Evaluation of different selection indices combining Pilodyn penetration and growth performance in <i>Eucalyptus</i> clones

The present study aimed to evaluate the selection indices efficiency for Pilodyn penetration combined with growth traits in Eucalyptus clones. It was carried out experiments in a randomized block design, with single tree plots and 30 replications. Diameter at breast height (DBH), total height (TH), and Pilodyn penetration as an indicator of basic density (BD) were measured. The volume was estimated. Based on predicted genotypic values, three indices presented the highest accuracies: I₈ (based on partial correlation), I₇ (based on the concept of multivariate BLUP) and I₃ (based on two variables as ratio, which uses a third heritability estimate associated to the ratio DBH/BD, besides the two heritabilities of DBH and BD). Thus, it is possible to optimize the selection by combining properly the variables using their genetic control, precision and the relationships between them. The best options came from using only two no redundant traits DBH and BD.

Key words:
Selection criteria; accuracy; wood quality; partial correlation; path analysis

Authorship

Andrei Caíque Pires Nunes

Universidade Federal de Viçosa (UFV), Departamento de Engenharia Florestal, Avenida Peter Henry Rolfs, s/n, Campus Universitário, 36.570-900, Viçosa, MG, Brazil. Universidade Federal de ViçosaBrazilViçosa, MG, BrazilUniversidade Federal de Viçosa (UFV), Departamento de Engenharia Florestal, Avenida Peter Henry Rolfs, s/n, Campus Universitário, 36.570-900, Viçosa, MG, Brazil.

Marcos Deon Vilela de Resende

Empresa Brasileira de Pesquisa Agropecuária, Centro Nacional de Pesquisa de Florestas, Estrada da Ribeira, km 111, Bairro Guaraituba, 83.411-000, Colombo, PR, BrazilEmpresa Brasileira de Pesquisa AgropecuáriaBrazilColombo, PR, BrazilEmpresa Brasileira de Pesquisa Agropecuária, Centro Nacional de Pesquisa de Florestas, Estrada da Ribeira, km 111, Bairro Guaraituba, 83.411-000, Colombo, PR, Brazil

Glêison Augusto dos Santos

Rodrigo Silva Alves

UFV, Departamento de Biologia GeralUFVBrazilBrazilUFV, Departamento de Biologia Geral

* E-mail: andreicaiquep@gmail.com

SCIMAGO INSTITUTIONS RANKINGS

UFV, Departamento de Biologia GeralUFVBrazilBrazilUFV, Departamento de Biologia Geral

Tables | Formulas

Tables (4)
Formulas (2)

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Table 1
Description of the indexes and their accuracies used

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Table 2
Estimates of genetic parameters (individual REML) and genotypic correlations (below the genetic parameters) for basic density (BD in kg m^-3), diameter at breast height (DBH in cm), total height (Th in m), volume (Vol in m³ ha^-1 year), phenotypic index DBH×BD (I₁), and phenotypic index Vol×BD (I₂) for Eucalyptus clones evaluated in the joint analysis between environments, at three years of age

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Table 3
Heritabilities and correlations of a ratio between two variables

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Table 4
Accuracies and Cronbach's alpha coefficients (1951) for I₁, I₂, I₃, I₄, I₅, I₆, I₇, I₈, I₉, I₁₀ indices, which are based on the concepts of phenotypic index, ratio between two variables (Resende et al. 2014Resende MDV, Silva FF and Azevedo CF (2014) Estatística matemática, biométrica e computacional: modelos mistos, multivariados, categóricos e generalizados (reml/blup), inferência bayesiana, regressão aleatória, seleção genômica, qtl-gwas, estatística espacial e temporal, competição, sobrevivência. Editora Suprema, Viçosa, 881p.), genotypic index, multivariate blup (Viana and Resende 2014Viana AP and Resende MDV (2014) Genética quantitativa no melhoramento de fruteiras. Interciência, Rio de Janeiro, 296p.), partial correlation (Viana and Resende 2014), ordinary correlation and direct effects of path analysis (Resende et al. 2014), respectively

