StudyDaddy Biology Behavioral genetic research designs have often been attacked because they rely on comparing monozygotic twins (MZ) to dizygotic twins (DZ). Critics of twin-based research maintain that MZ twins look m

Behavioral genetic research designs have often been attacked because they rely on comparing monozygotic twins (MZ) to dizygotic twins (DZ). Critics of twin-based research maintain that MZ twins look m

Geneticall y Informativ e Design s fo r th e Stud y of Behavioura l Developmen t Kathry n S. Lemer y an d H. Hil l Goldsmit h Universit y of W isconsin – Madison , US A Geneti c an d environmen ta l in uence s on behaviou r an d developm en t ca n be examine d by studyin g mor e tha n on e individua l withi n a family , usin g quantitativ e geneti c theor y an d behaviour al geneti c (BG ) methodolog y. Speci Ž c environmen ta l an d geneti c in uence s ca n be measure d an d effec t size s estimated , an d man y assumption s of th e methodolog y ca n be explicitl y tested . BG design s ca n identif y speci Ž c aspect s of th e environmen t tha t hav e th e greates t in uenc e on behaviour al variation , an d the y ca n pinpoin t critica l period s in whic h environmen ta l in uence s ar e mos t malleable , bot h of whic h ar e usefu l whe n designin g interventio ns . Trait s tha t ar e show n to be th e mos t heritabl e throug h traditiona l famil y resemblanc e method s ca n no w be explore d furthe r an d actua l gene s ma y be identi Ž ed , usin g ne w molecula r methods . By identifyin g speci Ž c geneti c an d environmen ta l in uence s on behaviour , an d modellin g th e structur e of thes e in uence s ove r time , we ca n rapidl y advanc e ou r understand in g of huma n developme nt . Importanc e of B ehavioura l Geneti c M ethodolog y fo r Developmenta l P sycholog y Mos t psychologic al theor y consider s th e observable , or phenotypi c level , bu t phenotyp e is a functio n of bot h gene s an d environment . Eve n longitudina l design s ar e confounde d by geneti c change s withi n an d geneti c difference s amon g individuals . On e wa y to examin e geneti c an d environ - menta l in uence s withou t activel y manipulatin g individual ’ s biolog y or experienc e is to stud y mor e tha n on e individua l withi n a family , usin g quantitativ e geneti c theor y an d behavioura l geneti c (BG ) methodology . In a geneticall y informe d design , tru e environment al effect s ma y be identi Ž ed an d studied . Environment al in uence s ar e furthe r parse d int o thos e tha t mak e individual s simila r (shared , or commo n environment ) an d Request s fo r reprint s shoul d be sen t to Kathry n S. Lemery , Psycholog y Department , 120 2 W. Johnso n Street , Universit y of Wisconsin – Madison , WI 53706 , USA ; e-mail : [email protected] . c 199 9 Th e Internationa l Societ y fo r th e Stud y of Behavioura l Developmen t INTERNATIONA L JOURNA L OF BEHAVIORA L DEVELOPMENT , 1999 , 23 (2) , 293 – 31 7 294 LEM E R Y AN D GOLDSM IT H thos e tha t mak e individual s differen t fro m on e anothe r (nonshare d environmen t) . Interestingl y, man y kinshi p studie s in th e personalit y domai n hav e demonstrat ed tha t it is share d gene s tha t accoun t fo r th e similarit y betwee n individuals , rathe r tha n th e share d environmen t (Rowe , 1994) . Finding s suc h as thes e ar e usefu l in identifyin g th e speci Ž c aspect s of th e environmen t tha t hav e th e greates t in uenc e on behaviour , in recognisin g critica l period s durin g whic h thes e phenotype s ar e mos t malleable , an d fo r designin g interventions . Clearly , a geneticall y informa - tiv e desig n is a usefu l wa y to stud y developmen t. Thi s pape r is an introductio n to methodologic al an d conceptua l frontier s in BG designs . Thi s Ž el d ha s move d beyon d simple , univariat e biometri c estimate s of proportion s of behaviour al varianc e du e to geneti c or environmen ta l in uences . Speci Ž c environmen ta l an d geneti c in uence s ca n be measure d an d effec t size s estimated . Man y assumption s of th e methodolog y ca n be teste d explicitly . Developmen ta l function s ca n be Ž t to explai n th e structur e of continuit y an d chang e acros s age . Th e differentia l heritabilit y of behaviou r ca n be examine d betwee n categorica l groups . Thi s pape r illustrate s th e powe r of BG design s to enric h th e inference s possibl e fro m studie s of developmen t. We begi n wit h a brie f explanatio n of BG logi c an d design , procee d wit h an explicatio n of multipl e regressio n an d structura l equatio n mode l Ž ttin g wit h famil y data , an d continu e by introducin g commo n longitudina l model s an d BG methodolog y fo r categorica l data . B G Logi c an d Methodolog y We provid e an outlin e of BG logi c an d methodology . Thes e issue s ar e treate d in mor e detai l in an y behavioura l geneti c textboo k (e.g . Plomin , DeFries , McClearn , & Rutter , 1997) , an d quantitativ e genetic s backgroun d is provide d in text s suc h as Falcone r (1989) . Quantitativ e genetic s theor y is a genera l accoun t of th e aetiolog y of individua l differences . It is a progressiv e theor y in tha t it lead s to ne w prediction s tha t ca n be teste d empirically , an d th e assumption s of th e theor y ca n be teste d as well . Th e basi c linea r mode l of quantitativ e genetic s parse s th e phenotypi c varianc e int o tha t du e to geneti c an d environmen ta l in uences . Symbolically , V P = V G + V E + 2Cov ( G ) ( E ) + V G E , where V P is th e phenotypi c varianc e (th e su m of th e individuals ’ square d deviation s fro m th e mean , divide d by th e numbe r of individuals) , V G is th e geneti c variance , V E is th e environment al variance , 2Cov(G)(E ) is th e covarianc e betwee n G an d E, an d V G E represent s an y nonadditiv e effec t of G an d E. Man y model s do no t estimat e th e covarianc e an d interactio n terms , assumin g tha t the y ar e insigni Ž cant . However , by considerin g th e formula , we ca n se e tha t eve n if th e covarianc e betwee n G GE NETI C ALL Y IN F OR M ATIV E DESIGN S 295 an d E is ignored , th e estimate s of th e varianc e of G an d E remai n th e same . Also , th e correlatio n betwee n G an d E add s to V P substantiall y onl y if bot h G an d E ar e large . Becaus e we canno t estimat e al l of thes e component s directl y by measurin g gene s an d environment s, we indirectl y estimat e the m fro m th e resemblanc e of relatives . If relative s ar e mor e simila r to eac h othe r tha n individual s picke d randoml y fro m th e populatio n on a particula r trait , the n ther e is covariatio n fo r tha t trait . Thi s phenotypi c covariatio n is the n parse d int o geneti c an d environmen ta l in uences , dependin g on ho w simila r individual s ar e geneticall y an d environmen tally . Geneti c effect s ca n be partitione d int o additive , dominant , an d epistati c components . Th e additiv e componen t is th e aspec t tha t is mos t typicall y estimate d an d is th e su m of th e averag e effect s of individua l allele s acros s th e genotype . Sibling s shar e 1 2 of th e additiv e geneti c varianc e becaus e the y receiv e th e sam e allele s fro m thei r parent s 1 2 of th e time . Parent-offspri ng pair s als o shar e 1 2 , half-sib s shar e 1 4 , and , of course , identica l twin s shar e al l of thei r additiv e geneti c variance . If a dominanc e componen t is present , the n th e averag e effect s of allele s do no t ad d up in a linea r fashion . Dominanc e is th e interactio n betwee n allele s at th e sam e locus . Assumin g rando m mating , childre n do no t shar e dominanc e deviatio n wit h thei r parent s becaus e the y canno t receiv e bot h allele s at on e locu s fro m th e sam e parent . Sibling s shar e 1 4 of the dominanc e varianc e becaus e the y shoul d receiv e th e sam e allele s fro m bot h parent s 1 4 of th e time . Half-sib s do no t shar e an y of thei r dominanc e deviation , becaus e the y do no t hav e bot h parent s in common . Identica l twin s shar e al l of thei r dominanc e deviation . Thus , if dominanc e is present , the n monozygoti c (MZ ) correlation s woul d be mor e tha n hal f dizygoti c (DZ ) correlations , an d th e twi n desig n woul d yiel d highe r heritabilit y estimate s tha n othe r famil y design s (e.g . parent-offspr in g studies , adoptio n studies) . In th e presenc e of dominance , siblin g correlation s woul d als o be highe r tha n parent-offspri ng correlations , bu t on e mus t als o conside r tha t th e heritabilit y of th e chil d an d adul t form s of th e trai t ma y be different . Dominanc e effect s ar e als o confounde d wit h siblin g environmen ta l effects , whic h bot h lea d to greate r siblin g tha n parent-offspri ng resemblanc e. A secon d typ e of geneti c interactio n is terme d epistasi s an d is th e interactio n of gene s at differen t loci . Ther e