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?