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Table 1 Description of the indexes and their accuracies used

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Description of the indexes components and accuracies: 𝐵𝐷: basic density indirectly estimated by the Pilodyn’s method; 𝐷𝐵𝐻: diameter at breast height; 𝑆 𝐷𝐵𝐻 : standard deviation of diameter at breast height; 𝑆 𝐵𝑑 : standard deviation of basic density; 𝑉𝑜𝑙: volume of wood without bark; 𝑆 𝑉𝑜𝑙 : standard deviation of the volume without bark; 𝐿𝑜𝑔(1/𝐵𝐷): inverse of the basic density indirectly estimated by the Pilodyn’s method on the logarithmic scale; 𝐿𝑜𝑔𝐷𝐵𝐻: diameter at breast height on the logarithmic scale; 𝐿𝑜𝑔𝑉𝑜𝑙: volume of wood without bark on the logarithmic scale; 𝑉𝐺 𝐵𝐷 : genotypic value of the indirectly estimated basic density; 𝑉𝐺 𝐷𝐵𝐻 : genotypic value of the diameter at breast height; 𝑆 𝑉𝐺 𝐷𝐵𝐻 : standard deviation of the genotypic value of the diameter at breast height; 𝑆 𝑉𝐺 𝐵𝐷 : standard deviation of the genotypic value of the basic density; 𝑉𝐺 𝑉𝑜𝑙 : genotypic value of volume without bark; 𝑆 𝑉𝐺 𝑉𝑜𝑙 : standard deviation of the genotypic value of Vol; 𝑔 0 : standard genotypic value of the objective character (DBHxBD); 𝑔 𝑎𝑖 : is the standard genotypic value of the auxiliary characters (DBH and BD). The weighting coefficients ( 𝑏 𝑖 ) of the index are given by (Viana and Resende 2014Viana AP and Resende MDV (2014) Genética quantitativa no melhoramento de fruteiras. Interciência, Rio de Janeiro, 296p.); 𝑟 𝑔𝑔 : accuracy of the index; 𝑛: number of individuals per clone; ℎ 𝑦∗ 2 : heritability of the ratio between two variables given by Resende et al. (2014); ℎ 2 : heritability of the phenotypic index; 𝐴𝑐 𝐼5 : accuracy of the I₅ genotypic index; 𝑠𝑑(𝐼5): standard deviation of the I₅ genotypic index score; 𝐴𝑐(𝐼3): accuracy of the I₃ optimum index; 𝑠𝑑(𝐼3): standard deviation of the I₃ optimum index score; 𝐴𝑐 𝐼6 : accuracy of the I₆ genotypic index; 𝑠𝑑(𝐼6): standard deviation of the I₆ genotypic index score; 𝐴𝑐(𝐼4): accuracy of the I₄ optimum index; 𝑠𝑑(𝐼4): standard deviation of the I₄ optimum index score; 𝑉𝑎𝑟(𝐼𝑛𝑑𝑒𝑥)/ 𝜎 𝑔 2 : ratio between the index and additive variances of the objective trait; 𝑠𝑑(𝑠𝑐𝑜𝑟𝑒 𝐼 𝑥 ): standard deviation of the I₈, I₉ or I₁₀ indexes score; 𝑠𝑑(𝑠𝑐𝑜𝑟𝑒 𝐼 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 ): standard deviation of the score of the index with greater variance among I₇ and I₁₀.

Table 2 Estimates of genetic parameters (individual REML) and genotypic correlations (below the genetic parameters) for basic density (BD in kg m^-3), diameter at breast height (DBH in cm), total height (Th in m), volume (Vol in m³ ha^-1 year), phenotypic index DBH×BD (I₁), and phenotypic index Vol×BD (I₂) for Eucalyptus clones evaluated in the joint analysis between environments, at three years of age

¹
Description of genetic parameters: ℎ 𝑔 2 : coefficient of individual heritability in the broad-sense (corrected to variance of block), free from interaction; ℎ 𝑚𝑔 2 : heritability of clone mean; 𝐴𝑐𝑔𝑒𝑛: genetic accuracy in clone selection; 𝑐 𝑏𝑙𝑜𝑐 2 : coefficient of determination of block; 𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝑚𝑒𝑎𝑛: overall mean of characters between different environments; 𝐶𝑉𝑔𝑖 % : coefficient of genotypic variation; 𝐶𝑉𝑒 (%): coefficient of experimental variation; 𝐶𝑉𝑟 coefficient of relative variation.

