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## Response to selection and selection efficiency

The genetic advance achieved through selection depends on the total variation, the repeatability of the trait (h²) and the selection pressure imposed. The selection pressure implies the proportion of the population selected. Even if the repeatability is high the genetic advance (genetic gain) would be small without a large genetic variation. With selection the genetic variation and consequently the repeatability and thus the advance from one to the next generation decline while the mean value of the trait increases (or decreases, depending on the trait).

Response to selection (R) is the difference between the mean phenotypic value of the offspring of the selected parents and the whole of the parental generation before selection. The response to selection (Selektionsgewinn) is the expected future superiority of selected genotypes compared to the expected future population mean. The response to selection in one generation may be expressed mathematically as

$x_{0} - x_{p} = R = ci h^{2} s_{d}=h^{2}S$                                                   BREEDERS EQUATION

where Xo is tge mean phenotype of the offspring of the selected parents; Xp is the mean phenotype of the parental population before selection; R is the advance in one generation of selection; c is the extent of parental control; i is the intensity of selection, so the fraction of the current population retained to be used as parents for the next generation; sd is the phenotypic standard deviation of the phenotype; h² is the heritability /repeatability; S is the selection differential.

The is determined according to the mating system or the number of values over which the phenotypic values are averaged (field repetitions, years, environments).

Intensity of selection
i at 1% is 2.668, at 5% i is 2.06, at 10% i is 1.755
Independent curling: Selection for multiple traits. 50% of genotypes are selected for trait A, and then 40% for trait B and then 50% for C. The selection efficiency is thus 0.5 x 0.4 x 0.5 = 0.1 = 10%

The selection differential (S) is the mean phenotypic value of the individual selected as parents expressed as a deviation from the population mean. For example the yield of a selected line is 2.9 dt/ha higher than the average yield of all lines in the trial. The repeatability of the trial was 0.79. Thus the expected future yield of the line is 0.79 x 2.9 dt/ha higher than the expected average yield.

$S=(x_{s}-\bar{x})=i(N,G )\sigma _{p}$,
N is the number of genotypes selected out of G

The selection differential can be estimated with the selection intensity. The expected selection differential can be obtained with a normal approximation from the selected fraction α=N/G.

Post-test estimation of response to selection

• a field trial was carried out, phenotypic data were collected
• h² was determined considering the field replications, environments and years
• selection decision is still pending or was just made
$R =h^{2}S$

The selection differential can be estimated with the selection intensity. Pre-test estimation of response to selection can be estimated with the estimated selection differential.

Pre-test estimation of response to selection

• aim is to develop new varieteis which have at least 105% of the yield of check varieties
• the genotypic and phenotypic variances as well as the heritability are known from previous experiments
• test the response to selection with different selection intensities
$R = i h^{2} s_{d}$

$i(N,G)=i(\alpha )-\frac{G-N}{2N(G+1)i(\alpha)}$  after Burrows 1972

in R:
alpha<- (1:10)/100
i<-dnorm(qnorm(1-alpha,0,1)0,1)/alpha

The expected response to selection can be used to determine the required size of a field trial to obtain a desired response to selection and to compare expected response to selection for alternative scenarios.

Selection efficiency

The selection efficiency can be calculated by deviding the correlated response and the response to selection (CR/R).

Correlated response (CR)

Selection is carried out for the phenotype of a trait 1 in order to improve the genotypic value of trait 2. The prerequisite for indirect selection is that the genotypic values of both traits are highly correlated. If trait x changes, trait y changes too. Indirect selection based on trait x will be more efficient than direct selection, if h² of the secondary trait (x) is high and the genetic correlation to the trait of interest is high.

$CR_{y}= i_{x}h_{x}h_{y}r_{g}\sqrt{\sigma _{p}^{2}}=i_{x}r_{g}h_{x}\sqrt{\sigma _{g}^{2}}$,
where rg is the genetic correlation between trait x and y;  h is the square root of the repeatability of trait x and y.

$CR/R=\frac{i_{1}h_{1}r_{g}}{i_{2}h_{2}}$

If CR/R is 2, than the selection based on the secondary trait is twice as efficient as the selection on the primary trait.  If CR/R is negative, then the selection to an increase of the secondary traits leads in parallel to a decrease in the other trait. Thus low values in trait 2 have to be selected to achieve an increase in trait 1.

Literature:
Acquaah G. 2007: Principles of plant genetics and plant breeding. Blackwell Publishing. Malden, Oxford.
Burrows, P.M. 1972. Expected selection differentials for directional selection. Biometrics 28, 1091-1100.

December 12th, 2010
Topic: Crop Science, Plant breeding Tags: None

### 4 Responses to “Response to selection and selection efficiency”

1. Heritability / Repeatability of a trait | cropscience.ch Says:

[...] Response to selection and selection efficiency [...]

2. Index selection | cropscience.ch Says:

[...] Response to selection and selection efficiency [...]

3. Breeding crops for organic agriculture | cropscience.ch Says:

[...] reduced compared to conventional conditions, but still appropriate for selection (h² ~ 0.7). The selection gain of cultivars bred under organic conditions is until now limited and comparable to those bred under [...]

4. Estimates of genetic correlation between two traits / one trait in two selection environments | cropscience.ch Says:

[...] estimating selection efficiency, an estimate of the genetic correlation has to be given. This value can be estimated using [...]