Longitudinal analysis in the selection of Análise longitudinal na seleção de clones de Rodolfo Schmit
Recebido em 21/04/2014 - Aceito para publicação em 16/12/2014 Resumo O objetivo deste trabalho foi avaliar o crescimento de clones de Abstract The objective of this study was to evaluate the growth of INTRODUCTION
The Due to the benefits of the raw material, the global production of Supplemental irrigation of In Chile, To elucidate the effect of irrigation in the cultivation of MATERIALS AND METHODS The experiment was conducted in the administrative region of Bío-Bío, southern Chile (37°45´S and 72°18´W) with assessments performed between 2008 and 2011. The selected area corresponds to a seed orchard of The experiment considered the evaluation of 30 clones of The irrigation treatment was applied only during summer due to the high water retention capacity of the soil and the clay texture. The amount of daily irrigation was estimated considering the replacement of the water content lost by evaporation with a maximum of 3.2 mm.day
Consider the following mixed effects model that represents the experimental data (MORA et al., 2010; CANÉ-RETAMALES et al., 2011) in which Z_{i}, and W_{i} are the incidence matrices (known) of the vectors ß that represent the fixed effects of irrigation, year, and block, respectively; c, represents the random effect due to clone and the clone*irrigation interaction; and _{i}p, represents the effects of the plots._{i}The other interaction effects were not considered in the model for simplification (convergence of the restricted maximum likelihood function) and to further acquire the most appropriate variance and covariance structure for the data (GONÇALVES; FRITSCHE-NETO, 2012). The estimation of variance and covariance components and broad-sense heritability and prediction of clonal effects were performed by the REML/BLUP methodology (Restricted Maximum Likelihood/Best Linear Unbiased Prediction). The broad-sense heritability for each response variable was calculated using the following expression in which corresponds to clonal variance, is the variance of the clone*irrigation interaction, and is the residual variance. After the characterization of the general model, the following variance-covariance structures were fitted to the residual matrix: a) First-order autoregressive, AR(1): b) Heterogeneous autoregressive, ARH(1): c) Unstructured, UN: d) Heterogeneous compound-symmetry, CSH: where is the correlation coefficient between two consecutive years (-1 < < 1). , and are the variance, covariance and standard deviation, respectively. The best variance-covariance structures for representing the dependence or independence between observations were determined. The hypothesis of correlated error arises for the continuous evaluation of the same trees over the years. The growth traits are larger in magnitude in the final year of assessment. For this reason, data were corrected by the variance and covariance matrices to better represent the error in the evaluation of longitudinal data and to assess and correct for the existence of heteroscedasticity. To test the best model (according to the variance-covariance structure), the Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used: where L corresponds to the (restricted) maximum likelihood value, d is the number of model dimensions, and n is the number of observations. Pearson's correlation coefficients were calculated among growth traits using the prediction of clonal effects (BLUP), as a measurement of the genetic association between two traits. RESULTS AND DISCUSSION In the present study, the AIC and BIC obtained by the REML method indicate lower values (best model) for the UN (unstructured) variance-covariance matrix (Table 1). The information criteria are important in statistical analysis because they penalize models with excessive numbers of parameters and identify the most parsimonious models (parsimony) that best explain the data.
For all growth traits, the AR(1) matrix showed the highest AIC and BIC values (Table 1). In fact, the residual variance differed each year (p<0.01). The AR(1) matrix was the only matrix that represented homoscedasticity in the structuring of residual variances. The greatest inadequacy of this model is its exclusion of specific variances for each year of assessment (LITTELL, 2006). In general, the correlations of errors in assessments over the years follow a random behavior (i.e., unstructured), which can be explained by the UN matrix. According to Zamudio et al. (2008), the linear mixed model methodology permits the presence of heterogeneity of variance in the linear model and allows the researcher to directly address the covariance structure. Modeling the covariance structure of the data can improve the analysis of repeated measures data by providing valid standard errors and efficient statistical tests. In general, the residual variance increased proportionally over time, and the largest covariance was detected between the years of 2010 and 2011 (Table 2). Variation values among replicates of the same clone increased due to the sum of environmental effects assigned to the four consecutive years of assessment. The highest values are always found between two consecutive years, and higher covariance values allow more accurate prediction of statistical inferences by reducing the predicted residual variance (FORTIN, 2007).
