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Ch.4 Genetic analysis of quantitative traits

1. Component of quantitative genetic variation

2. Variance component of a quantitative trait in the populations

3. Heritability (유전력, 유전율)

4. QTL analysis

- described in terms of the degree of expression: metric traits

- continuous variation

- under polygenic control

- influenced by environments

- population genetics

1. Component of quantitative genetic variation

(1) Types of gene action

a. an additive portion : describing the difference between homozygotes at any single locus (Aa = ½(AA + aa)

b. a dominance components : arising from interaction of alleles ---> intra-locus interaction (Aa > ½(AA + aa)

c. an epistatic part ; associated with interaction of non-alleles ---> inter-locus interaction or epistasis

* Application to plant breeding : in choosing parents for crossing and breeding methods to maximize the selection gain

Gene models (Allard) for the expression of a quantitative trait

a. Model 1 : additive model

b. Model 2 : dominance model

c. Model 3 : Epistasis ---

complementary model

d. Model 4 complex model

2. Variance component of a quantitative trait in the populations

- 1) F2
- - Genotypic value
- Frequency ¼ ½ ¼
- - Generation mean of F2 = ¼(-da) + ½(ha) + ¼(da) = ½ha
- - Variance of F2 = ¼(da-½ha)2 + ½(ha-½ha)2 + ¼(-da-½ha)2 = ½da2 + ¼ha2
- * Many independent loci are involved for the trait ; A-a, B-b, C-c, ...
- (Assume that the effects of the genes are cumulative)
- da2 + db2 + dc2 + ... = D (Variance for additive effects of genes)
- ha2 + hb2 + hc2 + ... = H (Variance for dominant effects of genes)
- Then, VF2 = ½ D+ ¼ H + E1 (environmental variance among individuals)

Epiatisis, GxE

not included

2) VB1, VB2

VB1 : F1 (Aa) x P1 (AA) ---> AA : Aa= 1 : 1

Genotype Freq. Genotypic value Generation mean of B1

AA ½ da ½da+ ½ha

Aa ½ ha

VB1 = ½ (da-½da-½ha)2 + ½ (ha-½da-½ha)2 = (½da-½ha)2 + E1

Aa

AA

aa

-da

ha

VB2 : F1 (Aa) x P2 (aa) ---> Aa : aa = 1 : 1

Genotype Freq. Genotypic value Generation mean of B2

Aa ½ ha ½ha - ½da

aa ½ -da

VB2 = ½ (ha-½ha+½da)2 + ½ (-da-½ha+½da)2 = (½da+½ha)2 + E1

==> VB1 + VB2 = ½da2 + ½ha2 + 2E1 = ½ D + ½ H + 2E1

+da

0

3) VF3 (Variance of F3 population)

Genotype Freq. Genotypic value Mean

AA 3/8 da

Aa 2/8 ha ¼ ha (=3/8 da + 2/8 ha -3/8 da)

aa3/8 -da

VF3 = ⅜(da-¼ha)2 + ¼(ha-¼ha)2 + ⅜(-da-¼ha)2

= ¾da2 + 3/16 ha2 + E1 = ¾ D+ 3/16 H+ E1

4) VF3(Variance among F3 lines)

(F2) Genotype of F3 lines Freq. Mean of each line Grand mean of lines

AA ---> AA ¼ da ¼ha

Aa ---> ¼AA+½Aa+¼aa ½ ½ha(=¼da+½ha-¼da) (= ¼da+½(½ha)-¼da)

aa---> aa ¼ -da

VF3 = ¼(da-¼ha)2 + ½(½ha-¼ha)2 + ¼(-da-¼ha)2

= ½da2 + 1/16 ha2 = ½ D + 1/16 H + E2 (Environm. variation among lines)

5) VF3(Mean of variance of each F3 line)

Genotype of lines Freq. Mean of each line Variance within line

AA ¼ da 0

¼AA+½Aa+¼aa ½ ½ha(=¼da+½ha-¼da) ½da2+¼ha2

aa ¼ -da 0

VF3 = ¼(0) + ½ (½da2+¼ha2) + ¼(0) = ¼da2 + ⅛ha2

= ¼ D + ⅛ H + E3 (Mean of environmental variance within line ( ≒ E1))

