Understanding Assortative Mating and Its Genetic Implications

1. Assortative mating(Falconer & Mackay: chapter 10) Sanja Franic VU University Amsterdam 2012

2. ‘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?

3. Plomin, R., DeFries, J.C., Roberts, M.K. (1977). Assortative mating by unwed biological parents of adopted children. Science, 196(4288), 449-450.

4. degree of assortative mating: correlation r of the phenotypic values of the mated individuals

5. 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

6. 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

7. 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)

8. 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)

9. 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)

10. 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

11. Primary genetic or primary environmental resemblance of mates:

12. Primary genetic or primary environmental resemblance of mates: • occurs e.g. in groups that are genetically or environmentallly differentiated from each other

13. 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

14. 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

15. 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

16. 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

17. 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 • covA1A2 = mVA (because m=covA1A2/VA) • so that: • rh2VA = mVA • m = rh2

18. the correlation m between the breeding values causes an increase of the additive genetic variance, and consequently of the heritability • why?

19. 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)

20. 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

21. 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)

22. 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

23. By how much is h2 increased?

24. Change in variance components under assortative mating: • VA0 = .5 • VP0 = 1 • → h20 = .5 • m = .4 • h2n = .67 n

25. Change in variance components under assortative mating: • VA0 = .5 • VP0 = 1 • → h20 = .5 • m = .5 • h2n = .75 n

26. Change in variance components under assortative mating: • VA0 = .5 • VP0 = 1 • → h20 = .5 • m = .6 • h2n = .875 n

27. Change in variance components under assortative mating: • VA0 = .5 • VP0 = 1 • → h20 = .5 • m = .4 • VA0 = .5 • VP0 = 1 • → h20 = .5 • m = .5 • VA0 = .5 • VP0 = 1 • → h20 = .5 • m = .6 • h2n = .67 • h2n = .75 • h2n = .875

28. Change in variance components under assortative mating: • VA0 = .5 • VP0 = 1 • → h20 = .5 • m = .4 • Dh2 = .17 n

29. Change in variance components under assortative mating: • VA0 = .6 • VP0 = 1 • → h20 = .6 • m = .4 • Dh2 = .16 n

30. Change in variance components under assortative mating: • VA0 = .7 • VP0 = 1 • → h20 = .7 • m = .4 • Dh2 = .14 n

31. Change in variance components under assortative mating: • VA0 = .5 • VP0 = 1 • → h20 = .5 • m = .4 • VA0 = .6 • VP0 = 1 • → h20 = .6 • m = .4 • VA0 = .7 • VP0 = 1 • → h20 = .7 • m = .4 • Dh2 = .17 • Dh2 = .16 • Dh2 = .14

32. Questions?