Extended Twin-Kinship Designs Lindon Eaves, NIDA Workshop, VIPBG, Richmond, October 2010.

Some issues Human = DNA x Brains x Feet x World People live in families and society “Environment” matters as much as “Genes” Focus on ideas Illustrate with real world applications No “one-size-fits-all”: design and model depends on question and context

The Extended Phenotype Me World Parents Siblings Child Spouse Extended Phenotype

Nuclear Families

Non-Genetic Inheritance

Genetic Inheritance

Nuclear Families “Typical” Common (large samples) Test for spousal resemblance Biological and cultural transmission confounded Age/secular differences between generations

Classical Twin Design Easy to get large samples Matched for age Gives preliminary estimates of major components (“A,C,E”) Test for sibling interaction/imitation/contrast Test for interaction with covariates Easy Extension to multivariate/longitudinal case

Limitations of Twin Study Focus on phenotype of individual twin (ignores “extended phenotype”) Twins may be “special” Matched for age (no rest for Gx Age interaction, in cross-sectional data) No generally applicable test of “D” (non-additive genetic effects) in presence of ACE. Can’t fit A,C, E and “D” at same time. Estimates of ACE biased by “D”. “C” is a mixture of effects (“real” shared environment, “passive rGE”, effects of parental assortative mating)

Extensions of the Twin Study Twins and Siblings (“TAS”) Twins and Parents (“TAP”) Children of Twins (“COT”) Spouses of Twins (“SPOT”) All of the above (“E-Twin”) Longitudinal extensions (e.g. “L-TAP”)

Twins and Siblings MZ DZ

Twins and Siblings: Test Assumptions 1.Compare means of twins and sibs 2.Compare DZ and Sib correlations 3.Test for and analyze birth order effects 4.Test for interaction of sib-resemblance with age 5.Add parents?

MZ DZ “TAP”: Twins and Parents

Combining Twins and Nuclear Families Familial Transmission in the US and Australia Eaves, Hatemi, Heath and Martin (2010, in press) in Hatemi and McDermott “Man is a Political Animal”. Univ. Chicago Press

Twins, Parents of Twins, Nuclear Families Twins Parents of Twins Offspring of Twins Siblings of Twins Spouses of Twins © Lindon Eaves, 2009

Twins and Parents Resolve biological and cultural transmission if measure same phenotype in both generations Include some analysis of assortment Some test for non-additive effects (dominance, GxAge) Some test of child-parent interaction (evocative rGE) “Easy to do” especially with juveniles. Lots of ways of using. But need to be careful.

The Virginia 30,000 Men Women Total Twins Parents of Twins Spouses of Twins Children of Twins Siblings of Twins Other Total

The Australia 22,000 Men Women Total Twins Parents of Twins Spouses of Twins Children of Twins Siblings of Twins Total

Relationship Sample Sizes (N pairs) Virginia AustraliaTotal MinMaxMedianMinMaxMedian Spouses Mother- Daughter Mother-Son Father- Daughter Father-Son Par.-Offspring Male siblings Female siblings Male-Female siblings Siblings Male DZ twins Female DZ twins Male-Female DZ twins DZ Twins Male MZ twins Female MZ twins MZ Twins Sample Sizes (Number of Pairs of Relatives) for Participating Families. Note: variation occurs in the number of pairs for different variables because of patterns of missing variables. For the purposes of this analysis values are assumed to be missing at random.

Nuclear Family Correlations for Stature (Virginia 30,000 and OZ 22,000) © Lindon Eaves, 2009

Nuclear Family Correlations for Stature and Liberalism/Conservatism (Virginia 30,000) © Lindon Eaves, 2009

Nuclear Family Correlations for Liberalism/Conservatism (Virginia 30,000 and Australia 22,000) © Lindon Eaves, 2009

Nuclear Family Correlations for Stature and EPQ Neuroticism (Virginia 30,000) © Lindon Eaves, 2009

Nuclear Family Correlations for Socially Significant Variables (Virginia 30,000) © Lindon Eaves, 2009

Nuclear Family Correlations for Socially Significant Variables (Australia 22K) © Lindon Eaves, 2009

Twin Correlations for Stature (Virginia 30,000 and Australia 22,000) © Lindon Eaves, 2009

Twin Correlations for Stature and Liberalism (Virginia 30,000 and Australia 22,000) © Lindon Eaves, 2009

Twin Correlations for Socially Significant Variables (Virginia 30,000) © Lindon Eaves, 2009

Twin Correlations for Socially Significant Variables (Australia 22,000) © Lindon Eaves, 2009

