Lattice and Lattice Square Designs with Oat Uniformity Data and in Variety Trials<sup>1</sup>

Johnson, I. J.; Murphy, H. C.

doi:10.2134/agronj1943.00021962003500040004x

Cited by 9 publications

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“…Gains in efficiency up t o 362% have been reported-the relative efficiency depending largely upon soil variability in the experimental area. Wilsie (1954) states that theoretically, under average conditions, the efficiency of lattice designs would be expected to increase with the number of strains in the test and points out that data reported by Cochran (1941), Johnson and Murphy (1943) and Robinson, Rigney and Harvey (1948) tend t o confirm this principle. Wilsie (1954) showed that for a series of alfalfa trials the average efficiency of the lattice design compared with the randomized block was 164%.…”

Section: Literature Reviewmentioning

confidence: 97%

The Analysis of a Series of Wheat Varietal Trials1

Balaam

Hunter

1962

Australian Journal of Statistics

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Section: Literature Reviewmentioning

confidence: 97%

The Analysis of a Series of Wheat Varietal Trials1

Balaam

Hunter

1962

Australian Journal of Statistics

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“…Since then, the efficiency of the lattice design, with and without recovery of inter--block information, as compared to complete block design and neighbor analysis, has been analyzed by many researchers. The superior accuracy of the lattice design was demonstrated in many studies (Atwood & Garber, 1942;Myers, 1942;Zuber, 1942;Johnson & Murphy, 1943;Wellhausen, 1943;Lin et al, 1993;Saad, 1994a,b). However, in some studies the block design was more efficient (Torrie et al, 1943, andBancroft &Smith, 1949).…”

Section: Introductionmentioning

confidence: 98%

Estimation of genetic parameters in the square lattice analysis

Viana

Regazzi

1999

Bragantia

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This paper shows how to obtain unbiased estimates of genetic parameters of base populations, e.g., genotypic variance among families, heritability on a family mean basis, genotypic correlation and direct and indirect expected genetic gains, when the sampled families were evaluated in square lattice experiment. The theoretical part presents the variance and covariance components of the intra-block analysis of square lattice and the estimators of the components associated to treatment effect, considering the ordinary least squares method. In the analysis with treatments not corrected for blocks/replications, the estimator of the component due to treatment effect is equal to that of the analysis considering the complete block model. Experimental data from a breeding program of Eucalyptus pyrocarpa were used for genetic analysis. The high estimates of narrow sense heritabilities and additive genetic correlation, related to height and diameter, indicate that selection of the superior families will be effective in changing the means of the base population.Index terms: quantitative genetics, genetic parameters, variance components, covariance components, square lattice.(1) Received for publication in April 23, 1997, and approved in December 9, 1998.(2) Departamento de Biologia Geral, Universidade Federal de Viçosa, 36570-000 Viçosa (MG). RESUMO ESTIMAÇÃO DE PARÂMETROS GENÉTICOS NA ANÁLISE DE LÁTICE QUADRADONeste trabalho, apresenta-se um procedimento para a obtenção de estimativas não viesadas de parâmetros genéticos de populações-base, como variância genotípica entre famí-lias, herdabilidade em nível de média de família, correlação genotípica entre caracteres e ganhos genéticos esperados, diretos e indiretos, quando as progênies amostradas foram avaliadas no delineamento em látice quadrado. Na parte metodológica, são apresentados os componentes de variância e da covariância da análise intrablocos de látice quadrado e os estimadores dos componentes associados a efeito de tratamento, considerando estimação pelo método dos quadrados mínimos ordinário. Os estimadores dos componentes da variância e da covariância associados a efeito de tratamento da análise com tratamentos não ajustados são iguais aos da análise considerando modelo em blocos. Dados de um experimento de programa de melhoramento de Eucalyptus pyrocarpa foram usados para análise genética. Em vista dos elevados valores da herdabilidade em sentido restrito e da correlação genética aditiva, em relação a altura e diâmetro, a seleção das melhores famílias será eficiente em alterar as médias da população base.Termos de indexação: genética quantitativa, parâmetros genéticos, componentes da variância, componentes de covariância, látice quadrado.

