Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFLA |
Texto Completo: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1413-70542003000500020 http://repositorio.ufla.br/jspui/handle/1/5780 |
Resumo: | The diallel analysis model proposed by Gardner and Eberhart (1966) has been used to evaluate and select superior genotypes in plant breeding programs and to study several characters of genetic inheritance. However, the diallel model is non orthogonal as pointed out by the authors. Dependencies can also be generated by losses of genotypes' means, and that can lead to erroneous interpretation of the tested hypotheses because when the model is non orthogonal or unbalanced there are different approaches to the proposed hypotheses that generate different values for the sums of squares. This work intends to determine how the sums of squares of the diallel model effect and their associated hypotheses are affected, including the situations of losses of genotype means. Examples of complete and partial diallels were used and the type I sums of squares were determined by means of successive reductions of the unrestricted model according to the procedure used by the SAS and they were compared with the type III sums of squares, obtained through the inverse-of-part-of-inverse algorithm. The associated hypotheses were also compared. The type I was obtained through the estimable functions reported in the GLM of the SAS system and the type III was obtained by means of the procedure described by Searle (1987), that are correspondent to obtain the solution of Wrβ = Wβ. The analysis of the complete and partial diallel models, with or without losses of means, was affected in a way similar to the sums of squares and associated hypotheses. It was verified that the losses of crossing means affected in a different way the type I and III sums of squares and the associated hypotheses of most of the effects and that heterosis was not affected by losses of parents' means. The complete and partial diallel, without losses of means, only presented differences between the sums of squares and associated type I and III hypotheses for parents confirming the natural non-orthogonality of the adopted model. |
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Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e EberhartSome insights into the sums of square and associated hypotheses of the Gardner and Eberhart diallel modelTestes de hipóteses estatísticasGenética – Modelos matemáticosStatistical hypothesis testingGenetics – Mathematical modelsThe diallel analysis model proposed by Gardner and Eberhart (1966) has been used to evaluate and select superior genotypes in plant breeding programs and to study several characters of genetic inheritance. However, the diallel model is non orthogonal as pointed out by the authors. Dependencies can also be generated by losses of genotypes' means, and that can lead to erroneous interpretation of the tested hypotheses because when the model is non orthogonal or unbalanced there are different approaches to the proposed hypotheses that generate different values for the sums of squares. This work intends to determine how the sums of squares of the diallel model effect and their associated hypotheses are affected, including the situations of losses of genotype means. Examples of complete and partial diallels were used and the type I sums of squares were determined by means of successive reductions of the unrestricted model according to the procedure used by the SAS and they were compared with the type III sums of squares, obtained through the inverse-of-part-of-inverse algorithm. The associated hypotheses were also compared. The type I was obtained through the estimable functions reported in the GLM of the SAS system and the type III was obtained by means of the procedure described by Searle (1987), that are correspondent to obtain the solution of Wrβ = Wβ. The analysis of the complete and partial diallel models, with or without losses of means, was affected in a way similar to the sums of squares and associated hypotheses. It was verified that the losses of crossing means affected in a different way the type I and III sums of squares and the associated hypotheses of most of the effects and that heterosis was not affected by losses of parents' means. The complete and partial diallel, without losses of means, only presented differences between the sums of squares and associated type I and III hypotheses for parents confirming the natural non-orthogonality of the adopted model.Quando o modelo estatístico não é ortogonal ou nos casos de desbalanceamento, existem diferentes critérios para a formulação de hipóteses que geram diferentes valores para as somas de quadrados. O modelo de análise dialélica proposto por Gardner e Eberhart (1966) é um dos mais utilizados, mas apresenta uma não-ortogonalidade dos parâmetros genéticos. Objetivou-se com este estudo determinar de que forma são afetadas as somas de quadrados dos efeitos do modelo e suas hipóteses associadas, inclusive em casos de perdas de parcelas. Foram utilizados exemplos de dialelos completos e parciais, obtendo-se as somas de quadrados do tipo I por meio de reduções sucessivas do modelo superparametrizado, que foram comparadas com as somas de quadrados do tipo III, obtidas com o algorítmo inversa-de-parte-da-inversa. As hipóteses associadas a essas somas de quadrados também foram comparadas, sendo as do tipo I obtidas pelas funções estimáveis conforme o GLM do SAS, e as do tipo III, por meio do procedimento descrito por Searle (1987), que corresponde à obtenção da solução de Wrβ=Wβ. Pelos resultados, verificou-se que a análise dos dialelos completos e parciais, com ou sem perdas de parcelas, foi afetada de maneira análoga nas somas de quadrados e hipóteses associadas. Também verificou-se que as perdas de cruzamentos provocaram variação nas somas de quadrados tipos I e III e hipóteses associadas da maioria dos efeitos, e que as hipóteses sobre a heterose não foram afetadas por perda de parcelas de genitores. Os dialelos completos e parciais, sem perdas de parcelas, apresentaram variação entre as somas de quadrados e hipóteses associadas tipos I e III apenas para genitores, confirmando tratar-se de modelo naturalmente não-ortogonal.Editora da Universidade Federal de Lavras2003-10-012015-04-30T13:32:51Z2015-04-30T13:32:51Z2015-04-30info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articletext/htmlhttp://www.scielo.br/scielo.php?script=sci_arttext&pid=S1413-70542003000500020LIMA, P. C. et al. Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart. Ciência e Agrotecnologia, Lavras, v. 27, n. 5, p. 1113-1121, set./out. 2003.http://repositorio.ufla.br/jspui/handle/1/5780Ciência e Agrotecnologia v.27 n.5 2003reponame:Repositório Institucional da UFLAinstname:Universidade Federal de Lavras (UFLA)instacron:UFLALima, Paulo CésarFerreira, Daniel FurtadoBueno Filho, Julio Sílvio de SousaRamalho, Magno Antônio Pattoporinfo:eu-repo/semantics/openAccess2016-10-10T12:03:26Zoai:localhost:1/5780Repositório InstitucionalPUBhttp://repositorio.ufla.br/oai/requestnivaldo@ufla.br || repositorio.biblioteca@ufla.bropendoar:2016-10-10T12:03:26Repositório Institucional da UFLA - Universidade Federal de Lavras (UFLA)false |
dc.title.none.fl_str_mv |
Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart Some insights into the sums of square and associated hypotheses of the Gardner and Eberhart diallel model |
title |
Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart |
spellingShingle |
Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart Lima, Paulo César Testes de hipóteses estatísticas Genética – Modelos matemáticos Statistical hypothesis testing Genetics – Mathematical models |
title_short |
Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart |
title_full |
Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart |
title_fullStr |
Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart |
title_full_unstemmed |
Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart |
title_sort |
Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart |
author |
Lima, Paulo César |
author_facet |
Lima, Paulo César Ferreira, Daniel Furtado Bueno Filho, Julio Sílvio de Sousa Ramalho, Magno Antônio Patto |
author_role |
author |
author2 |
Ferreira, Daniel Furtado Bueno Filho, Julio Sílvio de Sousa Ramalho, Magno Antônio Patto |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Lima, Paulo César Ferreira, Daniel Furtado Bueno Filho, Julio Sílvio de Sousa Ramalho, Magno Antônio Patto |
dc.subject.por.fl_str_mv |
Testes de hipóteses estatísticas Genética – Modelos matemáticos Statistical hypothesis testing Genetics – Mathematical models |
topic |
Testes de hipóteses estatísticas Genética – Modelos matemáticos Statistical hypothesis testing Genetics – Mathematical models |
description |
The diallel analysis model proposed by Gardner and Eberhart (1966) has been used to evaluate and select superior genotypes in plant breeding programs and to study several characters of genetic inheritance. However, the diallel model is non orthogonal as pointed out by the authors. Dependencies can also be generated by losses of genotypes' means, and that can lead to erroneous interpretation of the tested hypotheses because when the model is non orthogonal or unbalanced there are different approaches to the proposed hypotheses that generate different values for the sums of squares. This work intends to determine how the sums of squares of the diallel model effect and their associated hypotheses are affected, including the situations of losses of genotype means. Examples of complete and partial diallels were used and the type I sums of squares were determined by means of successive reductions of the unrestricted model according to the procedure used by the SAS and they were compared with the type III sums of squares, obtained through the inverse-of-part-of-inverse algorithm. The associated hypotheses were also compared. The type I was obtained through the estimable functions reported in the GLM of the SAS system and the type III was obtained by means of the procedure described by Searle (1987), that are correspondent to obtain the solution of Wrβ = Wβ. The analysis of the complete and partial diallel models, with or without losses of means, was affected in a way similar to the sums of squares and associated hypotheses. It was verified that the losses of crossing means affected in a different way the type I and III sums of squares and the associated hypotheses of most of the effects and that heterosis was not affected by losses of parents' means. The complete and partial diallel, without losses of means, only presented differences between the sums of squares and associated type I and III hypotheses for parents confirming the natural non-orthogonality of the adopted model. |
publishDate |
2003 |
dc.date.none.fl_str_mv |
2003-10-01 2015-04-30T13:32:51Z 2015-04-30T13:32:51Z 2015-04-30 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1413-70542003000500020 LIMA, P. C. et al. Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart. Ciência e Agrotecnologia, Lavras, v. 27, n. 5, p. 1113-1121, set./out. 2003. http://repositorio.ufla.br/jspui/handle/1/5780 |
url |
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1413-70542003000500020 http://repositorio.ufla.br/jspui/handle/1/5780 |
identifier_str_mv |
LIMA, P. C. et al. Somas de quadrados e hipóteses associadas ao modelo dialélico de Gardner e Eberhart. Ciência e Agrotecnologia, Lavras, v. 27, n. 5, p. 1113-1121, set./out. 2003. |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Editora da Universidade Federal de Lavras |
publisher.none.fl_str_mv |
Editora da Universidade Federal de Lavras |
dc.source.none.fl_str_mv |
Ciência e Agrotecnologia v.27 n.5 2003 reponame:Repositório Institucional da UFLA instname:Universidade Federal de Lavras (UFLA) instacron:UFLA |
instname_str |
Universidade Federal de Lavras (UFLA) |
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UFLA |
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UFLA |
reponame_str |
Repositório Institucional da UFLA |
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Repositório Institucional da UFLA |
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Repositório Institucional da UFLA - Universidade Federal de Lavras (UFLA) |
repository.mail.fl_str_mv |
nivaldo@ufla.br || repositorio.biblioteca@ufla.br |
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1815439242179903488 |