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CROP BREEDING & GENETICS

A Selection Index Method Based on Eigenanalysis

^a Colegio de Postgraduados, Km 36.5, Carretera México-Texcoco, Montecillo, Edo. de México, México
^b Biometrics and Statistics Unit, International Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, México DF, México
^c Universidad Autónoma de Chapingo, CP 56230, Km 38.5, Carretera México-Texcoco, Chapingo, Edo. de México, México
^d Colegio de Postgraduados, Km 36.5, Carretera México-Texcoco, Montecillo, Edo. de México, México

^* Corresponding author (j.crossa{at}cgiar.org)

In plant breeding, selection indices (SI) help select the best individuals for the next breeding cycle on the basis of observed phenotypic values for several traits of each candidate individual. Selection indices, as originally defined by Smith (1936), assign subjective economic weights to each trait and are relatively simple to analyze. Their disadvantages are that they require large amounts of information; economic weights are difficult to assign; sampling error can be large; and the statistical sampling properties of SI of the selection response are unknown except in the case of two traits. The objective of this study is to propose and use an SI based on the eigenanalysis method (ESIM), in which the first eigenvector is used as the SI criterion and its elements determine the proportion of the trait that contributes to the SI and are used in the selection response. ESIM does not require assigning economic weights or estimates of the genotypic covariance matrix. Statistical properties of the estimators of ESIM and its response to selection are described. It is shown how ESIM estimates selection gains between selection cycles. A predictive function of the ESIM selection response in future selection cycles is proposed. Three data sets are used to show the properties of ESIM.