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

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- ‘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?

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

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

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- 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

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- 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

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- 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)

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- 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 = rh 2 (h 2 = heritability of the character with respect to which the mates are chosen)

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- 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 = rh 2 (h 2 = 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)

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- 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 = rh 2 (h 2 = 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

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Primary genetic or primary environmental resemblance of mates:

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- occurs e.g. in groups that are genetically or environmentallly differentiated from each other

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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

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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

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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

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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

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Primary phenotypic resemblance of mates: m = rh 2 cov A1A2 = cov(h 2 P 1, h 2 P 2 ) = h 4 cov(P 1,P 2 ) = h 4 rV P (because r=cov/V → cov=rV) = h 4 rV A /h 2 (because h 2 =V A /V P → V P =V A /h 2 ) = rh 2 V A cov A1A2 = mV A (because m=cov A1A2 /V A ) so that: rh 2 V A = mV A m = rh 2

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

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- 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)

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- 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

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- 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 h 2 under assortative mating: - determination of the resemblance betwen relatives (eq. 10.5: h 2 = b/r or t/r) - ratio of variance components (V A /V P )

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- 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 h 2 under assortative mating: - determination of the resemblance betwen relatives (eq. 10.5: h 2 = b/r or t/r) - ratio of variance components (V A /V P ) - the two are not the same under assortative mating! - here, we retain the latter definition

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By how much is h 2 increased? Additive variancePhenotypic varianceHeritability 1 generation V A1 = V A0 + 1/2m V A0 V A1 = V A0 (1 + 1/2m) V P1 = V P0 + 1/2mh 2 V P0 V P1 = V P0 (1 + 1/2mh 2 ) h 1 2 = V A1 /V P1 h 1 2 = V A0 (1+1/2m) / V P0 (1+1/2mh 2 ) h 1 2 = h 0 2 (1 + 1/2m) / (1+ 1/2mh 2 ) EquilibriumV A0 = V A (1 – m) V A = V A0 / (1 - m) V A = (1-m) -1 V A0 V P0 = V P (1 – mh 2 ) V P = V P0 / (1 – mh 2 ) V P = (1 – mh 2 ) -1 V P0 h 2 = h 0 2 (1 - m) / (1 + mh 2 )

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Change in variance components under assortative mating: V A0 =.5 V P0 = 1 → h 2 0 =.5 m =.4 h 2 n =.67 n

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Change in variance components under assortative mating: V A0 =.5 V P0 = 1 → h 2 0 =.5 m =.5 h 2 n =.75 n

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Change in variance components under assortative mating: V A0 =.5 V P0 = 1 → h 2 0 =.5 m =.6 h 2 n =.875 n

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Change in variance components under assortative mating: V A0 =.5 V P0 = 1 → h 2 0 =.5 m =.6 h 2 n =.875 V A0 =.5 V P0 = 1 → h 2 0 =.5 m =.5 h 2 n =.75 V A0 =.5 V P0 = 1 → h 2 0 =.5 m =.4 h 2 n =.67

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Change in variance components under assortative mating: V A0 =.5 V P0 = 1 → h 2 0 =.5 m =.4 h 2 =.17 n

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Change in variance components under assortative mating: V A0 =.6 V P0 = 1 → h 2 0 =.6 m =.4 h 2 =.16 n

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Change in variance components under assortative mating: V A0 =.7 V P0 = 1 → h 2 0 =.7 m =.4 h 2 =.14 n

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Change in variance components under assortative mating: V A0 =.7 V P0 = 1 → h 2 0 =.7 m =.4 h 2 =.14 V A0 =.6 V P0 = 1 → h 2 0 =.6 m =.4 h 2 =.16 V A0 =.5 V P0 = 1 → h 2 0 =.5 m =.4 h 2 =.17

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