ar e severa l differen t kind s of epistati c interaction , tha t is , betwee n additiv e geneti c value s at differen t loci , betwee n dominanc e deviation s at differen t loci , or betwee n additiv e geneti c value s at on e locu s an d dominanc e deviation s at anothe r locus . As wit h dominance , Ž rst-degre e relative s ar e les s tha n hal f as simila r as identica l twin s in th e presenc e of epistasis . Identica l twin s shar e 100 % of thei r epistati c interactions , wherea s fraterna l twin s an d sibling s shar e 25 % of thei r additiv e additiv e interaction s betwee n tw o loci , an d 12.5 % of 296 LEM E R Y AN D GOLDSM IT H thei r additiv e additive additiv e interaction s amon g thre e loci , or additive dominanc e interactio n betwee n tw o loci . We do no t kno w ho w man y loc i or wha t type s of epistati c interaction s ar e involve d in mos t behaviour s an d disorders . Se e Cro w (1986 ) fo r detail s concernin g geneti c interaction s an d famil y designs . In sum , geneti c effect s ca n be partitione d int o additive , dominance , an d epistati c components — al l of whic h ca n mak e famil y member s simila r to on e another . Othe r tha n fo r identica l twins , ther e ar e geneti c in uence s tha t mak e famil y member s differen t fro m on e anothe r as well . In addition , ther e ar e aspect s of th e environmen t tha t mak e individual s similar , an d othe r aspect s tha t mak e the m different . Share d environment al effect s explai n similarit y betwee n relative s in additio n to tha t accounte d fo r by genetics , an d als o explai n similarit y betwee n thos e wh o ar e geneticall y unrelate d bu t reare d together . Th e nonshare d environmen t is th e remainde r of th e varianc e no t explaine d by genetic s or by share d environmen t an d include s environ - menta l in uence s tha t ar e uniqu e to eac h individua l in a famil y an d thu s creat e differences . Th e estimat e of nonshare d environmen t is ofte n confounde d wit h measureme nt error . Studie s sho w tha t th e majorit y of environmen ta l in uence s on behaviou r ac t to mak e sibling s differen t fro m eac h othe r (Plomi n & Daniels , 1987 ; Rowe , 1994) . Wha t is th e implicatio n of thi s Ž nding ? Doe s it mea n tha t globa l famil y variables , suc h as parentin g style , ar e no t importan t fo r th e developmen t of children ’ s behaviour ? No , becaus e commo n factor s suc h as parentin g styl e ca n affec t individual s differently , an d thu s ma y contribut e to individua l differences . Th e impac t of environmen ta l factor s is speci Ž c to eac h child , dependin g on his / he r individua l phenotype , suc h as temperamen t. Dun n an d Plomi n (1986 ) foun d tha t mother s als o diffe r in ho w similarl y the y trea t thei r children . Thi s effec t is in uence d by materna l ag e an d personality , education , an d siblings ’ temperament . Parent s hav e differen t relationship s wit h eac h child , an d differentia l treatmen t is associate d wit h difference s in th e qualit y of th e siblin g relationship . Heritability. Thi s mean s les s tha n th e layperso n commonl y assume s bu t th e concep t nevertheles s is importan t fo r BG . Broad-sens e heritabilit y (h B 2 ) is th e proportio n of th e phenotypi c varianc e du e to geneti c varianc e amon g individual s in a population . Narrow-sens e heritabilit y (h 2 ) is the proportio n of phenotypi c varianc e du e to additiv e geneti c variance . Becaus e heritabilit y is a proportion , estimate s of heritabilit y wil l be differen t in differen t environmen ts . Som e environmen ts ar e mor e conduciv e to th e expressio n of geneticall y in uence d behaviour s tha n others . Heritabilit y decrease s whe n th e relevan t environmen t varie s a lo t fro m individua l to individual , an d heritabilit y increase s if th e environmen t GE NETI C ALL Y IN F OR M ATIV E DESIGN S 297 is nearl y th e sam e fo r al l individuals . Additionally , heritabilit y is clearl y greate r if th e populatio n ha s greate r variabilit y in th e relevan t genes , an d conversel y bu t les s intuitively , heritabilit y decrease s if th e populatio n share s nearl y al l gene s tha t affec t a particula r phenotype . Thus , th e heritabilit y of a huma n bein g bor n wit h tw o leg s is abou t zero , becaus e nearl y al l human s shar e th e gene s tha t contro l thi s phenotype . Fro m thes e quali Ž cations , it become s eviden t tha t estimate s of heritabilit y ar e speci Ž c to th e populatio n studie d becaus e population s diffe r in thei r distributio n of relevan t gene s an d environment s. A behaviou r tha t is heritabl e is no t necessaril y presen t at birt h or unmodi Ž able . Gen e actio n is dynami c an d th e in uenc e of gene s ma y chang e throughou t th e lifespan . Thus , a behaviou r tha t is foun d to be heritabl e at a particula r ag e ma y no t be heritabl e at another . Aspect s of th e environmen t (e.g . therapeuti c intervention ) ma y modif y heritabl e behaviou r as well . Fo r behaviour al trait s mos t commonl y studied , heritabilit y is typicall y in th e rang e of 30 – 70 % (Goldsmith , 1989) . Behavioura l Geneti c D esigns . Ther e ar e thre e basi c behavioura l geneti c designs : th e twi n study , adoptio n study , an d famil y study , an d thes e design s ca n be combined . In th e twins-reared- togethe r design , heritabilit y is implie d if monozygoti c (MZ ) twi n correlation s ar e highe r tha n dizygoti c (DZ ) twi n correlation s fo r th e trai t unde r study . Ther e ar e tw o mai n assumption s of th e twi n design : (1 ) tha t twin s ar e representat iv e of th e norma l population ; an d (2 ) tha t environment al similarit y doe s no t diffe r fo r MZ pair s an d DZ pair s fo r th e trai t unde r study . Dat a on singleton s wit h th e sam e assessmen t procedur e ca n be compare d to th e twi n dat a to tes t th e Ž rs t assumption . Th e secon d assumptio n ma y be examine d by considerin g th e parents ’ belief s abou t thei r twins ’ zygosity . As man y as 30 % of parent s ca n be mistake n in thei r belief s abou t thei r twins ’ zygosity , an d informatio n give n at birt h ca n be wron g in man y case s (Goldsmith , 1991) . Dat a fro m parent s wh o believ e tha t the y hav e fraterna l twin s wh o reall y hav e identica l twin s (o r vic e versa ) ca n be compare d to dat a fro m parent s wh o correctl y believ e thei r twin s ar e identical . Ther e ar e severa l limitation s of th e twi n desig n as well . First , it doe s no t allo w fo r an estimatio n of assortativ e mating . Assortativ e matin g is th e tendenc y to mat e wit h thos e simila r (positiv e assortativ e mating ) or dissimila r (negativ e assortativ e mating ) on som e characteristic . In th e presenc e of assortativ e mating , th e geneti c similarit y of sibling s an d parent-offspri ng is greate r tha n th e 50 % expecte d by chanc e du e to th e transmissio n of th e sam e gene s fro m bot h mothe r an d father . Assortativ e matin g increase s th e similarit y of DZ twin s compare d to MZ twin s (wh o ar e alread y at th e maximu m geneti c similarity) , thu s de atin g estimate s of heritability . In th e twi n design , assortativ e matin g effect s ar e confounde d 298 LEM E R Y AN D GOLDSM IT H wit h share d environmen t effects . Second , nonadditiv e geneti c varianc e an d gene-enviro nmen t correlatio n canno t be convincingl y isolated . Again , mor e informatio n is neede d (i.e . othe r kinshi p data ) to explor e thes e ideas . Th e secon d desig n is th e adoptio n study . Ther e ar e thre e mai n correlation s to conside r in an adoptio n design . Th e Ž rs t is th e correlatio n betwee n th e birt h paren t an d th e adoptee , wh o shar e 1 2 thei r gene s an d non e of thei r environmen t. (O f course , nongeneti c effect s ca n als o be transmitte d fro m biologica l mother s vi a prenata l effects. ) Th e secon d is th e correlatio n betwee n tw o biologicall y unrelate d relatives , suc h as childre n adopte d int o th e sam e family , whic h represent s effect s du e to th e commo n environmen t. Third , is th e correlatio n betwee n geneticall y relate d individual s wh o ar e reare d together , suc h as biologica l siblings , wh o shar e 1 2 thei r gene s an d al l of thei r commo n environmen t. Th e adoptio n desig n is strengthene d by havin g a contro l grou p of nonadoptiv e familie s studie d in th e sam e way . Heritabilit y is estimate d as twic e th e differenc e betwee n th e nonadoptiv e ( 1 2 h 2 + c 2 ) an d adoptiv e (c 2 ) correlations . Th e share d environmen t is usuall y estimate d directl y fro m adoptiv e siblin g correla - tions . Th e nonshare d environmen t is indirectl y estimate d by subtraction . Ther e ar e thre e mai n assumption s of th e adoptio n design . Th e Ž rs t is th e absenc e of selectiv e placement . Selectiv e placemen t is th e tendenc y of adoptio n agencie