Abstract
The main distinction in the linear phenotypic selection index (LPSI) theory is between the net genetic merit and the LPSI. The net genetic merit is a linear combination of the true unobservable breeding values of the traits weighted by their respective economic values, whereas the LPSI is a linear combination of several observable and optimally weighted phenotypic trait values. It is assumed that the net genetic merit and the LPSI have bivariate normal distribution; thus, the regression of the net genetic merit on the LPSI is linear. The aims of the LPSI theory are to predict the net genetic merit, maximize the selection response and the expected genetic gains per trait (or multi-trait selection response), and provide the breeder with an objective rule for evaluating and selecting parents for the next selection cycle based on several traits. The selection response is the mean of the progeny of the selected parents, whereas the expected genetic gain per trait, or multi-trait selection response, is the population means of each trait under selection of the progeny of the selected parents. The LPSI allows extra merit in one trait to offset slight defects in another; thus, with its use, individuals with very high merit in one trait are saved for breeding even when they are slightly inferior in other traits. This chapter describes the LPSI theory and practice. We illustrate the theoretical results of the LPSI using real and simulated data. We end this chapter with a brief description of the quadratic selection index and its relationship with the LPSI.
Highlights
The main distinction in the linear phenotypic selection index (LPSI) theory is between the net genetic merit and the LPSI
The net genetic merit of an individual is not observable; to select an individual as parent of the generation, it is necessary to consider its overall merit based on several observable traits; that is, we need to construct an LPSI of observable phenotypic values such that the correlation between the LPSI and H 1⁄4 w0g is at a maximum
Is the covariance between g and y weighted by the standard deviation of the variance of y, CovσðII;gÞ is the covariance between the breeding value vector and the LPSI values weighted by the standard deviation of the variance of LPSI
Summary
The study of quantitative traits (QTs) in plants and animals is based on the mean and variance of phenotypic values of QTs. Quantitative traits are phenotypic expressions of plant and animal characteristics that show continuous variability and are the result of many gene effects interacting among them and with the environment. QTs are the result of unobservable gene effects distributed across plant or animal genomes that interact among themselves and with the environment to produce the observable characteristic plant and animal phenotypes (Mather and Jinks 1971; Falconer and Mackay 1996).
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