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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. Quantitative traits

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slide1

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

slide2

Quantitative traits

- 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

slide3

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

slide4

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

slide5

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

slide6

3. Heritability (유전력, 유전율)

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,

slide7

- 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

slide8

(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             

slide9

(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

slide10

i) D

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

slide11

(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%)

slide12

(5) Selection experiment

= 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’’

slide13

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