6) WF2/F3 (Covcariance between a F2 individual and the F3 line)

F2 ind. Value F3 line Value 1/n {∑(x-x)(y-y)}

¼ AA da ¼ AA da ¼ (da-½ha)(da-¼ha)

½ Aa ha ½ (¼AA+½Aa+¼aa) ½ha ½ (ha-½ha)(½ha-¼ha)

¼ aa -da ¼ aa -da ¼ (-da-½ha)(-da-¼ha)

Mean ½ha ¼ha +)_______________________

½ da2 + ⅛ ha2

W F2/F3 = ½ D+ ⅛ H

Phenotype = Genotype + Environment + GxE

Vph= VG + VE + VGxE

= VA + VD + VE + VGxE(+ VEpi + Vinteractions)

* V: variance, Ph: phenotypic, G: genotypic, E: environmental

A: additive, D: dominant, Epi: epistatic

Broad sense heritability: the proportion of observed variation in a particular trait that can be attributed to inherited genetic factors in contrast to environmental ones (h2B)

h2B = (x 100 %)

Narrow sense heritability

(h2N)

: more useful

h2N =

*rice

20 vars.

3 repl.

IITA,

Afr. J. Plant

Sci. 5(3):

207-212,

- Heritability for a certain trait is a measure of the response to selection of the trait.

The higher the heritability of a trait, the easier it is to modify that trait by selection.

If heritability is very high, then phenotypic value is a good estimator of genotypic value.

- Although the heritability of a trait depends on how it is measured, in what environment(s) it is measured, and which plant materials are measured. Qualitative traits, such as flower color, often have a value of heritability close to 100.

Calculation of Heritability

(1) Use of variances in parents, F1, F2: VP , VF1 , VF2 --- h2B

VF2 : Variance of F2 population

VE : Variance caused by environments

-- variation among individuals of the same genotype

(2) Heritability estimation by ANOVA analysis --- h2B

n varieties, r replication

Ex) barly20 vars. 3 repl(RBD)--- no. of kernels per spike

ANOVA

df MS F EMS

Total 59 530

Variety19 410 ** σE2 + rσg2

Block 2 70 ns σE2 + nσB2

Error 38 50 σE2

σg2 = = 120 h2 = = 0.706 (= 70.6 %)

3

(3) Heritability estimation by variance component method

E1 : Variance among individuals of parents

E2 : Variance among lines of parents

E3 : Mean variance among lines of parents

Ex) Oats seed length data collected in an F2 population and F3 lines

E1 = 0.3427, E2 =0,0495, E3 =0.3110

Since there are experimental errors in

each components across populations

calculate an optimum estimates

of each component using least square method

ii) For other components, H, E1, E2, E3

iii) Optimum estimate of

each components

iv) Heritability

D = 1.3211

H = 1.0694

E1 = 0.3653

E2 = 0.1015

E3 = 0.3169

In F2 pop.

In F3 lines

(4) Use of parent-offspring regression

b: regression coefficient

rxy: probability which a specific gene of offspring

is identical to that of parents

h2N= b : in completely heterozygous parents vs offsprings

h2N = 2b : in bisexual populations

Parent-offspring

Regression rxyh2N

F1 --> F2 1/2 b

F2 --> F3 3/4 2/3 b

F3 --> F4 7/8 4/7 b

F4 --> F5 15/16 8/15 b

F5 --> F6 31/32 16/31 b

Ex) In a soybean population

(Wiggins, 2012)

h2N= 16/31 b = 0.222 (22.2%)

= M’’ – M : response to selection (Rs);

selection gain (Gs) ; genetic advance after selection

= M’ – M : Selection differential (선발차)

=

q = selection intensity (out of total)

: standard deviation of the trait in the pop.

Base population

q

Freq.

M’

M

Population

after selection

value determined by q

M

Character value

M’’

Application of heritability in plant breeding

heritability of target traits

Prediction of expected gain after selection

- across environments

- under different experimental designs

- using several type of populations

+ information about the relative costs

to determine the optimal selection strategy

to make the breeding scheme efficient

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