s to matc h childre n an d familie s on som e trait , usuall y physica l characteristics . If selectiv e placemen t is present , the n geneti c an d share d environmen t estimate s ma y be in ated . However , if bot h biologica l (typicall y onl y mothers ) an d adoptiv e parent s ar e measured , selectiv e placemen t ca n be controlle d fo r in mode l Ž tting . Th e secon d mai n assumptio n is tha t adoptiv e famil y environmen ts ar e represent ativ e of genera l famil y environmen ts , an d th e thir d assumptio n is th e absenc e of assortativ e mating . Bot h of thes e assumption s als o onl y appl y if the y affec t th e behaviou r unde r study , an d ca n be controlle d fo r in mode l Ž tting . Th e adoptio n study , unlik e th e twi n study , allow s fo r estimate s of assortativ e mating . However , development al maturit y an d generationa l difference s ar e confounde d in th e adoptio n desig n whe n comparin g individual s of differen t ages . Th e las t desig n is th e famil y study . Th e famil y desig n is ver y usefu l in testin g th e generalisati on of twi n an d adoptio n designs . On e ca n asses s sibling s (wh o shar e 1 2 thei r genes) , parent-offspri ng (wh o shar e 1 2 their genes) , half-sib s (wh o shar e 1 4 thei r genes) , uncle-nephew , aunt-niece , grandparen t-grandchil d (wh o shar e 1 4 thei r genes) , an d Ž rst-cousi n (wh o share 1 8 thei r genes ) pairs . If th e trai t unde r stud y is geneticall y in uenced , the n ther e shoul d be a linea r decreas e in similarit y acros s thes e groups . Today , ther e ar e ne w opportunitie s fo r studyin g reconstitute d familie s tha t migh t includ e full- , half- , an d step-siblings . Th e Nonshare d Environmen t an d Adolescen t Developmen t (NEAD ) project , fo r example , include d MZ GE NETI C ALL Y IN F OR M ATIV E DESIGN S 299 an d DZ twins , full-sibs , full-sib s in step-families , half-sib s in step-families , an d geneticall y unrelate d sib s in step-familie s (Pike , McGuire , Hether - ington , Reiss , & Plomin , 1996) . Th e larges t drawbac k wit h th e famil y desig n is tha t it confound s share d environmen t an d geneti c similarity . Ideally , al l of thes e method s shoul d be used . Thre e practica l way s to approac h thi s idea l ar e to includ e biologica l non-twi n sibling s in twi n designs , parent s in twi n designs , an d biologica l sibling s in adoptiv e designs . Ne w Methodologi ca l an d C onceptua l P er s pective s on Geneticall y Informe d D esign s Geneti c Analysi s of Fa m il y D ata . A quic k estimat e of heritabilit y ca n be obtaine d usin g Falconer ’ s (1989 ) formul a (2 time s th e differenc e betwee n MZ an d DZ twi n correlations) . Thi s formula , writte n in term s of varianc e components , is : 2{[(100 % geneti c variance ) + (100 % share d environmen ta l variance) ] ± [(50 % geneti c variance ) + (100 % share d environmen ta l variance)] } = 2{50 % geneti c variance } = heritability. Heritability , share d environmen tal , an d nonshare d environmen ta l esti - mate s ar e obtaine d wit h thi s method . However , mode l Ž ttin g give s a mor e accurat e estimat e becaus e it take s int o accoun t informatio n abou t phenotypi c variance s an d sampl e size s in additio n to th e covarianc e informatio n use d in th e Falcone r formula . Simultaneou s equation s mode l Ž ttin g solve s som e of th e problem s wit h constrainin g parameters , obtainin g statistica l tests , an d unequa l sampl e size s tha t th e intraclas s correlationa l approac h doe s no t address . Mode l parameter s explai n th e basi s of behavioura l covariation . Model s mak e assumption s explici t an d ca n incorporat e severa l differen t familia l relationship s simultaneous ly (e.g . family , twin , an d adoption) . In mode l Ž tting , th e expecte d covariance s base d on a theoretica l mode l ar e compare d wit h th e observe d covariances . Matrice s ar e forme d tha t carr y th e informatio n abou t covariance s of measure s an d occasions , an d covariance s of twins . Geneti c an d share d environment al effect s contribut e to betwee n pai r correlations , an d nonshare d environmen t an d erro r contribut e to residua l variance , as wel l as geneti c difference s betwee n individual s wh o do no t shar e al l of thei r genes . Multipl e regressio n geneti c analysi s (‘ ‘ DF regression ’ ’ ; DeFrie s & Fulker , 1985 , 1988 ) an d structura l equatio n modellin g (Neal e & Cardon , 1992 ) ar e use d to for m a serie s of equation s tha t tes t geneti c an d environmen ta l contribution s to behaviour . Thes e approache s permi t simultaneou s testin g an d estimatio n of bot h geneti c an d share d environ - menta l in uences . Structura l equatio n model- Ž ttin g programs , suc h as LISRE L (Joresko g & Sorbom , 1989 ) or Mx (Neale , 1994) , ar e use d to obtai n paramete r estimates , whic h ar e the n teste d fo r Ž t. 300 LEM E R Y AN D GOLDSM IT H Test s of Fit . If th e mode l hold s an d is identi Ž ed , the n th e Ž t is represente d in larg e sample s as chi-squar e wit h degree s of freedo m equa l to th e numbe r of independen t value s in th e covarianc e matri x minu s th e numbe r of unknown s bein g estimated . Th e chi-squar e tes t is use d to conclud e tha t a mode l doe s no t Ž t th e data , so a smal l chi-squar e correspond s to goo d Ž t an d a larg e chi-squar e correspond s to ba d Ž t. Th e chi-squar e goodnes s of Ž t tes t is in uence d by sampl e size . Wit h too-smal l samples , a poo r Ž t ma y no t be rejected , an d wit h too-larg e samples , a goo d Ž t ma y stil l resul t in a signi Ž can t chi-square . Th e change s in goodnes s of Ž t ca n be assesse d by th e chang e in th e chi-squar e valu e fro m on e neste d mode l to th e next . (Eac h successiv e mode l constitute s a mor e restricte d for m of th e prio r model. ) A nonsigni Ž can t differenc e in th e chi-squar e value s betwee n tw o model s implie s tha t th e additiona l speci Ž catio n di d no t signi Ž cantl y reduc e th e Ž t; thus , th e new , mor e restricte d mode l is tentativel y accepte d as th e mor e parsimoniou s model . Ther e is a larg e literatur e on alternativ e test s of goodnes s of Ž t tha t ar e typicall y use d in additio n to chi-squar e (se e Tanaka , 1993 , fo r a compariso n of man y of thes e indices) . Th e DF Regressio n Approac h to G eneti c M ode l Fitting . With DF regression , on e twin ’ s measur e is predicte d fro m th e othe r twin ’ s measur e an d th e degre e of geneti c relationshi p (DeFrie s & Fulker , 1985 , 1988) . To th e exten t tha t th e behaviou r is heritable , th e co-twi n regressio n to th e populatio n mea n wil l be les s fo r individual s wit h a close r geneti c relationshi p (e.g . MZ vs . DZ twins) . Th e regressio n equatio n simulta - neousl y estimate s bot h geneti c an d share d environmen ta l effects . Th e equatio n fo r th e augmente d mode l (fo r us e wit h ful l rang e variatio n rathe r tha n extrem e groups ) follows : T 2 = B 3 T 1 + B 4 R + B 5 T 1 R + A, where T 2 is th e co-twin ’ s predicte d score , T 1 is th e othe r twin ’ s score , R is th e coef Ž cien t of relationshi p (e.g . 1 fo r MZ twins ; .5 fo r DZ twin s fo r additiv e geneti c effects) , an d A is th e regressio n constant . Th e B’ s ar e least-square s regressio n coef Ž cients , wit h B 3 providin g an estimat e of th e share d environmen ta l in uenc e an d B 5 providin g an estimat e of heritability . (B 4 allow s th e simultaneou s analysi s of dat a fro m tw o or mor e groups , suc h as MZ an d DZ twins , an d is use d to tes t th e differenc e betwee n grou p heritabilit y an d ful l rang e heritabilit y whe n analysin g dat a fro m extrem e groups , se e later. ) Alternativ e model s ca n be tested . Fo r example , if th e estimat e of th e share d environmen t is nonsigni Ž cant , the n on e ca n dro p tha t ter m an d tes t th e reduced , neste d model . To conside r nonadditiv e effect s as wel l as additiv e geneti c effects , on e ca n ad d an additiona l coef Ž cien t of relationshi p (R 2 ) in an interactio n ter m wit h T 1 , coded 1 for MZ twins , .2 5 fo r DZ twin s an d full-sibs . Th e mode l ca n als o be extende d by includin g measure s of age , sex , ethni c group , socioeconomi c status , etc . GE NETI C ALL Y IN F OR M ATIV E DESIGN S 301 Fo r example , to conside r se x effects , on e ca n ad d a ter m fo r se x (code d 1, ± 1) and sex genotyp e (se x * T 2 R) to th e equation . DF regressio n is a exibl e approac h tha t is usefu l fo r considerin g speci Ž c measure s of gene s an d environmen t in th e equatio n an d fo r considerin g whethe r or no t heritabilit y differ s fo r extrem e scorer s compare d to th e norma l range , se e later . Univariat e Structura l E quatio n Models . Univariat e model s estimat e th e heritability , commo n environmen t, an d uniqu e environmen t fo r a particula r trai t fro m