RelationshipExpected Correlation Spouses  Mother-Daughter v f +  u f + ½ h f (H F +  H m ) Mother-Son v m +  u m + ½ h m (H F +  H m ) Father-Daughter u f +  v f + ½ h f (H m +  H f ) Father-Son u m +  v m + ½ h m (H m +  H f ) Male siblings  h m 2 + u m 2 + v m  u m v m + h m [v m (H f +  H m ) + u m (H m +  H f )] + c m 2 Female siblings  h f 2 + u f 2 + v f  u f v f + h f [v f (H f +  H m ) + u f (H m +  H f )] + c f 2 Male-Female siblings  h m h f + u m u f + v m v f +  u f v m + u m v f ) + ½h m [v f (H f +  H m ) + u f (H m +  H f )] + ½h f [v m (H f +  H m ) + u m (H m +  H f )] + c m c f Male DZ  h m 2 + u m 2 + v m  u m v m + h m [v m (H f +  H m ) + u m (H m +  H f )] + c m 2 + t m 2 Female DZ  h f 2 + u f 2 + v f  u f v f + h f [v f (H f +  H m ) + u f (H m +  H f )] + c f 2 + t f 2 Male-Female DZ  h m h f + u m u f + v m v f +  u f v m + u m v f ) + ½h m [v f (H f +  H m ) + u f (H m +  H f )] + ½h f [v m (H f +  H m ) + u m (H m +  H f )] + c m c f + t m t f Male MZ h m 2 + u m 2 + v m  u m v m + h m [v m (H f +  H m ) + u m (H m +  H f )] + c m 2 + t m 2 Female MZ h f 2 + u f 2 + v f  u f v f + h f [v f (H f +  H m ) + u f (H m +  H f )] + c f 2 + t f 2 Where:  = ½ (1+  H m H f ) Subject to: 1-h m 2 + u m 2 + v m  u m v m + h m [v m (H f +  H m ) + u m (H m +  H f )] + c m 2 + t m 2 +e m 2 = 0 1-h f 2 + u f 2 + v f  u f v f + h f [v f (H f +  H m ) + u f (H m +  H f )] + c f 2 + t f 2 +e f 2 = 0 H’ m - h m + ½H m (v m +  u m ) + ½H f (u m +  v m ) = 0 H’ f - h f + ½H m (v m +  u m ) + ½H f (u m +  v m ) = 0 Expected correlations between twins and nuclear families: Model for joint biological and cultural inheritance Note: The model tabulated does not incorporate genetic dominance, GxAge interaction or sex-specific genetic and environmental effects.

Males Females VAVA VDVD VEVE V EC V ET V CI VAVA VDVD VEVE V EC V ET V CI Stature US Au Conserve’m US Au Neuroticism US Au Church Attendance US Au Political Affiliation US Au Educational Attainment US Au Twins, Parents and Nuclear Families: Proportions (%) of variance in phenotype attributed to sources in best-fitting model. Sources of variance: V A =Additive genetic; V D = Dominance genetic ; V E = Residual, unique environmental, within sibships; V EC = Residual shared environmental among sibships; V ET = Additional shared environmental between twin pairs; V CI = Non-genetic (“cultural”) inheritance from parental phenotype.

Summary Results consistent across (western) samples – except for political affiliation Most parent-offspring transmission genetic after allowance for assortment – except for political affiliation Not much shared environment – except for education and political affiliation Consistently different patterns of transmission for different variables – assortment much more important for “social” variables

Spouses of Twins Unraveling the Process of Mate Selection

Classical Treatment (Fisher, 1918) Considered: 1. Assortment based on measured phenotype 2. Assortment for “essential genotype” 3. Assortment for correlated trait

Twins and Spouses Twins Parents of Twins Offspring of Twins Siblings of Twins Spouses of Twins © Lindon Eaves, 2009

Spousal Resemblance Based on Assortative Mating for Measured Phenotype

Spousal Resemblance Based on Assortative Mating for Phenotype Measured with Error

Assortment for a latent correlated variable (e.g. “social homogamy”)

Spousal Interaction See: Heath AC (1987) Acta Genetica Medica et Gemellelogiae

ModelRandom mating Phenotypic (P) P+Error Spousal Interaction Social Homogamy d.f Variable Sample S 2 StatureUS AU ConservatismUS AU NeuroticismUS See note AU See note Church attendance US AU Political affiliation US AU Educational attainment US AU Goodness-of-fit statistics (weighted residual sums of squares, S 2 ) for selected models for assortative mating in the US and Australia Notes: 1 Estimated regression of male outcome on latent trait on upper bound (1.000). 2 This model is poorly identified for Neuroticism because the correlation between mates is close to zero.

