“Theory of Index Selection”, 1997-08-04 (; backlinks; similar):
While Chapters 28 and 29 present the basic theory for multivariate response, how, in practice, does one perform artificial selection on multiple traits? One of the commonest schemes is to construct some sort of index, wherein the investigator assigns (either explicitly or implicitly) a weighting scheme to each trait, creating a univariate character that becomes the target of selection. For example, if z is the vector of character values measured in an individual, the most common index is a linear combination Pbizi = bT z and most of our discussion focuses on such linear indices.
We start with a general review of the theory of selection on a linear index and then cover in great detail the Smith-Hazel index (the index giving the largest expected response in a specified linear combination of characters) and its extensions. We also discuss a number of other indices for different purposes, such as restricted (constraining changes in specified traits) and desired-gains (specifying how the components, rather than the index, will evolve) indices. We conclude our discussion of index selection by considering how to best handle nonlinear indices.
We finish the chapter by examining the other approach for selecting on multiple traits, namely choosing traits sequentially. Tandem selection, focusing on a single trait each generation (where the focal trait changes over generations) is one such approach, while the other is to select different traits at different times within the life span of single individuals (independent culling and multistage index selection).
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