pattern s of observe d covariances , obtaine d fro m individual s of variou s degree s of geneti c relationshi p (e.g . adoption , twin , an d parent-offspri ng studies) . Figur e 1 depict s a pat h diagra m of a univariat e geneti c model . Fo r a twi n study , covariance s amon g th e phenotypi c measure s woul d be compute d separatel y fo r MZ an d DZ pairs . Thi s mode l evaluate s th e effect s of additiv e geneti c in uence s (A) , commo n environmen ta l in uence s (C) , an d nonshare d environmen ta l in uence s (E) . Thi s is calle d th e univariat e AC E model . Usin g pat h analysis , laten t geneti c an d environment al in uence s on th e phenotyp e ar e represente d by unidirectiona l arrows . Correlation s ar e double-heade d arrows . C is completel y share d betwee n individual s in thi s model , an d E is completel y independen t an d noncorrelate d betwee n individuals . Becaus e F IG. 1. Univariat e pat h diagra m tha t depict s th e correlatio n betwee n twin s or siblings . Additiv e geneti c (A) , share d environmenta l (C) , an d nonshare d environmenta l (E ) in uence s on th e phenotyp e ar e illustrated . R G is th e additiv e geneti c correlatio n betwee n th e twin s or sibling s fo r th e sam e trait . Lowe r cas e h, c, an d e ar e pat h coef Ž cient s fo r additiv e genetic , share d environmental , an d nonshare d environmenta l in uences , respectively . 302 LEM E R Y AN D GOLDSM IT H thes e individual s shar e som e genes , th e laten t A in uence s ar e correlated . Fo r MZ twins , th e geneti c correlatio n equal s 1 becaus e the y shar e 100 % of thei r genes , an d fo r DZ twin s an d ful l siblings , th e geneti c correlatio n equal s .5 becaus e the y shar e on averag e 50 % of thei r genes . Thus , in Fig . 1, th e phenotyp e is du e to additiv e geneti c effects , share d environmen ta l effects , an d nonshare d environment al effects . Th e percen t varianc e explaine d by eac h pat h is it s standardise d pat h coef Ž cien t squared . To comput e th e expecte d phenotypi c correlatio n betwee n sibling s usin g pat h analysis , on e sum s th e product s of th e path s tha t connec t thei r phenotype s (Wright , 1934) . Fo r MZ twins , th e expecte d phenotypi c correlatio n equal s h 2 + c 2 . Wit h DZ twin s or siblings , it is .5 h 2 + c 2 . If geneti c source s ar e importan t fo r th e phenotypi c covarianc e betwee n tw o traits , the n cross-siblin g correlation s shoul d yiel d th e followin g pattern : MZ twins . DZ twin s an d ful l sibling s . hal f sibling s . unrelated siblings , as illustrate d in dat a by Pik e et al . (1996) , fo r example . Simila r correlation s acros s al l siblin g type s indicat e an effec t of th e share d environmen t. If share d environmen t an d geneti c source s of varianc e canno t explai n th e phenotypi c correlations , thi s indicate s an effec t of th e nonshare d environment . A Multivariat e Extensio n of th e Univariat e Model . Th e purpos e of a multivariat e desig n is to uncove r th e aetiolog y of th e phenotypi c covariance s amon g th e variables . Th e mode l illustrate s th e exten t to whic h geneti c (o r environmen tal ) effect s mediat e th e phenotypi c correla - tio n amon g th e trait s (o r amon g differen t rater s of th e sam e trait) . Th e sam e gene s ma y in uenc e bot h phenotypes , a conditio n calle d ‘ ‘ pleio - tropy ’ ’ . Th e phenotypi c correlatio n coul d als o be du e to assortativ e matin g or commo n environment . Analogou s to th e intraclas s correlatio n use d in th e univariat e case , a cros s siblin g correlatio n is th e correlatio n betwee n on e sibling ’ s scor e at tim e 1 an d th e othe r sibling ’ s scor e at tim e 2 wit h a longitudina l design , or th e correlatio n betwee n on e sibling ’ s teacher-rate d scor e an d th e othe r sibling ’ s tester-rate d score , if considerin g differen t measure s of th e sam e trai t on on e occasion . If th e correlatio n amon g tim e point s or rater s is geneticall y in uenced , the n MZ cros s siblin g correlation s wil l be highe r tha n DZ cros s siblin g correlations . Cros s correlation s ca n als o be use d in parent-offspri ng designs . Th e geneti c correlatio n betwee n trait s indicate s ho w muc h tw o or mor e trait s ar e in uence d by th e sam e genes , an d th e environment al correlatio n betwee n trait s is ho w muc h tw o trait s ar e in uence d by th e sam e environment . Multivariat e mode l Ž ttin g typicall y begin s wit h th e Cholesk y decom - positio n (Gorsuch , 1983) , whic h sometime s is use d as a nul l mode l fo r mode l comparisons . Th e Cholesk y is simpl y a mathematical ly tractabl e startin g point , no t necessaril y a mode l of grea t substantiv e interest . In th e GE NETI C ALL Y IN F OR M ATIV E DESIGN S 303 Cholesky , al l variable s loa d on th e Ž rs t laten t facto r (muc h lik e a principa l component s analysis) , al l variable s excep t th e Ž rs t on e loa d on th e secon d factor , etc . Figur e 2 portray s th e Cholesk y decompositio n in th e bivariat e case , illustratin g bot h sibling s an d th e correlation s betwee n siblin g geneti c an d commo n environmen ta l laten t factors . Th e laten t variable s in th e to p portio n of th e Ž gur e represen t th e AC E in uence s commo n to bot h phenotypes . Th e laten t variable s belo w re ec t in uence s uniqu e to phenotyp e 2. Th e path s fro m th e commo n laten t factor s to phenotyp e 1 indicat e geneti c an d environment al in uence s on phenotyp e 1. Th e commo n A, C, an d E path s to phenotyp e 2 includ e varianc e speci Ž c to th e Ž rs t phenotyp e as well . Thes e path s indicat e th e exten t to whic h geneti c an d environment al in uence s on phenotyp e 1 als o in uenc e phenotyp e 2. Th e path s fro m AC E uniqu e factor s (below ) to phenotyp e 2 F IG. 2. Ful l bivariat e geneti c mode l illustratin g bot h siblings . Th e laten t variable s abov e represen t in uence s commo n to bot h phenotypes . Th e laten t variable s belo w represen t in uence s uniqu e to phenotyp e 2. 304 LEM E R Y AN D GOLDSM IT H represen t geneti c an d environmen ta l in uence s independen t of th e commo n geneti c an d environmen ta l in uences . To estimat e th e proportio n of varianc e accounte d fo r by phenotyp e 2, on e sum s th e square d pat h coef Ž cien t fro m th e pat h leadin g fro m th e commo n facto r to th e phenotyp e 2 an d th e square d pat h coef Ž cien t leadin g fro m th e uniqu e facto r to phenotyp e 2. Th e produc t of th e geneti c pat h fro m commo n A to phenotyp e 1 an d commo n A to phenotyp e 2 estimate s th e geneti c contributio n to th e covarianc e of phenotyp e 1 an d phenotyp e 2. Th e orde r of inpu t variable s int o thi s mode l in uence s th e speci Ž c pat h coef Ž cients , bu t th e varianc e accounte d fo r an d Ž t statistic s wil l no t differ . Severa l othe r multivariat e model s ar e commonl y use d in geneticall y informe d design s an d ar e introduce d next . Figur e 3A illustrate s Marti n an d Eaves ’ (1977 ) biometri c common - factor s model , whic h is a standar d mode l in th e Ž eld . In thi s model , AC E is speci Ž ed as bot h commo n an d uniqu e to th e thre e phenotypi c measures , an d eac h ha s a direc t effec t on th e phenotype . On th e othe r hand , Fig . 3B depict s McArdl e an d Goldsmith ’ s (1990 ) psychometri c common-facto r model . Thi s mode l assume s relate d phenotype s ar e in uence d by a singl e commo n factor , F, tha t in uence s al l phenotypes , an d uniqu e factor s (ACE ) speci Ž c to eac h phenotype . First , th e phenotypi c facto r structur e of th e observe d variable s is considered . Then , th e correlate d geneti c an d correlate d environment al effect s ar e speci Ž ed throug h th e singl e genera l phenotypi c factor , F. Last , commo n an d uniqu e facto r score s ar e teste d fo r geneti c an d environmen ta l source s of in uence . Comparin g Fig . 3A wit h Fig . 3B , we se e tha t Fig . 3B is mor e restrictiv e tha n Fig . 3A becaus e th e thre e matrice s of covariance s ar e constraine d to be proportiona l to on e anothe r (whe n formin g F) wherea s in Fig . 3A the y ar e allowe d to vary . Figur e 3B is a mor e restricte d for m of Fig . 3A , an d thu s th e tw o neste d model s ar e testabl e alternatives . Mor e comple x model s includ e model s tha t estimat e GE correlation , interactio n an d nonadditiv e source s of varianc e (Neal e & Cardon , 1994) . Longitudina l M odels . Thes e allo w fo r th e examinatio n of th e consistenc y of geneti c and / or environmen ta l in uence s acros s age . Ther e ar e tw o fundamenta l approache s to analysin g longitudina l data : th e autoregress iv e an d differenc e scor e models . In th e behaviour al geneti c literature , th e autoregress iv e approac h dominates . Fro m th e autoregress iv e perspective , investigator s typicall y begi n wit h th e Cholesk y (describe d earlie r an d illustrate d in Fig . 