Twins and Parents

Combine benefits of twin study and nuclear families Twins help separate genes and environment Parents allow test for and some analysis of assortative mating Parent-offspring data test some models for intergenerational transmission Test for evocative rGE if assess parenting towards individual twins

Example Parental Anti-Social Personality and Juvenile Conduct Disorder: A Longitudinal Study of Twins and Parents Eaves et al. (2010) Behavior Genetics

Observe Parental neglect correlates with child conduct disorder (CD) Parental ASP correlates with juvenile CD ASP parents tend to neglect their children

Question Does parental neglect cause child CD OR is the association a secondary consequence of: a) the fact that parental neglect is a “symptom” of ASP b) the fact that parental ASP shares a common familial (genetic?) association with juvenile CD?

To Answer the Question we need to: Sort out the genetics of adult ASP Sort out the genetics of juvenile CD Sort out the genetic and environmental relationships between adult and juvenile ASP and CD within and between generations Deal with spousal resemblance Model sex differences in transmission and effects of genes and environment Resolve direct causal effect (DCE) of neglect from secondary genetic association with juvenile CD

Design Twins and Parents: Parents measured as Adults (ASP and Neglect of Children) Same twins measured as juveniles (CD) and young adults (ASP)

Outcome Statistic N r a.s.e. Adult male Adult female Juvenile male Juvenile female Polychoric correlations between childhood adversity and anti-social behavior of adult and juvenile offspring. Relationship Statistic N r a.s.e. Mother-Father ASP Father ASP-Adversity Mother ASP.-Adversity Polychoric correlations between parental (adult) anti-social behavior (ASP) and childhood adversity Relationship Statistic N r a.s.e. Mother-adult son Mother-adult daughter Mother-juvenile son Mother-juvenile daughter Father-adult son Father-adult daughter Father-juvenile son Father-juvenile daughter Polychoric correlations between anti-social behavior of (adult) parents and adult (ASP) and juvenile (CD) anti-social behavior of their offspring.

Relationship Statistic N r a.s.e. Twins (as adults) MZm MZf DZm DZf DZmf Twins (as juveniles) MZm MZf DZm DZf DZmf Twins (adult-juvenile) MZm MZf DZm DZf DZmf DZfm Within subject (adult-juvenile) Males Females Polychoric correlations for juvenile conduct disorder and adult anti-social personality in YAFU/VTSABD twins.

Conceptual model for the effects of genes and the family environment on anti-social behavior.

Estimated contributions of parents and residual effects to the shared environment of twin offspring.

Effects of the unique and shared environment on adult and juvenile anti-social behavior and females.

Component Second sibling GAF GJF GAM GJM rGE First Sibling GAF GJF GAM GAF Estimated passive genotype-environment correlations and sibling correlations between additive genetic components assuming equilibrium under assortative mating and non-genetic parent-child transmission. Note: Under random mating, the diagonal genetic correlations are expected to be 0.5 and the off- diagonals zero. In the absence of either genetic or non-genetic transmission the genotype-environment correlations (the last column in the table) are expected to be zero.

The Children of Twins (“COT”) Effects of Maternal and Fetal Genotype on Preterm Birth York et al. (2010) PLoS-One

Children of Twins Twins Parents of Twins Offspring of Twins Siblings of Twins Spouses of Twins © Lindon Eaves, 2009

Varieties of COT “MZ-half siblings” (Corey and Nance, 1974) Children of MZ and DZ twins Twins and the children of twins Children of Twins and children of siblings

Children of twins Resolve effects of maternal/paternal and fetal genotype (care!!) Resolve genetic from environmental effects of parents on children (with parents) Need to be careful: assortative mating and home environment dyadic (depends on both parents)

European AmericanAfrican American Parental relationship N. FamiliesN. BirthsN. FamiliesN. Births Sibship284,446575,70966,983119,791 Maternal half-sibship6,73612,2692,4314,515 Paternal half-sibship5,4199,8002,8395,292 MZ male twin5951, MZ female twin6181, DZ male twin DZ female twin DZ male-female twin9361, Total299,511603,09272,683130,247 Virginia Preterm Birth Study Sample frequencies by parental relationship and race Source: York, TP et al (2010). Racial Differences in Genetic and Environmental Risk to Preterm Birth. PLoS One: 5(1), 1-6, e12391.