Table 3 Heritabilities and correlations of a ratio between two variables

¹
Description of the coefficients: ℎ 𝑦∗ 2 : heritability of the ratio between two variables (optimum index); 𝑟 𝐺 𝑌∗𝑊∗ : genotypic correlation of the index with the variable W*, which for I₃ is DBH, and for I₄ is Vol; 𝑟 𝐺 𝑌∗𝑋∗ : genotypic correlation of the index with variable X*, which for both indices is 1/BD; 𝑟 𝑃 𝑌∗𝑊∗ : phenotypic correlation of the index with variable W*, which for I₃ is DBH, and for I₄ is Vol; 𝑟 𝑃 𝑌∗𝑋∗ : phenotypic correlation of the index with the variable X*, which for both indices is 1/BD; 𝑘 2 : elasticity or relationship between variances, being the phenotypic variance of X (always BD) in the numerator, and the phenotypic variance of W (DBH or Vol) in the denominator; 𝑘 ℎ 2 : ratio between heritability of variable X (BD) estimated in the original scale and the calculated heritability of the ratio between two variables; 𝑘: square root of 𝑘 2 ; 𝑘 ℎ : square root of 𝑘 ℎ 2 . As mentioned in the material and methods, coefficient details can be found in Resende et al. (2014Resende MDV, Silva FF and Azevedo CF (2014) Estatística matemática, biométrica e computacional: modelos mistos, multivariados, categóricos e generalizados (reml/blup), inferência bayesiana, regressão aleatória, seleção genômica, qtl-gwas, estatística espacial e temporal, competição, sobrevivência. Editora Suprema, Viçosa, 881p.).

Table 4 Accuracies and Cronbach's alpha coefficients (1951) for I₁, I₂, I₃, I₄, I₅, I₆, I₇, I₈, I₉, I₁₀ indices, which are based on the concepts of phenotypic index, ratio between two variables (Resende et al. 2014Resende MDV, Silva FF and Azevedo CF (2014) Estatística matemática, biométrica e computacional: modelos mistos, multivariados, categóricos e generalizados (reml/blup), inferência bayesiana, regressão aleatória, seleção genômica, qtl-gwas, estatística espacial e temporal, competição, sobrevivência. Editora Suprema, Viçosa, 881p.), genotypic index, multivariate blup (Viana and Resende 2014Viana AP and Resende MDV (2014) Genética quantitativa no melhoramento de fruteiras. Interciência, Rio de Janeiro, 296p.), partial correlation (Viana and Resende 2014), ordinary correlation and direct effects of path analysis (Resende et al. 2014), respectively

¹
RBTV: Ratio between two variables; ² Multi Blup: multivariate Blup; ³ Path: direct effect of path analysis; ⁴ Cronbach's alpha coefficient (1951) modified by Resende et al. (2014Resende MDV, Silva FF and Azevedo CF (2014) Estatística matemática, biométrica e computacional: modelos mistos, multivariados, categóricos e generalizados (reml/blup), inferência bayesiana, regressão aleatória, seleção genômica, qtl-gwas, estatística espacial e temporal, competição, sobrevivência. Editora Suprema, Viçosa, 881p.); ⁵ Negative value.

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Crop Breeding and Applied Biotechnology Universidade Federal de Viçosa, Departamento de Fitotecnia, 36570-000 Viçosa - Minas Gerais/Brasil, Tel.: (55 31)3899-2611, Fax: (55 31)3899-2611 - Viçosa - MG - Brazil
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Evaluation of different selection indices combining Pilodyn penetration and growth performance in <i>Eucalyptus</i> clones

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[1] * E-mail: andreicaiquep@gmail.com