2) , an d dro p unnecessar y path s (wit h zer o or nonsigni Ž can t pat h coef Ž cients ) unti l the y obtai n th e simplest , mos t parsimoniou s model . Anothe r approac h is to begi n wit h severa l a-prior i models , som e of whic h ar e describe d later , an d tes t thei r Ž t to th e data . FIG.3. Biometriccommon-factorsmodel(PartA)andpsychometriccommon-factormodel(PartB)illustratingoneindividualforsimplicity.A c ,C c ,andE c arecommontoallthreephenotypicmeasures,whereastheA u ,C u ,andE u latentfactorsbelowareuniquetoeachphenotype.Fisasinglecommonfactorthatinuencesallthreephenotypes. 305 306 LEM E R Y AN D GOLDSM IT H Th e autoregress iv e simple x mode l speci Ž es tha t al l stabilit y is mediate d throug h intermediat e form s of th e trait , tha t is , ther e is no effec t of relativ e standin g at tim e 1 on tim e 3 othe r tha n tha t mediate d throug h tim e 2 (Guttman , 1954 ; Jo ¨ reskog , 1970) . Thus , thi s model , depicte d in Fig . 4, woul d Ž t dat a tha t is represente d by geneti c an d environment al correlatio n matrice s wit h th e highes t value s clos e to th e principa l diagonal , an d progressive ly lowe r value s farthe r fro m th e diagonal . Th e common-facto r model , whic h Ž ts if th e correlatio n matri x indicate s a time-independ en t relationship , is anothe r a-prior i longitudina l mode l fro m th e autoregress iv e perspective . Th e common-facto r mode l implie s a singl e underlyin g sourc e of variatio n tha t explain s th e patter n of acros s tim e continuit y (James , Mulaik , & Brett , 1982) . Thi s mode l represent s bot h pleiotropi c an d longitudina l effects . Th e commo n facto r ha s equa l effect s at al l ages . Th e persistenc e of th e geneti c deviatio n acros s tim e is F IG. 4. Autoregressiv e simple x mode l illustratin g additiv e geneti c (A ) an d nonshare d environmenta l (E ) in uence s on a singl e phenotyp e acros s time . Partia l regressio n coef Ž cient s b e and b g re ec t environmenta l an d geneti c stability , respectively ; l e and l g represen t uniqu e environmenta l an d geneti c effect s at a give n age . GE NETI C ALL Y IN F OR M ATIV E DESIGN S 307 represente d by th e path s fro m th e commo n geneti c facto r to th e measureme nt occasions . Thus , ther e ar e tw o source s of geneti c variance : tha t commo n acros s ages , an d tha t uniqu e to eac h age . Common-facto r model s ar e Ž t fo r eac h of th e effect s on th e phenotype : genetic , share d environmen t, an d nonshare d environmen t. Whe n thes e thre e source s of varianc e ar e considere d at once , th e covarianc e betwee n th e geneti c an d share d environment al factor s ar e als o considered . Wit h dat a on 24 7 adoptiv e familie s an d 24 6 nonadoptiv e familie s fro m th e Colorad o Adoptio n Projec t (CAP) , Phillip s an d Fulke r (1989 ) employe d th e longitudina l common-facto r mode l to represen t cognitiv e abilit y in th e CA P childre n fro m 1 to 7 year s of ag e an d thei r parents . Th e onl y signi Ž can t sourc e of longitudina l stabilit y fo r IQ in thi s dat a wa s genetic . Estimate s of newl y introduce d geneti c varianc e tapere d of f by ag e 3, an d th e increas e in parent-chil d correlation s ove r tim e wa s foun d to be du e to an increas e in th e geneti c correlation s betwee n chil d an d adul t measure s of IQ . Ther e wa s an absenc e of selectiv e placemen t an d cultura l transmissio n effect s fro m paren t IQ to chil d IQ . Fro m th e differenc e scor e perspective , individua l chang e ca n be depicte d wit h laten t growt h curv e analysis , whic h combine s an ANOV A approac h wit h a longitudina l facto r analysi s approac h (McArdl e & Epstein , 1987) . Laten t growt h curv e model s us e correlations , variances , an d mean s to structur e th e developmen t acros s time . Repeate d measure s on th e sam e subjects , wit h th e sam e variables , an d in th e sam e unit s of measureme nt ar e needed . Laten t growt h factor s summaris e th e long - itudina l means , correlations , an d variances , an d hypothese s abou t thes e laten t variable s (e.g . DZ twin s shar e 1 2 of thei r geneti c material ) ar e speci Ž ed . Parameter s ar e the n estimated , th e Ž t of th e mode l is tested , an d th e Ž t of alternativ e model s is compared . Parameter s ar e estimate d fo r bot h th e grou p an d th e individual . Facto r scores , th e l path s depicte d in Fig . 5, ca n be use d to describ e th e similarit y betwee n an individua l curv e an d th e grou p curve . Wherea s traditiona l structura l equatio n modellin g de Ž ne s change s as independen t of prio r changes , growt h curv e model s de Ž ne chang e as dependen t on prio r change . Conside r Fig . 5, a phenotypi c pat h mode l of a laten t growt h curv e model , wit h thre e measuremen t occasions . Thi s mode l ha s on e laten t commo n variable , F, wit h path s to al l observe d variables . Th e triangl e is a uni t constan t whos e pat h permit s F to hav e a mea n of M C (nonzero). Conside r thi s pat h mode l togethe r wit h Fig . 3B , th e psychometri c commo n facto r mode l to se e ho w thi s mode l coul d be adapte d fo r a geneticall y informe d design . Thi s mode l test s whethe r or no t th e mean s an d covariance s ca n be structure d wit h a commo n laten t factor . Th e facto r loadings , th e l’ s in Fig . 5, on thi s commo n facto r represen t an individual ’ s curv e scores . (Th e resultin g parameter s ar e average s of individua l curves. ) 308 LEM E R Y AN D GOLDSM IT H An individual ’ s laten t score , F, portray s an individual ’ s similarit y to th e grou p curve , wit h a hig h scor e portrayin g hig h similarity , an d a lo w scor e portrayin g larg e differences . Figur e 5 ca n be expande d wit h multipl e laten t variables , an d intercep t term s ca n be adde d as a varianc e component . Goldsmith , McArdle , an d Thompso n (1989 ) compare d an d contraste d th e autoregres siv e approac h wit h th e differenc e scor e approac h usin g longitudina l twi n temperamen t dat a at 4 an d 7 year s of age . Fro m psychologist s’ ratings , the y identi Ž ed tw o factors , Reactivit y an d Persis - tence . Fro m th e autoregres siv e perspective , geneti c difference s in uence d variabilit y at ag e 4 an d accounte d fo r essentiall y al l of th e stability . Geneti c difference s affecte d residua l varianc e at 7 year s in Reactivit y bu t no t Persistence . Fro m th e differenc e scor e perspective , geneti c difference s wer e relativel y les s in uentia l on chang e fro m 4 to 7 years . Thus , conclusion s abou t th e geneti c architectur e of developmen t ma y diffe r by th e metho d used . Measurin g Speci Ž c Geneti c an d Environme nta l C ontribution s to Vari - abilit y ove r Time . Th e classi c BG desig n parse s th e varianc e int o tha t F IG. 5. Phenotypi c laten t growt h curv e mode l (adapte d fro m McArdl e & Epstein , 1987) . F is a commo n laten t variabl e tha t in uence s al l thre e measuremen t occasions . Mc is th e mea n of F. Th e l’ s ar e facto r loading s whic h represen t averag e curv e scores . Th e U’ s ar e laten t factor s uniqu e to eac h measuremen t occasion . GE NETI C ALL Y IN F OR M ATIV E DESIGN S 309 whic h is du e to genetic , an d tha t whic h is du e to share d an d nonshare d environmen ta l in uences . However , thi s desig n doe s no t identif y th e speci Ž c aspect s of th e environmen t (o r speci Ž c genes ) tha t produc e th e effect . Contemporar y geneticall y informe d design s includ e speci Ž c measure s of th e environmen t and / or gene s in an attemp t to identif y th e causa l aspects . Thes e measure s ca n be adde d to curren t mode l Ž tting . DF regressio n is an exampl e of a metho d in whic h speci Ž c measure s ca n be adde d to th e mode l quit e easily . Row e an d Waldma n (1993 ) extende d th e DF regressio n approac h (describe d previously ) to includ e speci Ž c measure s of th e environment . Speci Ž c environment al measure s ar e adde d to th e regressio n equatio n as interaction s betwee n th e siblings ’ phenotyp e an d th e measure , an d th e coef Ž cien t of relationshi p (e.g . 