The traditional molecular selection index (MSI) employed in marker-assisted selection maximizes the selection response by combining information on molecular markers linked to quantitative trait loci (QTL) and phenotypic values of the traits of the individuals of interest. This study proposes an MSI based on an eigenanalysis method (molecular eigen selection index method, MESIM), where the first eigenvector is used as a selection index criterion, and its elements determine the proportion of the trait's contribution to the selection index. This article develops the theoretical framework of MESIM. Simulation results show that the genotypic means and the expected selection response from MESIM for each trait are equal to or greater than those from the traditional MSI. When several traits are simultaneously selected, MESIM performs well for traits with relatively low heritability. The main advantages of MESIM over the traditional molecular selection index are that its statistical sampling properties are known and that it does not require economic weights and thus can be used in practical applications when all or some of the traits need to be improved simultaneously.
M ARKER-ASSISTED selection (MAS) is an impor-tant breeding tool in which molecular marker alleles linked to quantitative trait loci (QTL) that control phenotypic variables of important traits are selected. Marker-assisted selection can be more efficient than selecting individuals on the basis of phenotypic trait values. Progeny of specific progenitors can be selected on the basis of molecular markers as long as these are associated with breeding values of the traits under consideration. This is one form of MAS (Dekkers and Dentine 1991; Arus and Moreno-Gonzalez 1993). Another form of MAS is based on the molecular selection index (MSI) proposed by Lande and Thompson (1990). In MSI the selection response is maximized by combining information on molecular markers linked to QTL and the phenotypic values of the traits of interest.To construct an MSI, it is necessary to identify the linkage between the molecular marker and the QTL, the estimated effect of the QTL linked to the molecular marker (MQTL effect), and the combination of MQTL effects and phenotypic information that allows genotypes to be classified and selected using a selection index. The MQTL effects can be identified and estimated through the linkage disequilibrium that arises when crossing inbred lines or divergent populations Smith 1992, 1993;Xie and Xu 1998). The MSI depends on various factors, such as number and density of molecular markers associated with QTL, population size, trait heritability, additive genetic variances that can be explained by molecular markers, and precision of the estimated effect of gene substitution (Dekkers and Dentine 1991;Moreau et al. 2000).The MSI is an application of the selection index methodology proposed by Smith (1936), in which MQTL effects are incorporated. As proposed by Lande and Thompson (1990), the MSI performs a linear regression of phenotypi...