Full Genetic Model (Model 2)Reduced Genetic Model (Model 12) Source Estimate95% CIPercentageEstimate95% CIPercentage African American Fetal genetic0.264(0.0, 2.302) Maternal genetic0.976(0.274, 1.357) (0.531, 1.445)14.7 Shared environment1.215(0.499, 1.666) (0.872, 1.781)18.0 Unique environment4.642(3.559, 4.899) (4.625, 4.927)67.3 European American Fetal genetic1.325(0.640, 1.927) (0.695, 1.964)35.2 Maternal genetic0.503(0.263, 0.767) (0.235, 0.758)13.4 Shared environment0.263(0.006, 0.537) (0.027, 0.537)7.0 Unique environment1.673(1.355, 2.024) (1.355, 1.990)44.5 Estimated variance components from Virginia Preterm Birth Study 95% bootstrap confidence intervals. Estimates adjusted for covariates (birth order, maternal age, fetal sex, source of care, smoking, maternal education). Source: York, TP et al (2010). Racial Differences in Genetic and Environmental Risk to Preterm Birth. PLoS One: 5(1), 1-6, e12391.

Notes Uncorrelated residual environmental effects on children are omitted from the figure. Key to symbols:T1=Twin 1; T2=Twin 2; S1=Spouse of Twin 1; S2=Spouse of Twin 2; O1=Offspring of Twin 1; O2=Offspring of Twin 2; A= additive genetic effects expressed in both adults and children (“life course persistent”); A’ = residual additive genetic effects specific to children (“juvenile limited”); C = shared environmental effects adults; C’= shared environmental effects on children explained by parental phenotype; C”= residual, juvenile specific, shared environmental effects in twins and siblings. E=adult unique environmental effect Source: Eaves, Maes and Silberg (2010), JCCP. Genetic and environmental influences on the transmission of parental depression to children’s depression and conduct disturbance

Twin correlationsDepression * Conduct Disturbance ** MZ adult 1.32 (n=498) DZ adult 1.12 (n=545) MZ child 2.34 (n=692).73 (n=684) DZ child 2.17 (n=645).34 (n=627) Adult - Child correlations 3 MZ parent.18 (n=753).21 (n=1347) DZ parent.20 (n=845).23 (n=1508) MZ avuncular.07 (n=661).11 (n=1141) DZ avuncular.01 (n=654).06 (n=1129) Cousin Correlations MZ twin pair families.01 (n=261).15 (n=526) DZ twin pair families.02 (n=185).15 (n=441) Twin, parent - child, avuncular – offspring, and cousin correlations for MZ and DZ twins. 1 Adult twin correlations - Children of Twins Study (COT) 2 Juvenile twin correlations - Virginia Twin Study of Adolescent Behavioral Development (VTSABD) 3 Complete and incomplete twin pair families * Child ratings of depression ** Parental ratings of conduct

ParameterFree?DepressionConduct Correlation between spouses F Persistent additive genetic effect to adult phenotype F Persistent additive genetic effect to juvenile phenotype F0.0000! Juvenile-limited genetic effect to juvenile phenotype F Adult shared environment to adult phenotype F0.0000! Parental phenotype to juvenile shared environment D Juvenile shared environment to juvenile phenotype F Juvenile-specific shared environment to phenotype F0.0000! Correlation between persistent genetic and shared environmental effects D Partial regression of juvenile outcome on parental phenotype D Correlation between genes of parents and phenotype of parents D Correlation between additive genetic effects of siblings/twins D lnL K 4 5 2 d.f. 3 2 P Summary of Model-Fitting Results for Adult Depression and Juvenile Outcome in Children of Twins Notes: K= # of free (unconstrained) parameters in the model. F=free; D=derived !=parameter fixed at zero ex hypothesi; “Comparison” denotes model with which reduced model is compared;  2 =log-likelihood ratio chi-square for model comparison; d.f. = degrees of freedom for  2 ;

The Full Monty….

ANZUS 50K: Extended Kinships of Twins Twins Parents of Twins Offspring of Twins Siblings of Twins Spouses of Twins © Lindon Eaves, 2009

The Full Monty Additive Assortment Dominant Parents Siblings Twins Within-family Short-term Genes Environment Any or all of the above effects may depend on sex

It can get complicated Caveat emptor

The First Model: “Stealth” Truett et al., 1994.

Sample sizes for in the Virginia 30,000

Summary Correlations for Stature in the Virginia 30,000

Relative Contributions to Stature Differences

Summary Correlations for Church Attendance in the Virginia 30,000

Summary Correlations for Stature and Church Attendance in the Virginia 30,000

Conservatism: Components of Variation Men Women

Summary Correlations for Conservatism in the Virginia 30,000

Summary Correlations for Stature and Conservatism in the Virginia 30,000

Church Attendance: Components of Variation

Overview of Statistical Findings Measures differ in effects of G and E Environmental effects on attitudes etc much larger than on stature Men and women differ significantly for size of G and E Biggest environmental effects not shared by siblings Family environment largest for religious and political affiliation - much smaller for “religious control” and church attendance Genetic effects largest on aggregate conservatism and on liberalism and “religious control” clusters Large spousal correlations Some negative gene-environment correlation Developmental change in effects of genes and shared environment