Report

Assortative mating (Falconer & Mackay: chapter 10) Sanja Franic VU University Amsterdam 2012 - ‘like with like’ - reflected in a phenotypic correlation between mated individuals - mating in human populations is assortative with respect to many characteristics, such as stature and IQ - how does assortative mating affect the estimation of heritability? Plomin, R., DeFries, J.C., Roberts, M.K. (1977). Assortative mating by unwed biological parents of adopted children. Science, 196(4288), 449-450. - degree of assortative mating: correlation r of the phenotypic values of the mated individuals - degree of assortative mating: correlation r of the phenotypic values of the mated individuals - the genetic consequences, however, depend on the correlation m between the breeding values of the mates - degree of assortative mating: correlation r of the phenotypic values of the mated individuals - the genetic consequences, however, depend on the correlation m between the breeding values of the mates - r: observed, m: not - degree of assortative mating: correlation r of the phenotypic values of the mated individuals - the genetic consequences, however, depend on the correlation m between the breeding values of the mates - r: observed, m: not - the relationship between r and m depends on what governs the choice of mates (phenotypic, genetic, or environmental resemblance) - degree of assortative mating: correlation r of the phenotypic values of the mated individuals - the genetic consequences, however, depend on the correlation m between the breeding values of the mates - r: observed, m: not - the relationship between r and m depends on what governs the choice of mates (phenotypic, genetic, or environmental resemblance) - primary phenotypic resemblance: m = rh2 (h2 = heritability of the character with respect to which the mates are chosen) - degree of assortative mating: correlation r of the phenotypic values of the mated individuals - the genetic consequences, however, depend on the correlation m between the breeding values of the mates - r: observed, m: not - the relationship between r and m depends on what governs the choice of mates (phenotypic, genetic, or environmental resemblance) - primary phenotypic resemblance: m = rh2 (h2 = heritability of the character with respect to which the mates are chosen) - this is how assortative mating is applied in breeding programmes (but NB: in man, assortative mating probably seldomly arises only in this way) - degree of assortative mating: correlation r of the phenotypic values of the mated individuals - the genetic consequences, however, depend on the correlation m between the breeding values of the mates - r: observed, m: not - the relationship between r and m depends on what governs the choice of mates (phenotypic, genetic, or environmental resemblance) - primary phenotypic resemblance: m = rh2 (h2 = heritability of the character with respect to which the mates are chosen) - this is how assortative mating is applied in breeding programmes (but NB: in man, assortative mating probably seldomly arises only in this way) - the consequences to be described are restricted to primary phenotypic resemblance as cause of assortative mating Primary genetic or primary environmental resemblance of mates: Primary genetic or primary environmental resemblance of mates: - occurs e.g. in groups that are genetically or environmentallly differentiated from each other Primary genetic or primary environmental resemblance of mates: - occurs e.g. in groups that are genetically or environmentallly differentiated from each other - this is probably how much of assort. mating in man arises Primary genetic or primary environmental resemblance of mates: - occurs e.g. in groups that are genetically or environmentallly differentiated from each other - this is probably how much of assort. mating in man arises - e.g., SES groups as environmentally differentiated groups: - environment within each group is relatively homogenous with respect to SES → mates within each group are more similar on SES to each other than to rest of the population Primary genetic or primary environmental resemblance of mates: - occurs e.g. in groups that are genetically or environmentallly differentiated from each other - this is probably how much of assort. mating in man arises - e.g., SES groups as environmentally differentiated groups: - environment within each group is relatively homogenous with respect to SES → mates within each group are more similar on SES to each other than to rest of the population - if primary correlation is wholly environmental (m = 0) → no genetic consequences of assortative mating Primary genetic or primary environmental resemblance of mates: - occurs e.g. in groups that are genetically or environmentallly differentiated from each other - this is probably how much of assort. mating in man arises - e.g., SES groups as environmentally differentiated groups: - environment within each group is relatively homogenous with respect to SES → mates within each group are more similar on SES to each other than to rest of the population - if primary correlation is wholly environmental (m = 0) → no genetic consequences of assortative mating - environmental correlation may be the basis of assortative mating on IQ in man - Rao, Morton, & Yee, 1976: r = .5 explained by people choosing a spouse with a similar family background Primary phenotypic resemblance of mates: m = rh2 covA1A2 = cov(h2P1, h2P2) = h4cov(P1,P2) = h4rVP (because r=cov/V → cov=rV) = h4rVA/h2 (because h2=VA/VP → VP=VA/h2) = rh2VA Relationship between genotypic (m) and phenotypic (r) correlation (because m=covA1A2/VA) 1.0 covA1A2 = mVA so that: h2=.5 h2=1 0.5 h2=0 0.0 -0.5 -1.0 m = rh2 r rh2VA = mVA -1.0 -0.5 0.0 m 0.5 1.0 - the correlation m between the breeding values causes an increase of the additive genetic variance, and consequently of the heritability - why? - the correlation m between the breeding values causes an increase of the additive genetic variance, and consequently of the heritability - why? because an increased covariance within groups implies an increased variance between groups (last lecture) - the correlation m between the breeding values causes an increase of the additive genetic variance, and consequently of the heritability - why? because an increased covariance within groups implies an increased variance between groups (last lecture) - the correlations between relatives, however, are increased by more than one would expect from increased heritability alone - the correlation m between the breeding values causes an increase of the additive genetic variance, and consequently of the heritability - why? because an increased covariance within groups implies an increased variance between groups (last lecture) - the correlations between relatives, however, are increased by more than one would expect from increased heritability alone - therefore, 2 meanings of h2 under assortative mating: - determination of the resemblance betwen relatives (eq. 10.5: h2 = b/r or t/r) - ratio of variance components (VA/VP) - the correlation m between the breeding values causes an increase of the additive genetic variance, and consequently of the heritability - why? because an increased covariance within groups implies an increased variance between groups (last lecture) - the correlations between relatives, however, are increased by more than one would expect from increased heritability alone - therefore, 2 meanings of h2 under assortative mating: - determination of the resemblance betwen relatives (eq. 10.5: h2 = b/r or t/r) - ratio of variance components (VA/VP) - the two are not the same under assortative mating! - here, we retain the latter definition By how much is h2 increased? 1 generation Additive variance Phenotypic variance Heritability VA1 = VA0 + 1/2m VA0 VP1 = VP0 + 1/2mh2 VP0 h12 = VA1/VP1 VA1 = VA0(1 + 1/2m) VP1 = VP0(1 + 1/2mh2) h12 = VA0(1+1/2m) / VP0(1+1/2mh2) h12 = h02 (1 + 1/2m) / (1+ 1/2mh2) Equilibrium VA0 = VA(1 – m) VP0 = VP (1 – mh2) VA = VA0 / (1 - m) VP = VP0 / (1 – mh2) VA = (1-m)-1VA0 VP = (1 – mh2)-1 VP0 h2 = h02 (1 - m) / (1 + mh2) 2.0 Change in variance components under assortative mating: VA0 = .5 1.5 VP0 = 1 → h20 = .5 m = .4 1.0 VA 0.5 h2 0.0 Variance h2n = .67 VP 2 4 6 Generation 8 n 10 2.0 Change in variance components under assortative mating: VA0 = .5 1.5 VP0 = 1 → h20 = .5 VP 1.0 VA 0.5 h2 0.0 h2n = .75 Variance m = .5 2 4 6 Generation 8 n 10 2.0 Change in variance components under assortative mating: VA0 = .5 1.5 VP0 = 1 → h20 = .5 VP m = .6 1.0 0.5 h2 0.0 Variance h2n = .875 VA 2 4 6 Generation 8 n 10 2.0 2.0 1.5 1.5 2.0 1.5 Change in variance components under assortative mating: VP VP h2 1.0 1.0 VA Variance VA Variance 1.0 VA h2 2 4 6 Generation 8 10 0.5 0.0 0.5 0.0 0.5 h2 0.0 Variance VP 2 4 6 Generation 8 10 2 4 6 Generation VA0 = .5 VA0 = .5 VA0 = .5 VP0 = 1 VP0 = 1 VP0 = 1 → h20 = .5 → h20 = .5 → h20 = .5 m = .4 m = .5 m = .6 h2n = .67 h2n = .75 h2n = .875 8 10 2.0 Change in variance components under assortative mating: VA0 = .5 1.5 VP0 = 1 → h20 = .5 m = .4 1.0 VA 0.5 h2 0.0 Variance Dh2 = .17 VP 2 4 6 Generation 8 n 10 2.0 Change in variance components under assortative mating: VA0 = .6 1.5 VP0 = 1 → h20 = .6 VP 1.0 VA 0.5 h2 0.0 Dh2 = .16 Variance m = .4 2 4 6 Generation 8 n 10 2.0 Change in variance components under assortative mating: VA0 = .7 1.5 VP0 = 1 → h20 = .7 VP m = .4 1.0 0.5 h2 0.0 Dh2 = .14 Variance VA 2 4 6 Generation 8 n 10 2.0 2.0 1.5 1.5 2.0 1.5 Change in variance components under assortative mating: VP VP VP h2 1.0 Variance VA 1.0 Variance 1.0 VA h2 2 4 6 Generation 8 10 0.5 0.0 0.5 0.0 0.5 h2 0.0 Variance VA 2 4 6 Generation 8 10 2 4 6 Generation VA0 = .5 VA0 = .6 VA0 = .7 VP0 = 1 VP0 = 1 VP0 = 1 → h20 = .5 → h20 = .6 → h20 = .7 m = .4 m = .4 m = .4 Dh2 = .17 Dh2 = .16 Dh2 = .14 8 10 Questions?