Construction and use of selection index

CONSTRUCTION AND USE OF SELECTION INDEX : 

CONSTRUCTION AND USE OF SELECTION INDEX Presented by Hetu Dan Dept. of Animal Genetics & Breeding C.V.A.S , Bikaner

Selection Index : 

Selection Index The breeder when wants to select the animal on the basis of several traits that can vary greatly are combined in to one value or total score which is known as selection index. The main aim of computing this index is to drive an estimate in which the various traits are weighted to give the best prediction of animal’s breeding value.

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The selection index for single trait can be formed on the basis of information from different relatives. When selecting two or more traits and information is available on the individual and its relatives .

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The amount of weight given to each trait depends upon its relative economic value, the heritability of the trait and genetic and phenotypic correlation between the traits. If the traits are uncorrelated, each character is weighted by the product of relative economic value and its heritability.

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Information required for construction of selection index :- Genetic and phenotypic variance for each trait considered in selection index. The genetic and phenotypic co-variances (Cova and Covp) between each pair of traits. Heritability, genetic and phenotypic correlation among traits. The heritability and genetic correlation are used to obtain the estimate of variance and co-variance component. The economic weights for each trait.

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The genetic worth of an individual is expressed as H=a1G1+a2G2+a3G3+…………….anGn Where : G1G2,……………Gn are the genotype value of individual character . a1,a2…………..an to their relative economic importance.

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The phenotype of an individual based on the phenotype performance of various traits is defined as: I=b1X1+b2X2+……………..bnXn Where X1,X2………………..Xn are the phenotypic value of the trait. b1, b2………………..bn are the coefficient for each trait. These coefficient are to be estimated in such a way that the correlation between H& I become maximum.

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The maximization of r (H,I) leads to the following equation: b1X11+b2X12+…...bnX1n=a1G11+a2G12+….a1nG1n b1X21+b2X22+….bnX2n=a1Gn1+a2Gn2+…..a2nGnn b1Xn1+b2Xn2+…...bnXnn=a1Gn1+a2Gn2+….anGnn

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Where, Xi=Phenotypic variance of ith trait Gi=Additive genetic variance of ith trait Xij=Phenotypic co-variance of ith and jth Gij=Additive genetic co-variance bi= Partial regression coefficient of ith trait ai= Economic weight of ith trait

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X11 X12 …….X1n b1 G11 G12 ……. G1n a1 X21 X22 …….X2n b2 G21 G22 ……. G2n a2 . . . . . . . . . . . * . = . . . * . . . . . . . . . . . . . . . . . Xn1 Xn2 Xij bn Gn1 Gn2 Gn an

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The solution of this equation give the estimate of b1 values in the following manner : b = X-1 G a Where, b=column vector X-1=inverse of phenotypic variance &co-variance matrix G = Genotypic variance & co-variance matrix a=column vector for the economic weights.

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Two traits selection index :- When two traits for construction of selection index are used then the genetic worth of an individual can be expressed as H=a1G1+a2G2 Where, G1,G2 are the genotype values of individual character and a1,a2, refer to their relative economic importance.

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The phenotype of an individual based on the phenotype performance is as : I=b1X1+b2X2 Where, X1,X2 are the phenotypic values of the traits 1 and 2 and b1, b2 are coefficient for each trait.

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The maximization of r(H,I) Leads to a set of simultaneous equation which upon solving give the desired estimate of b1 considering n traits , the simultaneous equation are as follows : b1X11+b2X12 = a1G11+a2G12……..(i) b1X21+b2X22 = a1Gn1+a2Gn2……..(ii) Where, X11 and X22 are variance component X12 and X21 are co-variance component

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Divide equation (i) by covariance X12 and equation (ii) by variance X22 , the resulting equation are:- X11 G11 G12 b1 + b2 = a1 + a2 ……(iii) X12 X12 X12 X21 G21 G22 b1 + b2 = a1 + a2 .......(iv) X22 X22 X22

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Subtracting the equation (iii) & (iv), we will get the value of b1 & b2 . a1(G11-G21) + a2(G12-G22) b1 = X11X22 – X12X21

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a1G11 + a2G12 X11 b2 = - b1 X12 X22

USES OF SELECTION INDEX : 

USES OF SELECTION INDEX Selection indexes have been extensively applied in the estimation of breeding value of animals for combinations of traits for selection purposes.

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Thanks