1 fo r MZ twins , .5 fo r DZ twins) , an d th e measure . On e limitatio n of thi s metho d of accountin g fo r environmen ta l contex t is th e lo w statistica l powe r associate d wit h interactio n term s in th e regressio n equation . Row e an d Waldma n (1993 ) demonstrat e tha t to achiev e hig h powe r to detec t thes e effect s wit h thi s method , on e mus t oversampl e th e extremes . Identifyin g Example s of Gene-Env ironmen t (G E ) Covarianc e an d Interaction. Behavioura l geneticist s ofte n theoris e abou t GE covariance s an d interactions , bu t empirically , thes e concept s ca n be dif Ž cul t to measur e an d ofte n ar e lef t unmeasured . GE covarianc e embrace s th e concep t of differentia l exposur e to environment s contributin g to th e developmen t of heritabl e traits . Ther e ar e thre e type s of GE covariance : passive , reactive , an d activ e (Plomin , DeFries , & Loehlin , 1977) . If a child ’ s genotyp e is correlate d wit h th e environmen t of his / he r parent s an d sibling s (wh o hav e simila r genotypes ) thi s is calle d passiv e gene-enviro nmen t covariance . A reactiv e GE covarianc e arise s fro m th e situatio n in whic h other s reac t to a particula r individua l on th e basi s of som e of th e individual ’ s inherite d characteristics . Fo r example , an inattentiv e chil d ma y be taugh t les s materia l in a les s effectiv e manne r in school . Thus , th e environmen t become s correlate d wit h genotypi c differences . Last , an activ e gene - environmen t covarianc e ca n aris e whe n an individua l seek s an environ - men t conduciv e to furthe r developin g som e of his / he r geneti c tendencies . Thus , aggressiv e youth s ma y activel y choos e to associat e wit h peer s wh o ar e als o easil y frustrate d an d pron e to attribut e hostil e inten t to benig n action s of others . Thes e friendship s woul d contribut e to furthe r develop - men t of th e aggressiv e phenotype . Clearly , man y development al pathway s migh t entai l th e presenc e of al l thre e type s of covariance . GE covariance s ma y be positiv e or negative . Caregiver s ma y provid e emotionall y labil e childre n wit h unsettle d an d unpredictabl e environment s (positiv e covariance) , or the y ma y provid e especiall y stabl e an d 310 LEM E R Y AN D GOLDSM IT H predictabl e environmen ts (negativ e covariance) . If thes e in uence s ar e no t take n int o accoun t in th e dat a analyti c model , positiv e GE covarianc e wil l increas e estimate s of geneti c an d share d environmen ta l in uences , an d negativ e GE covarianc e wil l decreas e thes e estimate s (Goldsmith , Gottesman , & Lemery , 1997) . Th e larges t portio n of th e covarianc e betwee n parenta l practice s an d chil d adjustmen t is accounte d fo r by GE correlation s (Pik e et al. , 1996 ; Reiss , 1995) . Geneticall y in uence d characteristic s of th e chil d (e.g . dif Ž cul t temperamen t) elici t speci Ž c response s fro m parents , an d thes e parenta l response s furthe r affec t th e developmen t of th e child . Patterson ’ s (1986 ) investigation s of coerciv e cycle s involvin g aggressiv e youth s an d thei r parent s provid e an exampl e of GE correlation . Initially , th e childre n ar e noncompliant , an d th e parent s ar e no t goo d disciplinarian s (i.e . th e parent s us e hars h discipline , lac k involvement , avoi d positiv e reinforce - ment , an d ar e remis s in monitoring) . Thes e initia l circumstance s se t up a situatio n in whic h th e chil d is reinforce d fo r coerciv e behaviour s suc h as whining , teasing , an d yelling . Th e proces s escalates , resultin g in increase d chil d aggression , whic h lead s to harshe r parenta l discipline . As explaine d by Goldsmit h et al . (1997) , som e behavioura l geneticist s questio n th e utilit y of th e concep t of GE correlation , claimin g tha t it canno t be distinguishe d fro m direc t geneti c effects . Th e argumen t is tha t direc t geneti c effect s als o requir e a relevan t environmen t in orde r to be expressed . However , wit h case s in whic h th e environmen t ma y be measured , th e concep t of GE covarianc e ca n be useful . GE interaction s refe r to th e sam e environmen t havin g differen t effects , dependin g on th e genotyp e of th e individual . GE interaction s ar e statistica l interactions . An exampl e woul d be a sociabl e chil d (sociabilit y bein g a geneticall y in uence d personalit y trait ) reactin g differentl y to a nove l environmen t tha n an inhibite d child . Thes e interaction s ar e dif Ž cul t to recognis e withou t identifyin g speci Ž c genotype s an d environmen ts fo r th e phenotype . On e dif Ž cult y is tha t scalin g irregularitie s ofte n mimi c interactions . Th e fe w attempt s to isolat e thes e interaction s in huma n data , usin g quantitativ e methods , hav e bee n largel y unsuccessfu l (Plomi n & Daniels , 1984) . Adoptio n studie s ar e th e mos t powerfu l quantitativ e metho d fo r detectin g GE interaction s if goo d measure s of th e birt h parent s ar e used . Fo r a heritabl e trait , th e parent ’ s (o r midparent ’ s) phenotyp e ma y be take n as an estimat e of th e child ’ s genotype , dependin g on th e heritabilit y an d th e associatio n betwee n th e childhoo d an d matur e form s of th e phenotyp e in question . Th e environmen ta l measur e ca n be , fo r example , a characteristi c of th e adoptiv e parents . A 2 2 ANOV A tabl e is se t up wit h on e variabl e bein g genotyp e an d th e othe r environmen t, wit h th e dependen t variabl e bein g som e characteristi c of th e chil d (Plomi n et al. , GE NETI C ALL Y IN F OR M ATIV E DESIGN S 311 1977) . Eac h mai n effec t indicate s an independen t effec t of genotyp e or environmen t, an d th e interactio n of th e tw o yield s th e GE interaction . Likewise , multipl e regressio n wit h famil y dat a ca n be use d to analys e continuou s data , an d logisti c regressio n ca n be use d whe n onl y th e outcom e is discontinuous . Th e varianc e explaine d previously , an d beyon d th e mai n effect s of genotyp e an d environmen t ar e measure s of GE interaction . Th e analysi s of GE interactio n in design s suc h as thos e describe d earlie r require s larg e sampl e sizes . GE interactio n effect s wil l be muc h easie r to detec t onc e gene s associate d wit h th e phenotyp e unde r stud y ar e identi Ž ed , usin g molecula r geneti c analysis . Onc e gene s associate d wit h a particula r phenotyp e ar e identi Ž ed , the n we ca n tes t whethe r thes e sam e gene s affec t th e phenotyp e in differen t environmen ts . Detectin g Heritabilit y D ifference s in E xtrem e Group s co m pare d wit h th e Norma l Range . On e metho d of testin g th e aetiolog y of extrem e score s on a continuou s variabl e is to us e DF regression , introduce d earlie r (DeFrie s & Fulker , 1985 , 1988) . Thi s metho d ha s bee n use d whe n on e membe r of eac h twi n pai r is selecte d du e to a devian t scor e (e.g . psychopathol ogy) . First , th e basi c mode l is Ž t to determin e th e exten t to whic h th e differenc e betwee n th e proban d mea n an d th e mea n of th e populatio n is heritable . Th e equatio n fo r th e basi c mode l follows : T 2 = B 1 T 1 + B 2 R + A, where T 2 is th e co-twin ’ s predicte d score , T 1 is th e proband ’ s score , R is th e coef Ž cien t of relationshi p (e.g . 1 fo r MZ twins ; .5 fo r DZ twin s fo r additiv e geneti c effects) , an d A is th e regressio n constant . Th e B’ s ar e least-square s regressio n coef Ž cients , wit h B 1 providin g an estimat e of resemblanc e independen t of zygosit y an d B 2 providin g an estimat e of grou p heritability , afte r dat a ar e transforme d to adjus t fo r covarianc e difference s betwee n th e mean s fo r MZ an d DZ probands . Second , th e augmente d mode l (describe d earlier ) is Ž t to obtai n an estimat e of ordinar y heritability . Ordinar y heritabilit y an d grou p heritabilit y ca n the n be compare d to tes t th e hypothesi s tha t th e aetiolog y of devian t or extrem e score s is differen t fro m tha t of norma l rang e variation . Wit h th e transforme d data , B 4 from th e augmente d mode l is a tes t of th e differenc e betwee n grou p heritabilit y an d ordinar y heritability . Regressio n is a goo d approac h fo r considerin g devian t group s becaus e it is les s affecte d by restrictio n of rang e tha n correlatio n (Cohe n & Cohen , 1983) . However , larg e sample s ar e neede d to hav e enoug h powe r to compar e grou p heritabilit y to norma l rang e heritability , an d difference s in heritabilit y ca n be du e to difference s in measureme nt erro r alon g th e continuu m of measuremen t. Deater-Decka rd , Reiss , Hetherington , an d Plomi n (1997 ) obtaine d mothe r an d fathe r rating s on a shortene d Chil d Behavio r Checklis t in a 312 LEM E R Y AN D GOLDSM IT H twi n an d step-famil y stud y includin g ove r 70 0 earl y adolescen t siblin g pairs . Fo r internalisin g an d externalisin g behavioura l symptoms , the y uncovere d moderat e geneti c (heritabilit y estimate s aroun d 50% ) an d modes t share d environmen ta l in uence s (estimate s aroun d 10% ) fo r th e ful l range . Grou p heritabilit y estimate s wer e lowe r tha n ordinar y heritabilit y fo r bot h externalisin g (estimate s aroun d 40% ) an d internalis - in g (estimate s aroun d 25%) , an d grou p share d environmen t estimate s wer e highe r fo r bot h internalisin g an d externalisin g (aroun d 20%) . Althoug h thes e difference s wer e no t statisticall y signi Ž cant , th e patter n of result s support s environmen t bein g mor e importan t