- By
**lance** - Follow User

- 144 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' PBG 650 Advanced Plant Breeding' - lance

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

PBG 650 Advanced Plant Breeding

Module 5: Quantitative Genetics

- Genetic variance: additive and dominance

Variance and Covariance - definition

- The variance of a variable X is:

V(X) = E[(Xi- X)2] = E(Xi2) - X2

- The covariance of variable X and variable Y is:

Cov(X,Y) = E[(X - X)(Y - Y)] = E(XY) - XY

Properties of variances

- The variance of a constant is zero

V(c) = 0 V(c+X) = V(X)

- The variance of the product of a variable and a constant is the constant squared times the variance of the variable

V(cX) = c2V(X)

- The variance of a sum of random variables is the sum of the variances plus twice the covariance between the variables

V(X + Y) = V(X) + V(Y) + 2Cov(X,Y)

Application to a genetic model

P = G + E

G = A + D + I

P = A + D + I + E

Gijkl = + (i +j + ij) + (k +l + kl) + Iijkl

Because there are no

covariances among

the components

Additive genetic variance

Variance of breeding values

(No adjustment for the mean is necessary because the mean of breeding values is zero)

When p=q=1/2

σA2 =(1/2)a2

When d=0

σA2 = 2pqa2

Dominance Variance

Variance of dominance deviations

(No adjustment for the mean is necessary because the mean of dominance deviations is zero)

When p=q=1/2

σD2 =(1/4)d2

When d=0, σD2 = 0

Regression of genotypic values on allele number

M

Mean(X) = (ΣfiXi) = q2(0) + 2pq(1) + p2(2) = 2p(q+p) = 2p

= p2(22) + 2pq(12) +q2(02) – (2p)2= 2pq

Covariance of genotypic values and allele number

M

= p2(2)(P+a) + 2pq(1)(P+d) + q2(0)(P-a)– (2p)(P+a(p-q)+2pqd)

= 2pq[a+d(q-p)] = 2pq

Same result with scaled values (a, d, -a) or the adjusted genotypic values:

= p2(2)(a-M) + 2pq(1)(d-M) +q2(0)(-a-M)-(2p)(0) 2pq

Genetic Variances - Example

p=0.6 q=0.4

- Options for estimating variances
- Use formulas with known values of a and d
- Calculate breeding values and dominance deviations, and estimate their variances
- Regress observed values on number of Z1 alleles

Example from Falconer & Mackay

Option 2 – calculate variances directly

σG2 = 0.16(-5.76)2+0.48(0.24)2+0.36(2.24)2-02 = 7.1424

σA2 = 0.16(-4.32)2+0.48(-0.72)2+0.36(2.88)2-02 = 6.2208

σD2 = 0.16(-1.44)2+0.48(0.96)2+0.36(-0.64)2-02 = 0.9216

Option 3 – Regress values on allele number

p=0.6 q=0.4

Mean(X) = 0.16(0) + 0.48(1) + 0.36(2) = 1.20

= 0.16(02) + 0.48(12) +0.36(22) – (1.20)2

= 0.4800 = 2pq

Option 3 – Regress values on allele number

= 0.16(0)(6) + 0.48(1)(12) + 0.36(2)(14)– (1.20)(11.76) =1.7280=2pq

The result is the same if we use the adjusted genotypic values:

= 0.16(0)(-5.76) + 0.48(1)(0.24) + 0.36(2)(2.24) – (1.20)(0) =1.7280

Magnitude of genetic variances

- With no dominance, all genetic variance is additive and maximum genetic variance occurs when p=q=0.5
- With complete dominance
- maximum additive genetic variance occurs when the unfavorable allele has a frequency of q=0.75
- maximum dominance variance occurs when q=0.5
- maximum genetic variance occurs when q2=0.5 (q=0.71)

Effect of Inbreeding (selfing) on Variances

Total genetic variance increases with selfing!!

Hallauer, Carena and Miranda, 2010

Download Presentation

Connecting to Server..