A Molecular Selection Index Method Based on Eigenanalysis

Cerón-Rojas, J. Jesús; Castillo-González, Fernando; Sahagún-Castellanos, Jaime; Santacruz-Várela, Amalio; Benítez-Riquelme, Ignacio; Crossa, J.

doi:10.1534/genetics.108.087387

Cited by 25 publications

(22 citation statements)

References 18 publications

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“…By this reasoning, the PPG-PSI should be the basic tool for selecting individuals as parents of the next generation. We think that the Lande and Thompson (1990) index, the molecular eigen selection index (Cerón-Rojas et al, 2008b), and the Dekkers (2007) index, which use molecular marker information for making selections (the first two combine quantitative trait loci information with phenotypic information, whereas the third combines genomic estimated breeding values with phenotypic information), should be adapted to the PPG-PSI or the PPG-ESIM. The same should be done with the genomic selection indices of Togashi et al (2011) and Ceron-Rojas et al (2015).…”

Section: Importance Of the Ppg-psimentioning

confidence: 99%

“…For this reason, the sign and proportion values of the first eigenvectors for each selection cycle should follow the direction given by the breeder's interest on the expected genetic gain per each trait (Cerón-Rojas et al, 2008a, 2008b. Thus, if the expected genetic gain values for T1 and T3 are positive and negative for T2, if it is necessary, the sign of the values of the first eigenvector will be according to this objective, from where the diagonal matrix F should have a combination of signs and proportional values to achieve predetermined and positive values for T1 and T3 and predetermined and negative values for T2 in the linear transformation b = Fb PPG-ESIM .…”

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A Predetermined Proportional Gains Eigen Selection Index Method

et al. 2016

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The most general linear phenotypic selection index (PSI) is the predetermined proportional gains phenotypic selection index (PPG‐PSI) that allows imposing restrictions on the trait expected genetic gain values to make some traits change their mean values based on a predetermined level, while the rest of the traits remain without restrictions. However, due to the increasing number of restricted traits: (i) PPG‐PSI accuracy decreases; (ii) the proportional constant associated with this index can be negative, in which case, its results have no meaning in practice; and (iii) the PPG‐PSI can shift the population means in the opposite direction to the predetermined desired direction. Based on the eigen selection index method (ESIM), we propose a PPG‐ESIM that does not require a proportional constant, and due to the properties associated with eigen analysis, it is possible to use the theory of similar matrices to change the direction of the eigenvector values without affecting PPG‐ESIM accuracy, which helps to eliminate the problem indicated in the third point above, associated with the standard PPG‐PSI. The PPG‐ESIM uses the first eigenvector as its vector of coefficients, and the first eigenvalue in the selection response. Two simulated and one real data set, each with four traits, were used to validate PPG‐ESIM efficiency vs. PPG‐PSI efficiency; the simulated and real results indicated that PPG‐ESIM efficiency was higher than PPG‐PSI efficiency. We concluded that PPG‐ESIM is an efficient selection index that can be used in any selection program as a good alternative to PPG‐PSI.

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Section: Importance Of the Ppg-psimentioning

confidence: 99%

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confidence: 99%

A Predetermined Proportional Gains Eigen Selection Index Method

et al. 2016

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“…This selection index, which is a linear combination of the phenotypic values of the traits of interest with their previously defined economic weights (Smith 1936;Hazel 1943), will assess the total breeding value of individual offspring or families for several traits, and allow maximizing the response to selection for the set of traits. A molecular eigen selection index method (MESIM) based on the estimated effect of QTL linked to DNA markers can be further used to increase the response to selection when selecting simultaneously for several traits (Cerón-Rojas et al 2008). The first eigenvector is used as a selection index criterion, and its elements determine the percentage of the trait's contribution to this selection index.…”

Section: Plant Genomics and Marker-assisted Selectionmentioning

confidence: 99%

Population Improvement

Ríos

2015

Plant Breeding in the Omics Era

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Cyclical phenotypic selection methods such as mass selection in open-pollinated (OP) cultivars were used widely in plant breeding until the inbred-hybrid approach began in the first half of the twentieth century. Mass selection was very effective to breed distinct OP cultivars but not for selecting high-yielding cultivars. This failure was due to selecting individual plants for a low heritability trait such as edible yield, low correlation of traits used in selection with edible yield, inappropriate male gamete control resulting from weak plot isolation, and poor plot techniques unable to control local environmental effects. Hence, population improvement methods, such as recurrent selection aiming to increase the frequency of favorable alleles by selecting the superior individuals in a population, intermating them, and selecting the best among their offspring, were sought in plant breeding (Hallauer et al. 2010). Recurrent selection differs from mass selection because selected individuals from the base population undergo progeny testing, and thereafter those selected based on this progeny testing data are intermated with each other to form the new population. Selection ensuing from recurrent selection can be further used in pedigree breeding for recycling inbred lines.

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“…In addition to the relationships of b and b KN with the RESIM presented in this paper, we would like to point out the relationship of two indices developed in the molecular marker‐assisted selection (MAS) context: the Lande and Thompson (1990) and Dekkers (2007) selection indices with the molecular eigen selection index method (MESIM) of Cerón‐Rojas et al (2008a) which, besides the phenotypic information, also uses molecular information to predict the net genetic merit. In theory, MESIM is very similar to RESIM.…”

Section: Resultsmentioning

confidence: 99%

“…[1]. From the covariance matrix of x , we can find one measure of the association between p and g using the canonical correlation theory (Anderson, 1999, 2003; Cerón‐Rojas et al, 2008a). In this case, the solution is

({normalP}^{- 1} G - {normalλ}_{j}^{2} I) {normalβ}_{j} = 0

where β j , the j th eigenvector, and λ j , the j th

(j = 1, 2, \cdot \cdot \cdot, t)

canonical correlation of p and g can be used to find the sampling statistical properties of Eq.…”

Section: Methodsmentioning

confidence: 99%

Statistical Sampling Properties of the Coefficients of Three Phenotypic Selection Indices

2016

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The aim of the Smith phenotypic selection index (SPSI), the restricted phenotypic selection index (RPSI), and the predetermined proportional gains phenotypic selection index (PPG‐PSI) is to maximize the response to selection and provide the breeder with an objective rule for evaluating and selecting several traits. When the phenotypic and genotypic variances and covariances are known, these three indices are the best linear predictors. When these parameters are estimated, the three indices will be optimal only if the estimators of the index weights are unbiased and have minimal variance. There are many methods for determining the sampling properties of the SPSI but there is no method for determining the sampling properties of RPSI and PPG‐PSI coefficients. Using the canonical correlation theory, we proposed an asymptotic method for determining the statistical sampling properties of the estimators of the coefficients of the three phenotypic selection indices. We showed that under some assumptions, the sampling properties of the RPSI and PPG‐PSI coefficient estimators could be obtained using the sampling properties of the SPSI coefficient estimator. We validated the theoretical results using two real datasets. The theoretical and numerical results indicated that the three estimators of the weights for the three indices were unbiased with minimal variances. We concluded that when the number of genotypes is large, the proposed method could be used to find the sampling properties of the coefficient of the three indices.

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A Molecular Selection Index Method Based on Eigenanalysis

Cited by 25 publications

References 18 publications

A Predetermined Proportional Gains Eigen Selection Index Method

A Predetermined Proportional Gains Eigen Selection Index Method

Population Improvement

Statistical Sampling Properties of the Coefficients of Three Phenotypic Selection Indices

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