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Some statistical properties of an index of multiple traits

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Hazel (1943) defined a selection index that maximizes the correlation, RIH, between the index, I=ΣbiXi and its aggregate genetic value, H=Σaigi, where the bi's are the derived coefficients of the observed traits, Xi, the ai's are their relative economic values and the gi's are their respective breeding values. This is called an optimum index. The expected value of the index is not H but rather K=Σbigi. The ratio of RHI/RKI is always less than or equal to 1.0. With selection on I, the ratio of the change in K to the change in H is the true heritability of the indez, that is, h I 2 =Δ(K)/ΔH. This is not the same as R IH 2 , which serves only as the predictor of the change in H with selection on I. If the index, I, itself is considered as a unit trait, studies can then be made of correlated response in I when selection is based only on a single trait in the index. I is then called a performance index. This approach provides for additional insight into the question of the failure of selection to make gains in total performance over many generations.

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  1. Hazel, L.N.: The genetic basis for constructing selection indexes. Genetics 28, 476–490 (1943)

  2. Kinney, T.B.; Bohren, B.B.; Craig, J.V.; Lowe, P.C.: Responses to individual, family or index selection for short term rate of egg production in chickens. Poultry Sci. 49, 1052–1064 (1970)

  3. Nordskog, A.W.: Multi-trait selection and egg production in chickens. Proc. 1st World Cong. Genet. Appl. to L.S. Prod. 1, 917 (1974)

  4. Nordskog, A.W.; Tolman, H.S.; Cascy, D.W.; Lin, C.Y.: Selection in small populations of chickens. Poultry Sci. 53, 1188–1219 (1974)

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Journal Paper No. J-8176 of the Iowa Agriculture and Home Economics Experiment Station, Project 1711.

Editor's Note: This paper and one closely similar (Lin and Allaire T.A.G. 51, 1–3 (1977) were independently derived and reviewed by different corresponding editors. The earlier paper, however, lacks numerical examples and a possible application as discussed in the present paper.

Communicated by H. Abplanalp

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Nordskog, A.W. Some statistical properties of an index of multiple traits. Theoret. Appl. Genetics 52, 91–94 (1978).

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Key words

  • Selection index
  • Performance Index
  • I