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Assortative mating(Falconer & Mackay: chapter 10)
Sanja FranicVU 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
covA1A2 = mVA (because m=covA1A2/VA)
so that:
rh2VA = mVA
m = rh2
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Relationship between genotypic (m) and phenotypic (r) correlation
m
r
h2=1h2=.5h2=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?
Additive variance Phenotypic variance Heritability
1
generation
VA1 = VA0 + 1/2m VA0
VA1 = VA0(1 + 1/2m)
VP1 = VP0 + 1/2mh2 VP0
VP1 = VP0(1 + 1/2mh2)
h12 = VA1/VP1
h12 = VA0(1+1/2m) /
VP0(1+1/2mh2)
h12 = h0
2 (1 + 1/2m) / (1+
1/2mh2)
Equilibrium VA0 = VA(1 – m)
VA = VA0 / (1 - m)
VA = (1-m)-1VA0
VP0 = VP (1 – mh2)
VP = VP0 / (1 – mh2)
VP = (1 – mh2)-1 VP0
h2 = h02 (1 - m) / (1 + mh2)
Change in variance components under assortative mating:
VA0 = .5
VP0 = 1
→ h20 = .5
m = .4
h2n = .67
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance
VA
VP
h2
n
Change in variance components under assortative mating:
VA0 = .5
VP0 = 1
→ h20 = .5
m = .5
h2n = .75
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance VA
VP
h2
n
Change in variance components under assortative mating:
VA0 = .5
VP0 = 1
→ h20 = .5
m = .6
h2n = .875
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance
VA
VP
h2
n
Change in variance components under assortative mating:
VA0 = .5
VP0 = 1
→ h20 = .5
m = .6
h2n = .875
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance
VA
VP
h2
VA0 = .5
VP0 = 1
→ h20 = .5
m = .5
h2n = .75
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance VA
VP
h2
VA0 = .5
VP0 = 1
→ h20 = .5
m = .4
h2n = .67
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance
VA
VP
h2
Change in variance components under assortative mating:
VA0 = .5
VP0 = 1
→ h20 = .5
m = .4
Dh2 = .17
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance
VA
VP
h2
n
Change in variance components under assortative mating:
VA0 = .6
VP0 = 1
→ h20 = .6
m = .4
Dh2 = .16
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance VA
VP
h2
n
Change in variance components under assortative mating:
VA0 = .7
VP0 = 1
→ h20 = .7
m = .4
Dh2 = .14
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance
VA
VP
h2
n
Change in variance components under assortative mating:
VA0 = .7
VP0 = 1
→ h20 = .7
m = .4
Dh2 = .14
VA0 = .6
VP0 = 1
→ h20 = .6
m = .4
Dh2 = .16
VA0 = .5
VP0 = 1
→ h20 = .5
m = .4
Dh2 = .17
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance
VA
VP
h2
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance VA
VP
h2
2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
Generation
Variance
VA
VP
h2
Questions?