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Measures to Improve Selection Efficiency


CR y = b A(yx) R x

σ A(y)

= r A i x h x σ A(x)σ A(x)

= i x h x r A σ A(y)

Because: h = σ / σ , so σ = h σ

2 2 2 2

y A(y) P(y) A(y) y P(y)

Therefore:

CR y = i x h x h y r A σ P(y)

2

If we directly select for trait y, we will get the selection effect: R y = i y h y σ P(y) ; meanwhile, selecting for trait x will also get the indirect selection effect for trait y: CR y = i x h x h y r A σ P(y) .

The ratio of the indirect selection effect to the direct selection effect for trait y will be:

CR y i x h x h y r A σ P(y)

=

2

R y i y h y σ P(y)

CR y i x h x

= r A (calculated for one potential) [6.8] R y i y h y

CR y i x h x /L x

= r A

R y i y h y /L y


CR y i x h x L y

= r A (calculated for one year) [6.9] R y i y h y L x

2 2

For example: The genetic correlation coefficient between the two traits of weight (y) and body length (x) of pigs is: r A = 0.95, the corresponding genetic coefficients are: h y = 0.09 and h x = 0.16. Although pigs are only selected based on weight, they will still have a selection effect on the trait of body length.

Suppose: i x = i y and L x = L y , so the ratio between indirect and direct selection efficiency for trait y according to [6.9] is calculated as follows:

CR y i x h x /L x h x

= r A = r A

R y i y h y /L y h y


√ 0.16

= 0.95 = 1.27 or 127%.

√ 0.09

Thus, if direct selection for trait y only achieves 100% efficiency, selection for trait x brings about an indirect effect for trait y of 127%, which is 27% higher than the efficiency of direct selection.


9. Measures to improve selection efficiency

Selection efficiency is the most important goal for breeding livestock selection. Based on [6.3], the following main directions can be proposed to improve selection efficiency:

- Increased selectivity:

High selection intensity can only be achieved by selecting at a low rate. It is important to ensure the accuracy of selection, that is, to select the animals with the highest breeding value in the herd, as errors in selecting the best animals will lower the selection intensity and thus reduce the selection efficiency.

For example, there are 9 individuals that have been ranked, their values ​​are expressed in standard deviation units, the average value of the 9 individuals is 0.

Ranking order

squirrel family

The value of i is represented by

by standard deviation

1

1.49

2

0.93

3

0.57

4

0.29

5

0.00

6

-0.29

7

-0.57

8

-0.93

9

-1.49

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Measures to Improve Selection Efficiency

If the 4 best individuals are correctly selected, the selection intensity will be: i = (1.49 + 0.93 + 0.57 + 0.29)/4 = 0.82

If the assessment is incorrect, the best individual of the herd is mistakenly eliminated, and individuals from 2nd to 5th are selected, the selection intensity will be equal to:

i = (0.93 + 0.57 + 0.29 + 0.00)/4 = 0.445.

However, some basic factors that limit the selection rate are: reproduction, herd size and inbreeding. For livestock species that can multiply quickly such as poultry, pigs or in males, low selection rates can be applied, so the selection intensity will be high. On the contrary, for mono-fertile livestock species, groups of livestock with low reproduction rates, or in females, high selection rates will reduce the herd size. Too few male breeders in the herd will easily lead to inbreeding.

- Increase the value of the genetic coefficient:

To increase the value of the heritability coefficient, measures can be applied: reducing the variation of external conditions, monitoring many repeated observations in the individual's life.

- Increase the phenotypic standard deviation of the selected trait:

For livestock populations that have just begun to be selected, the phenotypic standard deviation of the selected trait is still high, so the selection efficiency is high. For livestock populations that have undergone many generations of selection for a certain trait, the phenotypic standard deviation of this trait gradually decreases, so the selection efficiency also decreases.

- Shorten the generation gap:

Common measures are: early mating of sexually mature male and female cattle, reduction of the interval between calvings in female cattle, and not prolonging the shelf life of breeding cattle.


However, the limiting factor in shortening the generation gap is to ensure that

Accurate livestock evaluation, waiting time for evaluation results is often prolonged.


Chapter 7

Estimated breeding value - selection index


The basic content of breeding livestock selection is to select animals with high cumulative genetic value (breeding value). Over the years, statistical methods using productivity monitoring data have been used to estimate breeding value. Advances in computing tools (electronic computers: memory capacity, storage capacity, calculation speed), and the application of mathematical models have made the estimation of breeding value increasingly more complete. Among the systems for estimating breeding value, the selection index is the basic method that has been used.

was widely applied in production in the 70s and 80s and had a great influence on current varietal value assessment systems.


1. Estimate the breeding value of livestock

We know the genetic model for quantitative traits as follows:

G = A + D + I

in which, A: Cumulative genetic value caused by the separate effects of many alleles, each gene having only a small effect;

D: Dominant deviation caused by the combined effect of 2 alleles at the same locus;

I: Interaction deviation caused by the combined effects of 2 or more alleles at different loci.

