, Volume 51, Issue 1, pp 1-3

Heritability of a linear combination of traits

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The heritability, h I 2 , of a linear combination of phenotypes, I, when defined as the ratio of the variance of the genetic index, σ g⋆ 2 *, to the variance of the index, σ I 2 , is shown to be different from the square of the correlation, r HI 2 , between the index and an arbitrary linear combination of genetic effects, H. The gain in H fror selection on I is shown to be proportional to h I 2 . bHg⋆ for any index.

Approved for publication as Journal Article No. 183-76 of the Ohio Agricultural Research and Development Center, Wooster, Ohio 44691.
Communicated by L.D. Van Vleck