in th e extremes . Parent-Of fsprin g (P- O ) M odels . Thes e ar e use d to stud y behaviour s tha t sho w heritabilit y durin g bot h childhoo d an d adulthood . It is dif Ž cul t to detec t geneti c effects , bu t interestin g to se e geneti c relationship s acros s man y years . In orde r to detec t a geneti c relationship , th e childhoo d an d adulthoo d behaviour s mus t bot h be heritable , an d th e childhoo d an d adulthoo d behaviour s mus t be geneticall y correlated . A geneti c correlatio n is th e exten t to whic h th e sam e gene s affec t bot h phenotypes . P- O model s typicall y includ e bot h geneti c an d cultura l transmission ; however , in biologica l families , chil d behaviou r an d paren t behaviou r coul d be geneticall y or sociall y linked . Cultura l transmissio n is th e in uenc e of paren t behaviou r on th e share d environmen t of thei r offspring . Rando m environmen ta l effect s ar e assume d no t to transmi t acros s generations . A, C, an d E in bot h th e paren t an d offsprin g generation s determin e th e phenotypes . It is importan t to us e additiona l information , suc h as establishe d heritabilitie s of eac h of th e trait s at eac h age , whe n usin g thes e model s (DeFries , Plomin , & LaBuda , 1987) . Also , th e magnitud e of th e P- O correlatio n predicte d fro m a geneti c hypothesi s is low . Heritabilitie s rangin g fro m .4 0 to .50 — wit h no share d environmen ta l component — predic t lo w parent-offspri ng correlation s rangin g fro m .2 0 to .2 5 (Gold - smith , Losoya , Bradshaw , & Campos , 1994) , an d th e predicte d P- O correlation s ar e eve n lowe r if ther e ar e differen t geneti c in uence s on th e earl y an d late r form s of th e trait . Speci Ž cally , ‘ ‘ th e regressio n of offsprin g on midparen t value s (b po ) is equa l to th e produc t of th e squar e root s of th e infant (h i ) an d adul t (h a ) heritabilitie s an d th e geneti c correlatio n (r g ) from infanc y to adulthood , or b po = h i h a r g ’ ’ (Goldsmit h et al. , 1994 , p. 258) . Wit h thi s formul a th e rang e of reasonabl e correlation s is typicall y in th e .20s , give n fe w heritabilitie s of behaviou r in childhoo d or adulthoo d ove r .50. P- O design s ar e mos t powerfu l whe n use d in th e contex t of an adoptio n or twi n design . P- O model s withi n adoptio n design s allo w separatio n of effect s of gene s an d th e share d environmen t by comparin g childre n to bot h GE NETI C ALL Y IN F OR M ATIV E DESIGN S 313 thei r biologica l an d adoptiv e parents . Th e parent-twi n desig n allow s fo r th e separatio n of geneti c an d environmen ta l in uence s as well , bot h betwee n co-twin s an d betwee n paren t an d offspring . Thus , th e share d environmen ta l effec t on th e behaviou r of th e twin s is mad e up of tw o components : environmen ta l in uence s share d wit h th e co-twin , an d cultura l transmissio n fro m th e parents . Thes e model s ca n als o allo w fo r differen t geneti c factor s operatin g in th e paren t generatio n an d chil d generation , an d the y ca n includ e path s accountin g fo r assortativ e mating , selectiv e placemen t in adoptio n designs , an d passiv e GE correlation . Koopman s an d Boomsm a (1996 ) use d a parent-twi n desig n to decompos e familia l resemblanc es in alcoho l use . Questionnair e dat a on health-relate d behaviou r wa s collecte d fro m adolescen t twin s an d thei r parents . Fo r 15 - to 16-year-old s (40 3 families) , share d environmen t accounte d fo r mos t of th e varianc e in alcoho l us e (M Z correlatio n = .80, DZ correlatio n = .8 9 fo r males , averag e P- O correlatio n = .25) . Onl y 10 % of thi s effec t ma y be du e to parenta l alcoho l us e throug h cultura l transmission . Th e resemblanc e betwee n parent s an d offsprin g coul d be geneti c or cultura l transmission ; th e model s Ž t equall y wel l fo r thi s ag e range . On th e othe r hand , fo r 17 - to 21-year-old s (80 5 families) , geneti c in uence s bes t explaine d th e varianc e in alcoho l us e (M Z correlatio n = .74 , DZ correlatio n = .6 0 fo r males , averag e P- O correlatio n = .31), both betwee n co-twin s an d betwee n parent s an d thei r children . Th e geneti c correlatio n betwee n parent s an d offsprin g wa s high , wit h estimate s rangin g fro m .6 4 to 1.00 , dependin g on th e model . Laten t Clas s Analysis . Base d on pattern s of response s to intervie w an d questionnair e items , laten t clas s analysi s identi Ž es underlyin g categorie s of peopl e (Lazarsfeld , 1950 , applie d to BG design s by Eave s et al. , 1993) . Laten t clas s analysi s is an excellen t metho d fo r considerin g whethe r a dimensiona l or categorica l approac h explain s th e dat a better . It is typicall y use d wit h categorica l dat a suc h as psychopathol og y diagnoses . Dimen - siona l variation s in personalit y coul d affec t liabilit y to psychopathol ogy , an d at th e sam e time , categorica l distinction s ca n be impose d by th e actio n of majo r gene s or majo r environmen ta l events . Ther e ar e tw o part s to executin g a geneti c laten t clas s analysis . First , laten t clas s analysi s is performe d at th e phenotypi c leve l to determin e ho w man y classe s ar e neede d to explai n th e phenotype s (Eave s et al. , 1993) . Thi s proces s is simila r to facto r analysis , onl y rathe r tha n searchin g fo r linea r associations , on e seek s underlyin g classe s of peopl e tha t woul d predic t al l of th e differen t pattern s of responses . Then , fo r eac h putativ e class , th e probabilitie s tha t an individua l in a give n clas s wil l respon d in a particula r wa y to a questio n ar e examined . Fo r psychopathol - ogy , conside r th e probabilit y tha t a perso n in a particula r clas s woul d sho w 314 LEM E R Y AN D GOLDSM IT H a symptom , an d if he / sh e does , the n comput e th e probabilit y tha t it wa s mil d versu s severe . Next , usin g maximu m likelihood , th e Ž t of differen t model s is compare d (e.g . 3 classe s vs . 4 classes) , an d th e mos t parsimoniou s mode l is retained . Thi s metho d ha s prove n usefu l fo r heterogeneo us disorder s lik e attentio n de Ž ci t hyperactivit y disorde r (ADHD ) (Eave s et al. , 1993) . Fo r ADH D data , ther e is evidenc e of dimensiona l orderin g of severit y at th e phenotypi c level , an d evidenc e fo r a majo r gen e effec t contributin g to risk . Second , on e ca n conside r whethe r or no t ther e is an associatio n betwee n twi n (o r sib ) pair s fo r membershi p in a laten t clas s (Eave s et al. , 1993) . If MZ twin s ar e mor e likel y to be in th e sam e laten t class , the n a geneti c effec t of clas s membershi p is indicated . Laten t classe s ca n be geneti c categorie s or environment al ris k factors . Variou s model s ar e explored , tha t is , no famil y resemblanc e (th e phenotypi c mode l above) , a geneti c effec t (M Z associatio n greate r tha n DZ) , an d a share d environmen ta l effec t (M Z associatio n equal s DZ) . In addition , mor e speci Ž c geneti c hypothesi s testing , suc h as singl e gen e model s wit h complet e or incomplet e penetranc e ca n be examine d wit h thi s method . Again , maximu m likelihoo d estimate s th e probabilitie s of eac h of th e models . Laten t clas s analysi s ca n be extende d to th e analysi s of ver y larg e pedigree s an d linkag e analysis . Molecula r G eneti c M ethods . On e of th e mos t excitin g frontier s in behavioura l genetic s is th e ne w molecula r method s available . Trait s tha t ar e show n to be th e mos t heritabl e throug h traditiona l famil y resemblanc e method s ca n no w be explore d furthe r an d actua l gene s ma y be identi Ž ed . Onc e a gen e is identi Ž ed , we ca n trac k th e correspondi ng protei n an d stud y ho w thi s protei n affect s behaviour , elucidatin g geneti c link s betwee n behaviours , geneti c interaction s an d correlations , an d tracin g th e aetiolog y of developmen ta l courses . Wit h th e continuin g succes s of th e Huma n Genom e Project , gene s fo r single-gen e disorder s ar e bein g foun d routinely . A gen e tha t in uence s a complex , quantitativ e trai t is calle d a quantitativ e trai t locu s (QTL ) (Gelderman , 1975) . Behavioura l phenotypes , suc h as aggression , ar e mos t likel y in uence d by multipl e genes . Curren t method s of considerin g th e geneti c aetiolog y of comple x trait s include : (1 ) examinin g phenotypi c result s of larg e crosse s of know n anima l strains ; (2 ) allele-sharin g (i.e . seekin g an associatio n betwee n particula r allele s an d a particula r phenotyp e in pair s of affecte d relative s in man y differen t families) ; (3 ) linkag e analysi s (i.e . mappin g gene s to chromosome s by examinin g whethe r or no t a DN A marke r an d a particula r allel e ar e inherite d together) ; an d (4 ) associatio n studie s (i.e . comparin