In selection, people pay more attention to the cumulative genetic value, because only this value is transmitted from the previous generation to the next generation. From the parent generation to the offspring generation, due to the combination of the chromosomes of the male and female gametes, the dominant deviation and interaction deviation in the parent generation are changed, forming new dominant deviations and interaction deviations that are completely different from the parent generation. Therefore, when conducting crossbreeding, people pay more attention to dominant deviation and interaction deviation.

Because the cumulative genetic value of the previous generation has a close relationship with the cumulative genetic value of the next generation, it is also called Breeding Value, symbolized as BV:

BV = A

Only 1/2 of the genetic value of the parent is passed on to the offspring, so the cumulative genetic value that the offspring receives from the parent is called the Transmitting Ability (TA) which is equal to 1/2 of the genetic value:

TA = 1/2 BV

For traits that are mentioned many times, people also refer to the concept of producing ability (Producing Ability, symbol PA) or also known as Most Probable Producing Ability (symbol MPPA), which is the sum of the breed value and the influence of the general external environment E G (also known as the regular external environment E P ):

PA = BV + EG = A + EG

We cannot directly assess the breed value and the productive capacity of the animal, because up to now and for a long time to come we will not know.

The influence of many genes contributes to the cumulative effect. Therefore we can only

estimated value of the breed.

Estimated Breeding Value is denoted as EBV (Estimated Breeding Value) or Â. The only method to estimate the breeding value of an animal for a certain trait is based on


based on the phenotypic value of this trait in the animal itself, or based on the phenotypic value of this trait in an animal related to the animal whose breeding value we want to estimate, or a combination of both types of phenotypic values. The way to estimate the breeding value of an animal for multiple traits will be similar. The phenotypic value of an animal that we use to estimate the breeding value is called the source of information that helps to evaluate the breeding value. This source of information can be just a single phenotypic value that we observe

can be obtained, but it can also be the average of many observations. These observations can be obtained from replicates on a single individual, or they can be obtained from different individuals (they have the same close kinship relationship with the animal whose breeding value we want to estimate, for example, they are the same offspring, the same full siblings, or the same half siblings).

Sources of information used to estimate seed value include:

- Information sources of the animal itself: productivity figures of the animal itself

object;

- Information sources of animal ancestors: productivity data of father, mother, grandparents

grandparents, of previous generations;

- Information sources of animal siblings: productivity data of full siblings (same father, same mother), half siblings (same father, different mother or same mother, different father);

- Information source from animal offspring: productivity data of animal offspring. Thus, we can estimate the breeding value of livestock by the following methods

This:

- Evaluate the cumulative genetic value of an animal for a trait based on information sources.

information about this trait of the animal itself (data from a single observation or the average of many repeated observations)

- Assess the cumulative genetic value of an animal for multiple traits based on information about these traits from the animal itself (data from a single observation or the average of many repeated observations for the traits)

- Assess the cumulative genetic value of an animal for a trait based on the animal's own information about this trait and the information of its relatives (data from a single observation or the average of many repeated observations).

- Assess the cumulative genetic value of an animal for multiple traits based on information about these traits from the animal itself and information about these traits from its relatives (data from a single observation or the average of many repeated observations).


2. Accuracy of seed value estimates

As mentioned above, there are many methods and many different sources of information used to estimate the breeding value of livestock. To be able to assess the accuracy of these estimates, people use the concept of Accuracy of breeding value estimates. In essence, the accuracy of a method of assessing breeding value or of an information source used to

Breeding value assessment is the correlation coefficient between the assessment method or information source and the breeding value of the animal:

Cov(A,P)

r AP =[7.1]

V(A)V(P)

where, r AP : Accuracy of the estimate of the seed value

Cov(A,P) : Covariance between methods or information sources used

to estimate the value of the breed and the value of the breed


V(A), V(P): Variance of the seed value and variance of the method or information source used to estimate the seed value


The accuracy of a seed value estimate ranges from 0 to 1 or is expressed as a percentage, from 0 to 100%. A larger value of accuracy indicates a more accurate estimation method or information source used to estimate the seed value.


3. Multiple trait selection methods

To meet the requirement of selecting livestock with high breeding value not only for one trait but for many different traits, such as male pigs that have fast weight gain, consume little feed per kg of weight gain and have low back fat thickness, people have proposed 3 different methods: sequential selection, independent culling and selection index.


- Tandem Selection: This is a method in which, over a certain period of time, people focus on selection to improve the genetics of the first trait. When the requirements are met, people move on to the second trait and so on for the third trait or back to the first trait. This method is simple, but it takes a long time to select many traits. On the other hand, some traits are inversely related to each other, so selecting to improve one trait also means reducing the other trait. For example, focusing only on increasing cow's milk production or increasing chicken egg production will lead to a decrease in the fat content of cow's milk or a decrease in the mass of chicken eggs and vice versa.


