Summary
Two methods of deriving linear selection indices for non-linear profit functions have been proposed. One is by linear approximation of profit, and another is the graphical method of Moav and Hill (1966). When profit is defined as the function of population means, the graphical method is optimal. In this paper, profit is defined as the function of the phenotypic values of individual animals; it is then shown that the graphical method is not generally optimal. We propose new methods for constructing selection indices. First, a numerical method equivalent to the graphical method is proposed. Furthermore, we propose two other methods using quadratic approximation of profit: one is based on Taylor series about means before selection, and the other is based on Tayler series about means after selection. Among these different methods, it is shown that the method using quadratic approximation based on Taylor series about means after selection is the most efficient.
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Communicated by J.S.F. Barker
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Itoh, Y., Yamada, Y. Linear selection indices for non-linear profit functions. Theoret. Appl. Genetics 75, 553–560 (1988). https://doi.org/10.1007/BF00289120
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DOI: https://doi.org/10.1007/BF00289120