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Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution

KEY MESSAGE: The expectation and variance of the estimator of the maximized index selection response allow the breeders to construct confidence intervals and to complete the analysis of a selection process. ABSTRACT: The maximized selection response and the correlation of the linear selection index...

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Autores principales: Cerón-Rojas, J. Jesus, Crossa, Jose
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7421161/
https://www.ncbi.nlm.nih.gov/pubmed/32561956
http://dx.doi.org/10.1007/s00122-020-03629-6
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author Cerón-Rojas, J. Jesus
Crossa, Jose
author_facet Cerón-Rojas, J. Jesus
Crossa, Jose
author_sort Cerón-Rojas, J. Jesus
collection PubMed
description KEY MESSAGE: The expectation and variance of the estimator of the maximized index selection response allow the breeders to construct confidence intervals and to complete the analysis of a selection process. ABSTRACT: The maximized selection response and the correlation of the linear selection index (LSI) with the net genetic merit are the main criterion to compare the efficiency of any LSI. The estimator of the maximized selection response is the square root of the variance of the estimated LSI values multiplied by the selection intensity. The expectation and variance of this estimator allow the breeder to construct confidence intervals and determine the appropriate sample size to complete the analysis of a selection process. Assuming that the estimated LSI values have normal distribution, we obtained those two parameters as follows. First, with the Fourier transform, we found the distribution of the variance of the estimated LSI values, which was a Gamma distribution; therefore, the expectation and variance of this distribution were the expectation and variance of the variance of the estimated LSI values. Second, with these results, we obtained the expectation and the variance of the estimator of the selection response using the Delta method. We validated the theoretical results in the phenotypic selection context using real and simulated dataset. With the simulated dataset, we compared the LSI efficiency when the genotypic covariance matrix is known versus when this matrix is estimated; the differences were not significant. We concluded that our results are valid for any LSI with normal distribution and that the method described in this work is useful for finding the expectation and variance of the estimator of any LSI response in the phenotypic or genomic selection context.
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spelling pubmed-74211612020-08-18 Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution Cerón-Rojas, J. Jesus Crossa, Jose Theor Appl Genet Original Article KEY MESSAGE: The expectation and variance of the estimator of the maximized index selection response allow the breeders to construct confidence intervals and to complete the analysis of a selection process. ABSTRACT: The maximized selection response and the correlation of the linear selection index (LSI) with the net genetic merit are the main criterion to compare the efficiency of any LSI. The estimator of the maximized selection response is the square root of the variance of the estimated LSI values multiplied by the selection intensity. The expectation and variance of this estimator allow the breeder to construct confidence intervals and determine the appropriate sample size to complete the analysis of a selection process. Assuming that the estimated LSI values have normal distribution, we obtained those two parameters as follows. First, with the Fourier transform, we found the distribution of the variance of the estimated LSI values, which was a Gamma distribution; therefore, the expectation and variance of this distribution were the expectation and variance of the variance of the estimated LSI values. Second, with these results, we obtained the expectation and the variance of the estimator of the selection response using the Delta method. We validated the theoretical results in the phenotypic selection context using real and simulated dataset. With the simulated dataset, we compared the LSI efficiency when the genotypic covariance matrix is known versus when this matrix is estimated; the differences were not significant. We concluded that our results are valid for any LSI with normal distribution and that the method described in this work is useful for finding the expectation and variance of the estimator of any LSI response in the phenotypic or genomic selection context. Springer Berlin Heidelberg 2020-06-20 2020 /pmc/articles/PMC7421161/ /pubmed/32561956 http://dx.doi.org/10.1007/s00122-020-03629-6 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Original Article
Cerón-Rojas, J. Jesus
Crossa, Jose
Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution
title Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution
title_full Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution
title_fullStr Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution
title_full_unstemmed Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution
title_short Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution
title_sort expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7421161/
https://www.ncbi.nlm.nih.gov/pubmed/32561956
http://dx.doi.org/10.1007/s00122-020-03629-6
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