E 2 G 1 P h e i g

C 2 U G 1 P h u c g a i

Total Environment (55%)

Twin Method (1) Rmz = .52 = h2 + he2 (2) Rdz = .31 = .5h2 + he2 Solution: (1) Subtract Equation (2) from Equation (1): Rmz = .52 = h2 + he2 -Rdz = -.31 = -.5h2 - he2 .21 = .5h2 (2) Multiply this result by 2: 2(.21) = 2(.5h2), so .42 = h2 (3) Substitute this quantity into Equation (3): .42 + e2 = 1, so e2 = .58 (4) Substitute the results from steps (2) and (3) into Equation (1) & solve for h: .52 = .42 + h(.58), so h = .10/.58 = .17

Adoption Method (1) RBioSibs = .24 = .5h2 + he2 (2) RAdpSibs = .06 = he2 (3) h2 + e2 = 1 Solution: (1) Subtract Equation (2) from Equation (1): RBioSibs = .24 = .5h2 + he2 - RAdpSibs = -.06 = - he2 .18 = .5h2 (2) Multiply this result by 2: 2(.18) = 2(.5h2), so .36 = h2 (3) Substitute this quantity into Equation (3): .36 + e2 = 1, so e2 = .64 (4) Substitute the results from steps (2) and (3) into Equation (1) & solve for h: .06 = h(.64), so h = .06/.64 = .09

Table 19.1. Values of g and h for different types of genetic and adoptive relationships under a general model and under a simple model that assumes only additive genetic action, random mating, and random placement of adoptees. g h Relationship: Notation: General Simple MZ twins together mzt 1.0 hmzt htwin MZ twins apart mza hmza DZ twins together dzt gsibs .50 hdzt DZ twins apart dza hdza Siblings together sibst hsibst hsib Siblings apart sibsa hsibsa Parent-offspring together pot gpo hpot hpo Parent-offspring apart poa hpoa Grandparent-grandchild gg ggg .25 hggt hgg Uncle/aunt-nephew/niece uann guann huannt huann Half-sibs, together hst ghs hhst Half-sibs, apart hsa hhsa Cousins cous gcous .125 hcous Adoptive parent-offspring apo gapo 0.0 hapo Adoptive sibs asibs gasibs hasibs

Table 19.2. Estimation of heritability, environmentability, and the correlation between twins’ environments using the twin method and the assumptions of equal environments for MZ and DZ twins raised together and no selective placement of adoptees. Notation follows that in Table 19.1 and Figure 19.1. A dot (.) denotes that a quantity cannot be estimated using that design. Design: h2 e2 htwin Twins raised together = 2(Rmzt – Rdzt) 1 – h2 Twins raised apart = Rmza . = .5Rdza

Sibs Apart and Together = .5Rsibsa 1 – h2 Table 19.3. Estimation of heritability, environmentability, and the correlation between relatives’ environments using the adoption method and assumption of no selective placement. Notation follows that in Table 19.1 and Figure 19.1. Design: h2 e2 h Sibs Apart and Together = .5Rsibsa 1 – h2 Sibs Together and Adoptive Sibs = 2(Rsibst – Rasibs) Parent-offspring Together and Apart = 2Rpoa

Table 19.4. Estimation of heritability, common environmentability, and unique environmentability in twin studies using the assumptions of equal environments for MZ and DZ twins raised together and no selective placement of adoptees. Notation follows that in Figure 19.2. A dot (.) denotes that a quantity cannot be estimated using a particular design. Design: h2 ci2 ui2 Twins raised together = 2(Rmzt – Rdzt) = 2Rdzt - Rmzt = 1 – h2 – c2 Twins raised apart = Rmza . = .5Rdza

Sibs Apart and Together = .5Rsibsa = Rsibst – .5h2 = 1 – h2 – c2 Table 19.5. Estimation of heritability, environmentability, and the correlation between relatives’ environments using the adoption method and assumption of no selective placement. (Notation follows that in Table 19.1 and Figure 19.2). Design: h2 ci2 ui2 Sibs Apart and Together = .5Rsibsa = Rsibst – .5h2 = 1 – h2 – c2 Sibs Together and Adoptive Sibs = 2(Rsibst – Rasibs) Parent-offspring Together and Apart = 2Rpoa = Rapo

Table 19.6. Twin correlations for the English and Mathematics subtests of the National Merit Scholarship Qualifying Test. (From Loehlin & Nichols, 1976) Correlation: Zygosity: MZ (N = 509 pairs) DZ (N = 330 pairs) Within Individuals .61 .59 Cross-Twin: . Twin 1: Twin 2: English .75 .56 Math .37 .72 .44

Table 19.7. Testing mathematical models. Quantity: Observed General h2 = 0 htwin = 0 Rmzt .41 .34 .43 Rdzt .27 c2 0.00 4.94 1.60