g unrelate d affecte d an d unaffecte d individual s on presenc e or absenc e of a particula r allele) . Detaile d methodolog y is reviewe d by Lande r an d Schor k (1994 ) an d text s GE NETI C ALL Y IN F OR M ATIV E DESIGN S 315 suc h as Ot t (1991 ) an d McGuf Ž n, Owen , O’ Donovan , Thapar , an d Gottesma n (1994) . C onc lusion Contemporar y behavioura l geneti c design s ar e usefu l an d powerfu l fo r answerin g a variet y of researc h questions . Thi s pape r encourage s investigator s to mov e beyon d th e univariat e biometri c analysi s of th e proportio n of varianc e accounte d fo r by geneti c an d environment al effects . BG design s ar e a powerfu l wa y to stud y environment al in uence s on behaviour . Additionally , developmen ta l BG design s ar e usefu l whe n designin g interventions . The y ca n identif y speci Ž c aspect s of th e environmen t tha t hav e th e greates t in uenc e on behaviour , an d the y ca n pinpoin t critica l period s in whic h environment al in uence s ar e mos t malleable . By identifyin g speci Ž c geneti c an d environmen ta l in uence s on behaviour , an d modellin g th e structur e of thes e in uence s ove r time , we ca n rapidl y advanc e ou r understandi ng of huma n development . We no w hav e th e conceptua l an d methodologica l sophisticatio n necessary ; remain - in g barrier s primaril y involv e resource s neede d to obtai n larg e enoug h sample s an d theoreticall y interestin g measures . Manuscrip t receive d Jun e 199 8 Revise d manuscrip t receive d Septembe r 199 8 R E F E R E NC E S Cohen , J. , & Cohen , P. (1983) . Applie d multipl e regression /correlatio n analysi s fo r th e behaviora l science s (2n d ed.) . Hillsdale , NJ : Erlbaum . Crow , J.F . (1986) . Basi c concept s in population , quantitativ e, an d evolutionar y genetic s . New York : Freeman . Deater-Deckard , K. , Reiss , D. , Hetherington , E.M. , & Plomin , R. (1997) . Dimension s an d disorder s of adolescen t adjustment : A quantitativ e geneti c analysi s of unselecte d sample s an d selecte d extremes . Journa l of Chil d Psycholog y an d Psychiatr y , 38 , 515– 525. DeFries , J.C. , & Fulker , D.W . (1985) . Multipl e regressio n analysi s of twi n data . Behavior Genetics , 15 , 467– 473. DeFries , J.C. , & Fulker , D.W . (1988) . Multipl e regressio n analysi s of twi n data : Etiolog y of devian t score s versu s individua l differences . Act a Genetica e Medica e Gemellolog ia e , 37 , 205– 216. DeFries , J.C. , Plomin , R. , & LaBuda , M.C . (1987) . Geneti c stabilit y of cognitiv e develop - men t fro m childhoo d to adulthood . Development al Psycholog y , 23 , 4– 12. Dunn , J. , & Plomin , R. (1986) . Determinant s of materna l behavio r towar d three-year-ol d siblings. Britis h Journa l of Developmen ta l Psycholog y , 4 , 127– 137. Eaves , L. , Silberg , J. , Hewitt , J.K. , Meyer , J. , Rutter , M. , Simonoff , E. , Neale , M. , & Pickles , A. (1993) . Genes , personality , an d psychopathology : A laten t clas s analysi s of liabilit y to symptom s of attention-de Ž ci t hyperactivit y disorde r in twins . In R. Plomi n & G.E . McClear n (Eds) , Natur e an d nurtur e an d psycholog y . Washington , DC : America n Psychologica l Association . 316 LEM E R Y AN D GOLDSM IT H Falconer , D.S . (1989) . Introductio n to quantitativ e genetic s (3r d ed.) , Ne w York : Longman . Gelderman , H. (1975) . Investigation s on inheritanc e of quantitativ e character s in animal s by gen e markers : I. Methods . Theoretica l an d Applie d Genetic s , 46 , 319– 330. Goldsmith , H.H . (1989) . Behavior-geneti c approache s to temperament . In G.A . Kohn - stamm , J.E . Bates , & M.K . Rothbar t (Eds.) , Temperamen t in childhoo d (pp.111 – 132) . Ne w York : Wiley . Goldsmith , H.H . (1991) . A zygosit y questionnair e fo r youn g twins : A researc h note . Behavio r Genetic s , 21 , 257– 269. Goldsmith , H.H. , Gottesman , I.I. , & Lemery , K.S . (1997) . Epigeneti c approache s to developmenta l psychopathology . Developmen t an d Psychopathol og y , 9 , 365– 387. Goldsmith , H.H. , Losoya , S.H. , Bradshaw , D.L. , & Campos , J.J . (1994) . Genetic s of personality : A twi n stud y of th e Ž ve facto r mode l an d parent-offsprin g analyses . In C. Halverson , R. Martin , & G. Kohnstam m (Eds.) , Th e developin g structur e of temperamen t an d personalit y fro m infanc y to adulthoo d (pp.241 – 265) . Hillsdale , NJ : Erlbaum . Goldsmith , H.H. , McArdle , J.J. , & Thompson , B. (1989) . Longitudina l twi n analyse s of childhoo d temperament . Behavio r Genetic s , 19 , 759 – 760 . (abstract ) Gorsuch , R.L . (1983) . Facto r analysi s (2n d ed.) . Hillsdale , NJ : Erlbaum . Guttman , L. (1954) . A ne w approac h to facto r analysis : Th e radex . In P.F . Lazarsfel d (Ed.) , Mathematic al thinkin g in th e socia l science s (pp.258 – 349) . Glencoe , IL : Fre e Press . James , L.R. , Mulaik , S.A. , & Brett , J.M . (1982) . Causa l analysis : Assumptions , models , an d data . Beverle y Hills : Sage . Joreskog , K.G . (1970) . Estimatio n an d testin g of simple x models . Britis h Journa l of Mathematic al an d Statistica l Psycholog y , 23 , 121– 145. Joreskog , K.G. , & Sorbom , D. (1989) . LISRE L 7: A guid e to th e progra m an d application s (2n d ed.) . Chicago , IL : SPSS . Koopmans , J.R. , & Boomsma , D.I . (1996) . Familia l resemblance s in alcoho l use : Geneti c or cultura l transmission ? Journa l of Studie s on Alcoho l , 57 , 19– 28. Lander , E.S. , & Schork , N.J . (1994) . Geneti c dissectio n of comple x traits . Science , 265 , 2037– 2048. Lazarsfeld , P.F . (1950) . Th e logica l an d mathematica l foundation s of laten t structur e analysis . In S.A . Stouffe r et al . (Eds) , Measurem en t an d predictio n . Princeton , NJ : Princeto n Universit y Press . Martin , N.G. , & Eaves , L.J . (1977) . Th e genetica l analysi s of covarianc e structure . Heredity , 38 , 79– 95. McArdle , J.J. , & Epstein , D. (1987) . Laten t growt h curve s withi n developmenta l structura l equatio n models . Chil d Developmen t , 58 , 110– 133. McArdle , J.J. , & Goldsmith , H.H . (1990) . Alternativ e common-facto r model s fo r multi - variat e biometri c analysis . Behavio r Genetic s , 20 , 569– 608. McGuf Ž n, P. , Owen , M.J. , O’ Donovan , M.C. , Thapar , A. , & Gottesman , I.I . (1994). Seminar s in psychiatri c genetic s . London : Roya l Colleg e of Psychiatrists . Neale , M.C . (1994) . Mx : Statistica l Modelin g (2n d ed.) . Bo x 71 0 MCV , Richmond , VA 23298 : Departmen t of Psychiatry . Neale , M.C. , & Cardon , L.R . (1992) . Methodolog y fo r geneti c studie s of twin s an d familie s . Dordrecht : Kluwer . Ott , J. (1991) . Analysi s of huma n geneti c linkag e . Baltimore , MD : John s Hopkin s Universit y Press. Patterson , G.R . (1986) . Performanc e model s fo r antisocia l boys . America n Psychologis t , 41 , 432– 444. Phillips , K. , & Fulker , D.W . (1989) . Quantitativ e geneti c analysi s of longitudina l trend s in adoptio n design s wit h applicatio n to IQ in th e Colorad o Adoptio n Project . Behavior Genetics , 19 , 621– 658. GE NETI C ALL Y IN F OR M ATIV E DESIGN S 317 Pike , A. , McGuire , S. , Hetherington , E.M. , Reiss , D. , & Plomin , R. (1996) . Famil y environmen t an d adolescen t depressiv e symptom s an d antisocia l behavior : A multivariat e geneti c analysis . Development al Psycholog y , 32 , 590– 603. Plomin , R. , & Daniels , D. (1984) . Th e interactio n betwee n temperamen t an d environment : Methodologica l considerations . Merrill-Pa lme r Quarterl y , 30 , 149– 162. Plomin , R. , & Daniels , D. (1987) . Wh y ar e childre n in th e sam e famil y so differen t fro m eac h other? Behaviora l an d Brai n Science s , 10 , 1– 16. Plomin , R. , DeFries , J.C. , McClearn , G.E. , & Rutter , M. (1997) . Behaviora l Genetic s (3rd ed.) . Ne w York : Freeman . Plomin , R. , DeFries , J.C. , & Loehlin , J.L . (1977) . Genotype-environmen t interactio n an d correlatio n in th e analysi s of huma n variation . Psychologic al Bulleti n , 84 , 309– 322. Reiss , D. (1995) . Geneti c in uenc e on famil y systems : Implication s fo r development . Journa l of Marriag e an d th e Famil y , 57 , 1– 18. Rowe , D.C . (1994) . Th e limit s of famil y in uence : Genes , experience , an d behavio r . New York : Guilfor d Press . Rowe , D.C. , & Waldman , I.D . (1993) . Th e questio n ‘‘how ’’? reconsidered . In R. Plomi n & G.E . McClear n (Eds.) , Nature , nurture , an d psycholog y (pp.355 – 373) . Washington , DC : America n Psychologica l Association . Tanaka , J.S . (1993) . Multifacete d conception s of Ž t in structura l equatio n models . In K.A . Bolle n & J.S . Lon g (Eds.) , Testin g structura l equatio n model s (pp.10 – 39) . Newbur y Park , CA: Sage Wright , S. (1934) . Th e metho d of pat h coef Ž cients . Annal s of Mathemati ca l Statistic s , 5 , 161– 215.

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