Optimum and Decorrelated Constrained Multistage Linear Phenotypic Selection Indices Theory

Cerón-Rojas, J. Jesús; Toledo, Fernando H.; Crossa, José

doi:10.2135/cropsci2019.04.0241

Cited by 5 publications

(25 citation statements)

References 29 publications

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“…We found similar results for the simulated dataset. Our results were in accordance with those of Börner and Reinsch (2012) and Cerón-Rojas et al (2019b) when these authors compared the optimum with the decorrelated multistage indices in the genomic and phenotypic selection context, respectively. Börner and Reinsch (2012) called the decorrelated multistage index results counter-intuitive and difficult to interpret.…”

Section: Methods For Obtaining the Ocmlgsi Selection Intensitysupporting

confidence: 92%

Combined Multistage Linear Genomic Selection Indices To Predict the Net Genetic Merit in Plant Breeding

Cerón-Rojas¹,

Crossa

2020

G3 Genes|Genomes|Genetics

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A combined multistage linear genomic selection index (CMLGSI) is a linear combination of phenotypic and genomic estimated breeding values useful for predicting the individual net genetic merit, which in turn is a linear combination of the true unobservable breeding values of the traits weighted by their respective economic values. The CMLGSI is a cost-saving strategy for improving multiple traits because the breeder does not need to measure all traits at each stage. The optimum (OCMLGSI) and decorrelated (DCMLGSI) indices are the main CMLGSIs. Whereas the OCMLGSI takes into consideration the index correlation values among stages, the DCMLGSI imposes the restriction that the index correlation values among stages be zero. Using real and simulated datasets, we compared the efficiency of both indices in a two-stage context. The criteria we applied to compare the efficiency of both indices were that the total selection response of each index must be lower than or equal to the single-stage combined linear genomic selection index (CLGSI) response and that the correlation of each index with the net genetic merit should be maximum. Using four different total proportions for the real dataset, the estimated total OCMLGSI and DCMLGSI responses explained 97.5% and 90%, respectively, of the estimated single-stage CLGSI selection response. In addition, at stage two, the estimated correlations of the OCMLGSI and the DCMLGSI with the net genetic merit were 0.84 and 0.63, respectively. We found similar results for the simulated datasets. Thus, we recommend using the OCMLGSI when performing multistage selection.

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Section: Methods For Obtaining the Ocmlgsi Selection Intensitysupporting

confidence: 92%

Combined Multistage Linear Genomic Selection Indices To Predict the Net Genetic Merit in Plant Breeding

Cerón-Rojas¹,

Crossa

2020

G3 Genes|Genomes|Genetics

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“…Cerón-Rojas JJ, et al [3,4] developed decorrelated constrained selection indices for multi-stage selection. These indices minimize the mean-squared difference between the index and the aggregate genotype at each stage under the restriction that the covariance between the indices at different stages is zero, thus preventing correlation between index values at different stages.…”

Section: Two-stage Selection According To Decorrelated Constrained Selection Indicesmentioning

confidence: 99%

“…The profitability of breeding operations can be improved by reducing the cost of measuring traits expressed later in life, which is the cost of maintaining the animal for a longer period of time in single-stage selection. Cotterill PP and James JW [2] presented a general approximation of genetic gain after two stages of selection under the assumption that the distribution of traits after stage-one selection remains roughly normally distributed, and Cerón-Rojas JJ, et al [3,4] have presented an optimum multistage linear phenotypic selection index that reflects this assumption. In addition, Cerón-Rojas JJ, et al [3,4] have created a decorrelated multistage linear phenotypic selection index-that is, one that uses independent indices for selection during a generation to maximize the breeding goal.…”

Section: Introductionmentioning

confidence: 99%

“…Cotterill PP and James JW [2] presented a general approximation of genetic gain after two stages of selection under the assumption that the distribution of traits after stage-one selection remains roughly normally distributed, and Cerón-Rojas JJ, et al [3,4] have presented an optimum multistage linear phenotypic selection index that reflects this assumption. In addition, Cerón-Rojas JJ, et al [3,4] have created a decorrelated multistage linear phenotypic selection index-that is, one that uses independent indices for selection during a generation to maximize the breeding goal. Xu SZ and Muir WM [5,6] developed a fairly general approach that is based on transforming the indices during a generation to a set of orthogonal values that is, independent selection indices.…”

