, V., B. Meyer, M. S. Keele, S. J. Upton, nd R. D. Hgn Role of exercise in preventing involutionl bone loss. Med. Sci. Sports xercise. 15: Dniell, H. W Osteoporosis of the slender smoker. Vertebrl compression frctures nd loss of metcrpl cortex in reltion to postmenopusl cigrette smoking nd lck of obesity. Arch. Intern. Med. 136: Nilsson, B.., nd N.. Westlin Bone density in thletes. Clin. Orthop. Relt. Res. 77: Oyster, N., M. Morton, nd S. Linnell Physicl ctivity nd osteoporosis in postmenopusl women. Med. Sci. Sport xercise. 16: Pocock, N. A., J. A. ismn, M. G. Yetes, P. N. Smbrook, nd S. berl Physicl fitness is mjor determinnt of femorl neck nd lumbr spine bone minerl density. J. Clin. Invest. 78: Vernejoul, M. C., J. Bielkoff, M. Herve, J. Gueris, M. Htt, D. Mdrowski, D. Kuntz, L. Mirovet, nd A. Ryckewert vidence for defective osteoblst function. A role for lcohol nd tobcco consumption in osteoporosis in middle ged men. Clin. Orthop. Relt. Res. 179: Dequeker, J., J. Nijs, A. Verstreten, P. Geusens, nd G. Gevers Genetic determinnts of bone minerl content t the spine nd rdius: twin study. Bone (NY). In press. 12. Moller, M., A. Horsmn, B. Hrvld, M. Huge, K. Henningsen, nd B.. C. Nordin Metcrpl morphometry in monozygotic nd dizygotic elderly twins. Clcif Tissue Res. 25: Smith, D. M., W.. Nnce, K. W. Kng, J. C. Christin, nd C. C. Johnston Genetic fctors in determining bone mss. J. Clin. Invest. 52: Hrubec, Z., nd C. D. Robinette The study of humn twins in medicine nd reserch. N. ngl. J. Med. 31: Krlner, B., nd S. Pors Nielson Mesurement of bone minerl content (BMC) ofthe lumbr spine. 1. Theory nd ppliction of new two dimensionl dul photon ttenution method. Scnd. J. Clin. Lb. Invest. 4: Pocock, N. A., J. A. ismn, M. G. Yetes, P. N. Smbrook, S. berl, nd B. G. Wren Limittions of forerm bone densitometry s n index of vertebrl or femorl neck osteopeni. J. Bone Min. Res. 1: Riggs, B. L., H. W. Whner,. Seemn, K. P. Offord, W. L. Dunn, R. B. Mzess, K. A. Johnson, nd L. J. Melton Chnges in bone minerl density of the femur nd spine with ging. J. Clin. Invest. 7: Schlenker, R. A Percentges of corticl nd trbeculr bone minerl mss in the rdius nd uln. Am. J. RdioL. 126: Astrnd, P. O., nd I. Ryhming A nomogrm for clcultion of erobic cpcity (physicl fitness) from pulse rte during submximl work. J. AppL. Physiol. 7: Fisher, R. A The correltion between reltives on the supposition of Mendelin inheritnce. Trns. R. Soc. dinb. 52: Hopper, J. L., nd J. D. Mthews xtensions to multivrite norml models for pedigree nlysis. Ann. Hum. Genet. 46: Kendll, M. G., nd A. Sturt The dvnced theory of sttistics, Vol. 2. Chrles Griffin & Co. Ltd., London Lnge, K., J. Westlke, nd M. A. Spence xtensions to pedigree nlysis. Vrince components by the scoring method. Ann. Hum. Genet. 39: Lnge, K., M. Boehnke, nd D. Weeks Progrms for Pedigree Anlysis. Deprtment of Biomthemtics, UCLA School of Medicine. 25. Holzinger, K. J The reltive effect of nture nd nurture influences on twin differences. J. duc. PsychoL. 2: Astrnd, P. O., nd K. Rodhl Physicl work cpcity. In Textbook of Work Physiology. McGrw Hill, Inc., New York Cotes, J.., C. T. M. Dvies,. G. dholm, M. J. R. Hely, nd J. M. Tnner Fctors relting to the erobic cpcity of 46 helthy British mles nd femles ged 18 to 28 yers. Proc. R. Soc. Lond. (Biol.) B174: Pocock, ismn, Hopper, Yetes, Smbrook, nd berl