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PBG 650 Advanced Plant Breeding

Module 4: Quantitative Genetics

- Components of phenotypes
- Genotypic values
- Average effect of a gene
- Breeding values

What is Quantitative Genetics?

Definition:

“Statistical branch of genetics based upon fundamental Mendelian principles extended to polygenic characters”

Primary goal:

To provide us with a mechanistic understanding of the evolutionary process

Lynch and Walsh, Chapter 1

Questions of relevance to breeders

- How much of the observed phenotypic variation is due to genetic vs environmental factors?
- How much of the genetic variation is additive (can be passed on from parent to offspring)?
- What is the breeding value of the available germplasm?
- Are there genotype by environment interactions?
- What are the consequences of inbreeding and outcrossing? What are the underlying causes?
- Are there genetic correlations among traits?

Questions of relevance to breeders

- Answers to these questions will influence
- response to selection
- choice of breeding methods
- choice of parents
- optimal type of variety (pureline, hybrid, synthetic, etc.)
- strategies for developing varieties adapted to target environments

Phenotypic Value

P = phenotypic value

G = genotypic value

E = environmental deviation

Components of an individual’s Phenotypic Value

P = G + E

For individual k with

genotype AiAj

P(ij)k= + gij + e(ij)k

For the population as a whole:

E(E) = 0

= E(P) = E(G)

Cov(G, E) = 0

Bernardo, Chapt. 3; Falconer & Mackay, Chapt. 7; Lynch & Walsh, Chapt. 4

The origin ( ) is midway between the two homozygotes

Single locus modelA2A2

A1A2

A1A1

z z+a+d z+2a

Genotypic

Value

Coded

Genotypic Value

-a 0 d a

no dominance d = 0

partial dominance0 <d < +a or0 >d > –a

complete dominance d = +aor –a

overdominanced > +a or d < –a

degree of dominance =

Single locus model

Different scales have been used in the literature

A2A2

A1A2

A1A1

-a 0 d a

Falconer

0(1+k)a 2a

Lynch & Walsh

Comstock and Robinson (1948)

0 au a

0a 2a+d

Hill (1971)

Conversions can be readily made

Population mean

M =p2a + 2pqd – q2a

=a(p2 – q2) + 2pqd

= a(p +q)(p -q) + 2pqd

=a(p -q) + 2pqd

Mean on coded scale

(centered around zero)

This is a weighted average

contribution from homozygotes and heterozygotes

Mean on original scale

Population mean

M =a(p -q) + 2pqd

When there is no dominance a(p -q)

When A1 is fixed a

When A2 is fixed -a

Potential range 2a

If the effects at different loci are additive (independent), then

M =Σa(p -q) + 2Σpqd

F2=P+(1/2)d

BC1(A1A1)=P+(1/2)a + (3/8)d

For ½ A1A1, ½ A1A2

=P+½(a + d)

For ½ A1A2, ½ A2A2

= P+½(d - a)

BC1(A2A2)=P-(1/2)a + (3/8)d

Means of breeding populationsIn an F2 population, p = q = 0.5

In a BC1 crossed to the favorable parent, p = 0.75,

so after random mating

In a BC1 crossed to the unfavorable parent, p = 0.25,

so after random mating

Average effects

- We have defined the mean in terms of genotypic values
- Genes (alleles), not genotypes, are passed from parent to offspring
- Average effect of a gene (i)
- mean deviation from the population mean of individuals who received that gene from their parents (the other gene taken at random from the population)

subtract M =a(p -q) + 2pqd

Average effect of a gene substitution

Average effect of changing from A2 to A1

= 1 - 2

- a and d are intrinsic properties of genotypes
- 1, 2, and are joint properties of alleles and the populations in which they occur (they vary with gene frequencies)

q[a+d(q-p)] – (-p)[a+d(q-p)]

=a+d(q-p)

Average effect of changing from A1 to A2 = -

Relating this to the average effects of alleles:

1 = q 2 = -p

Breeding Value

Breeding value of individual Aij = i + j

- For a population in H-W equilibrium, the mean breeding value = 0
- The expected breeding value of an individual is the average of the breeding value of its two parents
- For an individual mated at random to a number of individuals in a population, its breeding value is 2 x the mean deviation of its progeny from the population mean.

Regression of breeding value on genotype

Breeding values

- can be measured
- provide information about genetic values
- lead to predictions about genotypic and phenotypic values of progeny

Additive genetic variance

- variance in breeding values
- variance due to regression of genotypic values on genotype (number of alleles)

● genotypic value

○breeding value

Genotypic values

- Genotypic values have been expressed as deviations from a midparent
- To calculate genetic variances and covariances, they must be expressed as a deviation from the population mean, which depends on gene frequencies

subtract M =a(p -q) + 2pqd

Remember = a + d(q - p) Substitute a= - d(q - p)

Dominance deviation

Components of an individual’s Phenotypic Value

P = G + E

G = A + D

- In terms of statistics, D represents
- within-locus interactions
- deviations from additive effects of genes
- Arises from dominance between alleles at a locus
- dependent on gene frequencies
- not solely a function of degree of dominance
- (a locus with completely dominant gene action contributes substantially to additive genetic variance)

Gij = + i +j + ij

Partitioning Genotypic Value

When p = q = 0.5 (as in a biparental cross between inbred lines)

Interaction deviation

- Components of an individual’s Phenotypic Value

P = G + E

P = A + D + E

- When more than one locus is considered, there may also be interactions between loci (epistasis)

G = A + D + I

P = A + D + I + E

- ‘I’ is expressed as a deviation from the population mean and depends on gene frequencies
- For a population in H-W equilibrium, the mean ‘I’ = 0

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