Section: Introductionmentioning

confidence: 99%

“…The main purpose of our current study was to develop formulas for predicting deterministically the genetic response due to two-stage selection composed of GEBVs from generation to generation until an asymptotic genetic response was reached. One formula incorporates the assumption that the traits in stages subsequent to the first round of selection remain roughly normally distributed [2], whereas the other formula uses independent indices during first-and secondstage selection [3,4]. Our secondary aims were to apply the formulas to several scenarios and to compare the asymptotic responses due to two-stage selection with those of single-stage selection, focusing on differences in economic weights, the selection percentage of young parents to all parents to produce the next generation, and the heritability of the component traits of the index.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Genetic Response Due to Two-Stage Genomic Index Selection Derived from Correlated or Independent Indices during Both Stages

Togashi¹,

Adachi²,

Kurogi³

et al. 2021

J Anim Sci Res

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We developed equations to predict the asymptotic response due to two-stage selection, where first-stage selection was performed by using GEBVs based solely on genotypes and second-stage selection was performed with GEBVs that combined genotypes and phenotypes. The situation that we considered involved four-path selection executed as sires to breed sons, sires to breed daughters, dams to breed sons, and dams to breed daughters. We established two procedures to predict the response. The first incorporated correlated indices during the first and second-stage selections of two-stage selection. The other procedure used independent indices during two-stage selection. The response per generation in the initial generation was greater for the correlated indices than for the independent indices. However, the asymptotic response per generation was slightly greater for the independent indices than for the correlated indices. The asymptotic response per generation was lower during two-stage selection than during single-stage selection. However, the asymptotic response per year was greater for two-stage selection than for single-stage selection. In addition, that trend was more conspicuous when the economic weight was 1:3 for the first (h2 =0.3) to second (h2 =0.05) index trait compared with economic weights of 1:1 and 3:1. However, the magnitude of the response to the aggregate genotype-relative not to single-stage selection but to absolute magnitude was greater at an economic weight of 3:1 than at those of 1:1 and 1:3. The reduction in genetic variance from the initial to an asymptotic generation was greater for a scenario where young parents selected at the first-stage accounted for 30% of all parents in two-stage selection than where they accounted for 70%. The reduction in genetic variance of the aggregate genotype over generations was smaller for independent indices than correlated indices during two-stage selection. Our new formula for predicting genetic response applies to any combination of accuracies of GEBVs and intensities of selection. Therefore, the formula presented is a general equation for predicting genetic response over generations due to two-stage genomic index selection.

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The statistical theory of linear selection indices from phenotypic to genomic selection

Cerón-Rojas

Crossa

2022

Crop Science

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A linear selection index (LSI) can be a linear combination of phenotypic values, marker scores, and genomic estimated breeding values (GEBVs); phenotypic values and marker scores; or phenotypic values and GEBVs jointly. The main objective of the LSI is to predict the net genetic merit (H), which is a linear combination of unobservable individual traits' breeding values, weighted by the trait economic values; thus, the target of LSI is not a parameter but rather the unobserved random H values. The LSI can be single-stage or multi-stage, where the latter are methods for selecting one or more individual traits available at different times or stages of development in both plants and animals. Likewise, LSIs can be either constrained or unconstrained.A constrained LSI imposes predetermined genetic gain on expected genetic gain per trait and includes the unconstrained LSI as particular cases. The main LSI parameters are the selection response, the expected genetic gain per trait, and its correlation with H. When the population mean is zero, the selection response and expected genetic gain per trait are, respectively, the conditional mean of H and the genotypic values,given the LSI values. The application of LSI theory is rapidly diversifying; however, because LSIs are based on the best linear predictor and on the canonical correlation theory, the LSI theory can be explained in a simple form. We provided a review of the statistical theory of the LSI from phenotypic to genomic selection showing their relationships, advantages, and limitations, which should allow breeders to use the LSI theory confidently in breeding programs.

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Optimum and Decorrelated Constrained Multistage Linear Phenotypic Selection Indices Theory

Cited by 5 publications

References 29 publications

Combined Multistage Linear Genomic Selection Indices To Predict the Net Genetic Merit in Plant Breeding

Combined Multistage Linear Genomic Selection Indices To Predict the Net Genetic Merit in Plant Breeding

Asymptotic Genetic Response Due to Two-Stage Genomic Index Selection Derived from Correlated or Independent Indices during Both Stages

The statistical theory of linear selection indices from phenotypic to genomic selection

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