A Molecular Selection Index Method Based on Eigenanalysis
Cerón-Rojas, J. Jesús, Castillo-González, Fernando, Sahagún-Castellanos, Jaime, Santacruz-Varela, Amalio, Benítez-Riquelme, Ignacio, Crossa, José, Genetics
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.
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MARKER-ASSISTED selection (MAS) is an important 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 ofMASis basedonthe molecular selection index (MSI) proposed by Lande andThompson (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 (Zhang and 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 phenotypic values on the coded values of the molecular markers such that selected molecular markers are those statistically linked to QTL that explain most of the variability in regression models. The coefficient of regression of the molecular marker is the MQTL effect. Statistical models and methods for mapping QTL and estimating their MQTL effects have been developed ( Jansen 2003). Several authors have pointed out the effectiveness of the MSI in inbred populations with large population sizes and traits with low heritability values (Zhang and Smith 1992, 1993; Gimelfarb and Lande 1994, 1995; Whittaker 2003) when only one trait (and its associated molecular score) is considered.
The selection index theory was originally developed by Smith (1936) and generalized by Kempthorne and Nordskog (1959) for a restrictive selection index. The standard selection index is defined as a linear combination of the observed phenotypic values of the traits of interest with the traits' previously defined economic weights. …