- Independent Culling Levels: This is a method in which the minimum level for each trait that needs to be selected is set at the same time. Selected animals are those that achieve at least the minimum level for all of these traits. Animals that do not

Any animal that achieves any minimum level of any trait is eliminated. For example, for selecting boars, two minimum standards are proposed: growth rate must be above 780 g/day and backfat thickness measured by ultrasound must be below 21 mm. This method has the advantage of being simple, and can simultaneously select for improvement of many traits. However, due to the independence of the traits to be selected, this method will lead to the elimination of animals with high productivity in traits with high heritability just because they do not meet the requirements in traits with low heritability.


- Selection Index: Is a method of combining the phenotypic values ​​of the traits determined on the animal itself or on its close relatives into a composite score and based on this score to select or eliminate the animal. For example, in the case of selecting male breeding pigs mentioned above, the selection index has the formula:

I = G - 12B

in which, I: Index of boar

G: Growth rate of male pigs (g/day)

B: Back fat thickness measured by ultrasound of male pigs (mm)

Thus, the index is calculated for each animal, based on the index to rank the animals. The animals with the highest index are the animals with the highest breeding value and vice versa. Selection or culling based on the index means based on the breeding value of the animal. Let's observe the data monitoring the growth rate and backfat thickness of 100 boars and the selection results of the 20 best boars of 2 independent culling methods and the selection index in the following graph:






650 750 G=780 g/day 850 g/day


B=21mm


mm


Figure 7.1. The minimum level of selection is shown by the two lines G and B (G=780 g/day, B=21mm), and the observed data of 100 boars are shown by dots. The 20 individuals that the selection method considers to be the best are located in the lower right corner of these two dividing lines, and the 20 individuals that the selection index method considers to be the best are shown by x. Note that: there are 6 individuals located in the lower right corner near the intersection of G and B that are not accepted by the selection index method. Conversely, there are also 6 individuals with x but located outside the lower right corner, these individuals either have very low backfat thickness or have very high weight gain.


4. Selectivity index

4.1. Concept

The theory of selection index was built by H. Smith in 1936 based on the basis of the discriminant function applied in plant breeding selection. Hazel (1943) was the first to apply the selection index to animal selection. The discussions of Lush, Lasley later as well as selection experiments all confirmed that the selection index is a method with many advantages over sequential selection methods as well as independent elimination.

In essence, the selection index is a linear function of observed data to estimate the breeding value of an animal. The observed data are the phenotypic values ​​of one or more traits observed on the animal itself or on related animals. These phenotypic values ​​can be a single value of an observation or can be the average value of many repeated observations on one animal or on many different animals that are related to the animal whose breeding value we want to estimate.


Thus, the selection index is not only used to select multiple traits but also used to select a single trait.


The selection index has the following form:

I = b 1 X 1 + b 2 X 2 + ... + b n X n

I = b i X i [7.2]

in which, I : Index value of the object

X i : Phenotypic value of the traits that we observe on the object itself

or on a relative of the animal

b i : Coefficient corresponding to each trait or each relative animal.


To eliminate the influence of the homologous group (animals raised in the same batch, same conditions...), the phenotypic values ​​of each trait are the difference between the phenotypic value of the individual and the average value of the homologous group , so that

I = b 1 (X 1 - X 1 ) + b 2 (X 2 - X 2 ) + ... + b n (X n - X n )

I = b i (X i - X i ) [7.3]

in which, I : Index value of the object

X i : Phenotypic value of the traits that we observe on the object itself

or on a relative of the animal

X i : Average phenotypic value of traits that we observe on animals in the homologous group

b i : Coefficient corresponding to each trait or each relative animal.


For example, when testing the performance of Landrace boars in the Netherlands, the following selection index was used:

I = -12.61 X 1 + 1.62 X 2 - 88 X 3 + 28.8 X 4

in which, X 1 : Feed consumption during the test period (kg feed/kg weight gain) X 2 : Average weight gain during the test period (g/day)

X 3 : Back fat thickness measured by ultrasound (mm)

X 4 : Area of ​​“flesh eye” measured by ultrasound (mm3)


The question arises as to what basis are the coefficients b i given in this example as well as in the example of selection for two traits, backfat thickness and average weight gain? The following sections will describe in detail the principles and methods for calculating the coefficients b i in the selection index.



max;

4.2. Equations of the selectivity index

The four criteria and also the four advantages of the selection index are as follows:

- The correlation between the index (I) and the breed value (A) of the animal is the largest, meaning that r AI =


- The probability that the order of animals arranged by index matches the order of animals arranged by price

their seed value is the greatest;

- Genetic progress achieved by selection based on the index is the largest, that is, g =

max;

- The square of the difference between the index and the breed value of the animal is the smallest, meaning that

E(IA) 2 = min.

The above four criteria are closely related, so satisfying only one of these four criteria is sufficient.

Starting from the first criterion, we seek to calculate the coefficients b i of the selection index.

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