To estimate the broad-sense heritability (genetic parameter of interest), only one residual variance must be selected. According to Zamudio et al. (2008), the residual variance that exhibits the lowest standard error must be selected. However, the best way to select the residual variance may use the proportion of variance and standard error (RESENDE, 2007). The calculation of heritability using any of the methods led to the same results. Therefore, the selected residual variances obtained by REML were 57.71 cm Clonal effects were predicted using BLUP and the unstructured variance-covariance matrix. Pearson's correlation coefficients were found to be high and highly significant (p<0.01) between pair of traits predicted using BLUP: r=0.97 between TTH and BSD, r=0.90 between TTH and WV, and r=0.88 between BSD and WV. These results agree with those reported by Mora and Serra (2014), and Bundock et al. (2008) in The variance of the clone x irrigation interaction contributed to 7%, 17%, and 9.5% of the phenotypic variance of the TTH, BSD, and WV traits, respectively (Table 3). The TTH trait exhibited high broad-sense heritability (0.61), which indicates effective selection of genetic gain in the height of
According to the values predicted via Best Linear Unbiased Prediction (BLUP) under irrigation conditions, the Eg28 (BLUP= 4.9 m), Eg29 (BLUP= 3.36 m), and Eg30 (BLUP= 3.34 m) clones exhibited the best responses for the trait tree height. In the treatment without irrigation, these clones exhibited the lowest values for height, which is not desirable for selection and confirms the existence of a significant (and complex) clone x irrigation interaction. In the cultivation without irrigation, the best clones according to BLUP were Eg3 (BLUP= 3.86 m), Eg18 (BLUP= 3.77 m), and Eg12 (BLUP= 2.83 m). According to the values predicted via BLUP, CONCLUSIONS The assessment of The difficulty of selection is given by the existence of a significant and complex clone x irrigation interaction. According to the values predicted via BLUP under water irrigation conditions, the Eg29 clone is of particular relevance given its promising performance for the three growth traits of interest. For the rainfed treatment, the Eg11, Eg23, and Eg18 clones were more promising for selecting larger wood volume. ACKNOWLEDGEMENTS The authors would like to thank the Chilean National Science and Technology Research Fund (FONDECYT), project n° 1130306 and 1085093. The authors would also like to FORESTAL MININCO S.A. REFERENCES ACUÑA, C. V.; FERNANDEZ, P.; VILLALBA, P. V.; GARCÍA, M. N.; HOPP, H. E.; POLTRI, S. N. M. Discovery, validation, and in silico functional characterization of EST-SSR markers in BARTHOLOMÉ, J.; SALMON F.; VIGNERON P.; BOUVET J. M.; PLOMION, C.; GION, J. M. Plasticity of primary and secondary growth dynamics in BUNDOCK, P. C.; POTTS, B. M.; VAILLANCOURT, R. E. Detection and stability of quantitative trait loci (QTL) in CALLISTER, A. N.; ENGLAND, N.; COLLINS, S. Genetic analysis of CANÉ-RETAMALES, C.; MORA, F.; VARGAS-REEVE, F.; PERRET, S.; CONTRERAS-SOTO, R. Bayesian threshold analysis of breeding values, genetic correlation and heritability of flowering intensity in CHENU, K.; COOPER, M.; HAMMER, G. L.; MATHEWS, K. L.; DRECCER, M. F.; CHAPMAN, S. C. Environment characterization as an aid to wheat improvement: interpreting genotype–environment interactions by modelling water-deficit patterns in North-Eastern Australia. COSTA E SILVA, F.; SHVALEVA, A.; BROETTO, F.; ORTUÑO, M. F.; RODRIGUES, M. L.; ALMEIDA, M. H.; CHAVES, M.M.; PEREIRA, J. S. Acclimation to short-term low temperatures in two CROUS, K. Y.; QUENTIN, A. G.; LIN, Y. S.; MEDLYN, B. E.; WILLIAMS, D. G.; BARTON, C. V. M.; ELLSWORTH, D. S. Photosynthesis of temperate FORTIN, M.; DAIGLE, G.; UNG, C. H.; BEGIN, J.; ARCHAMBAULT, L. A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling. FRITSCHE-NETO, R.; BORÉM, A. GONÇALVES, M. C.; FRITSCHE-NETO, R. GUARNASCHELLI, A. B.; PRYSTUPA, P.; LEMCOFF, J. H. Drought conditioning improves water status, stomatal conductance and survival of HARRAND, L.; HERNÁNDEZ, J. J. V.; UPTON, J. L.; VALVERDE, G. R. Genetic parameters of growth traits and wood density in KHATTREE, R.; NAIK, D. N. LI, R.; STEWART, B.; WEISKITTEL, A. A Bayesian approach for modelling non-linear longitudinal/hierarchical data with random effects in forestry. LITTELL, R. C.; MILLIKEN, G. A.; STROUP, W. W.; WOLFINGER, R. D.; SCHABENBERGER, O. LOPES, J. L. W.; GUERRINI, I. A.; SAAD, J. C. C.; DA SILVA, M. R. Efeitos da irrigação na sobrevivência, transpiração e no teor relativo de água na folha em mudas de LOPEZ, G. A.; POTTS, B. M.; DUTKOWSKI, G. W.; APIOLAZA, L. A; GELID, P. E. Genetic variation and inter-trait correlations in MORA, F.; PERRET, S.; SCAPIM, C. A.; ARNHOLD, E. Genetic parameters of growth and survival in MORA, F.; RUBILAR, R.; EMHART, V. I.; SAAVEDRA, J. Predicción bayesiana de parámetros genéticos en clones de MORA, F.; SERRA, N. Bayesian estimation of genetic parameters for growth, stem straightness and survival in NAVARRETE-CAMPOS, D., BRAVO, L. A.; RUBILAR, R. A.; EMHART, V.; SANHUEZA, R. Drought effects on water use efficiency, freezing tolerance and survival of RESENDE, M. D. V. SANTELICES, R. Desarrollo de una plantación de VELLINI, A. L. T. T.; DE PAULA N. F.; ALVES, P. L. C. A.; PAVANI, L. C.; BONINE, C. A. V.; SCARPINATI, E. A.; PAULA, R. C. Respostas fisiológicas de diferentes clones de eucalipto sob diferentes regimes de irrigação. YANG, R.; TIAN, Q.; XU, S. Mapping quantitative trait loci for longitudinal traits in line crosses. ZAMUDIO, F.; WOLFINGER, R.; STANTON, B.; GUERRA, F. The use of linear mixed model theory for the genetic analysis of repeated measures from clonal tests of forest trees. I. A focus on spatially repeated data. |