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?