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“…Due to its implication on the selective process by decreasing the correlation between phenotypic and genotypic values, the genotype x environment interaction is a complex and widely investigated problem, which must be considered in breeding programs. Since a high number of treatments is normally used in these experiments, the lattice design has been frequently used (Zuber, 1942;Johnson & Murphy, 1943;Torrie et al, 1943;Wellhausen, 1943;Bancroft & Smith, 1949;Sahagun-Castellanos & Frey, 1990;Beninati & Busch, 1992;Chaves & Miranda Filho, 1992;Singh et al, 1992;Arriel et al, 1993;Lin et al, 1993;Michelini & Hallauer, 1993;Moncada et al, 1993;Oliveira, 1993;Ferrão et al, 1994, andRezende &Ramalho, 1994), contributing to increase experimental error control efficiency (Cochran &Cox, 1957, andFederer, 1955).…”

Section: Introductionmentioning

confidence: 99%

Estimation of genetic parameters in the analysis of square lattice experiment group

Viana

Regazzi

1999

Bragantia

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Aiming to demonstrate how to obtain unbiased estimates of genetic parameters of base populations, unaffected by genotype x environment effects, this paper presents the variance and covariance components of the intra-block analysis of a group of square lattice experiments and the estimators of the components associated to treatment effect. Random model and mixed models with environment effect fixed and other effects random are considered. In the analysis with treatments not corrected for blocks/replications/environments, the estimators of the variance and covariance components due to treatment effect are different from those of the analysis considering the complete block model. Data from two experiments of a breeding program of Eucalyptus pyrocarpa were used for genetic analysis. The analysis of variance of height and diameter indicated absence of interaction between progeny and environment. Due to this result, the prediction of the direct and indirect genetic gains was based on the mean of the two environments. The high estimates of narrow sense heritabilities and additive genetic correlation indicate that selection of the superior families will be effective in changing the means of the base population for both traits.Index terms: quantitative genetics, genetic parameters, variance components, covariance components, joint analysis, square lattice.(1) Received for publication in April 23, 1997, and approved in December 9, 1998. RESUMO ESTIMAÇÃO DE PARÂMETROS GENÉTICOS NA ANÁLISE DE GRUPO DE EXPERIMENTOS EM LÁTICE QUADRADONeste trabalho, discute-se a estimação de parâmetros genéticos de populações-base, quando as famílias amostradas foram avaliadas em dois ou mais ambientes, no delineamento em látice quadrado. Na parte teórica, são apresentados os componentes de variância e covariância da análise intrablocos de grupo de experimentos em látice quadrado e os estimadores dos componentes associados a efeito de tratamento, considerando estimação pelo método dos quadrados mínimos ordinário. Os estimadores dos componentes da variância e covariância da análise com tratamentos não ajustados diferem dos da análise segundo modelo em blocos completos. Além de modelo aleatório, consideram-se também os mistos com efeito de ambiente fixo e demais efeitos aleatórios. Dados de dois experimentos de um programa de melhoramento de Eucalyptus pyrocarpa foram usados para análise genética. Como em relação às características altura e diâmetro não houve evidência de interação progênie x ambiente, a predição de ganhos diretos e indiretos foi feita com base na média dos dois ambientes. Os valores elevados da herdabilidade em sentido restrito e da correlação genética aditiva evidenciam que a seleção das famílias superiores será eficiente em alterar as médias da população-base, para as duas características.Termos de indexação: genética quantitativa, parâmetros genéticos, componentes da variância, componentes da covariância, análise conjunta, látice quadrado.

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Lattice and Lattice Square Designs with Oat Uniformity Data and in Variety Trials¹

Cited by 9 publications

References 0 publications

The Analysis of a Series of Wheat Varietal Trials1

The Analysis of a Series of Wheat Varietal Trials1

Estimation of genetic parameters in the square lattice analysis

Estimation of genetic parameters in the analysis of square lattice experiment group

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Lattice and Lattice Square Designs with Oat Uniformity Data and in Variety Trials1

Cited by 9 publications

References 0 publications

The Analysis of a Series of Wheat Varietal Trials1

The Analysis of a Series of Wheat Varietal Trials1

Estimation of genetic parameters in the square lattice analysis

Estimation of genetic parameters in the analysis of square lattice experiment group

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Lattice and Lattice Square Designs with Oat Uniformity Data and in Variety Trials¹