Heritability

1
Heritability
1

• Broad sense H2 s2G / s2P
• A trait is heritable in terms of being determined
  by a genotype
• Narrow sense h2 s2A / s2P
• This ratio measures the proportion of the total
  variance that can be transmitted from parent to
  offspring.

2
Estimation of additive genetic variance - s2A
2

• You cross among genotypes in a mating design and
  evaluate the resulting families (HS, FS, S1) in a
  trial
• The total variance s2g can be partitioned into
• Additive (s2A) and dominance (s2D) components

3
Covariance among relatives
3

• Genetic parameters can be estimated based on
  expectations of covariance among relatives
• It can be shown that covariance among relatives
  arises from the probability that relatives share
  alleles (one or two) at a given locus.

4
Covariance among relatives
4

• Cockerham, 1956
• Components of variance
• Relatives Additive Dominance
• Half-sibs 1/4 s2A 0
• Full-sibs 1/2 s2A 1/4 s2D
• Selfed s2A 1/4 s2D

5
Numerical example
5

• Assume a population
• Pq.5
• BB 20, Bb 10, Bb 0
• Our objective is to measure s2A
• Bb Bb BB Bb Bb BB
• BB bb bb Bb Bb Bb
• BB Bb Bb Bb bb bb

6
Mean and variance?
6

• Bb Bb BB Bb Bb BB
• BB bb bb Bb Bb Bb
• BB Bb Bb Bb bb bb
• If pq .5, and BB20, Bb 10 and bb0 then
• Mean freq x value 1/4(20) 1/2(10) 1/4(0)
  10
• Variance Freq x value2 - mean 2
• 1/4(20) 2 1/2(10) 2 1/4(0) 2 - 10 2 50

7
Mean and variance of among HS Families
7

• BB (1/4) Bb (1/2) bb (1/4)
• BB BB bB
• Bb Bb bb
• bB
• bb

pq .5
10
5
15
Mean 1/4 (15) 1/2 (10) 1/4 (5) 10
Variance) 1/4 (15)2 1/2 (10) 2 1/4 (5) 2 -
10 2 12.5
8
Mean and variance of among S1 Families
8

• BB (1/4) Bb (1/2) bb (1/4)
• BB (all) BB bb (all)
• Bb
• bB
• bb

pq .5
10
0
20
Mean 1/4 (20) 1/2 (10) 1/4 (0) 10
Variance) 1/4 (20)2 1/2 (10) 2 1/4 (0) 2 -
10 2 50
9
Mean and variance of among HS Families
9

• BB (.64) Bb (.32) bb (.04)
• BB (.8) BB (.4) bB (.8)
• Bb (.2) Bb (.1) bb (.2)
• bB (.4)
• bb (.1)

p.8,q.2
13
8
18
Mean .64 (18) .32 (13) .04 (8) 16
Variance) .64 (18)2 .32 (13) 2 .04 (8) 2 -
16 2 8
10
Mean and variance of among S1 Families
10

• BB (.64) Bb (.32) bb (.04)
• BB (all) BB bb (all)
• Bb
• bB
• bb

p.8, q.2
10
0
20
Mean .64 (20) .32 (10) .04 (0) 16
Variance) .64 (20)2 .32 (10) 2 .04 (0) 2 -
10 2 32
11
What is mean and variancefor dominance model?
11

• Bb Bb BB Bb Bb BB
• BB bb bb Bb Bb Bb
• BB Bb Bb Bb bb bb
• If pq .5, and BBBb 20, and bb0 then
• Mean freq x value 1/4(20) 1/2(20) 1/4(0)
  15
• Variance Freq x value2 - mean 2
• 1/4(20) 2 1/2(20) 2 1/4(0) 2 - 15 2 75

12
Mean and variance of among HS Families
12

• BB (1/4) Bb (1/2) bb (1/4)
• BB BB bB
• Bb Bb bb
• bB
• bb

pq .5 Complete dominance
15
10
20
Mean 1/4 (20) 1/2 (15) 1/4 (10) 15
Variance) 1/4 (20)2 1/2 (15) 2 1/4 (10) 2
- 15 2 12.5
13
Mean and variance of among S1 Families
13

• BB (1/4) Bb (1/2) bb (1/4)
• BB (all) BB bb (all)
• Bb
• bB
• bb

pq .5 Complete dominance
15
0
20
Mean 1/4 (20) 1/2 (15) 1/4 (0) 12.5
Variance) 1/4 (20)2 1/2 (15) 2 1/4 (0) 2 -
12.5 2 56.25
14
Means and variances
14

• HS S1 HS S1
• Model BB Bb bb p q mean mean var var
• Add 20 10 0 .5 .5 10 10 12.5 50
• .8 .2 16 16 8 32
• Dom 20 20 0 .5 .5 15 12.5 12.5 56.3
• .8 .2 19.2 17.6 1.28 18.2
• OD 10 20 10 .5 .5 15 12.5 0 6.5
• .8 .2 16.8 11.6 2.9 5.4