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Michel Génard and Claude Bruchou

An approach to studying fruit growth is presented for peach fruit (Prunus persica L. Batsch). It combines a functional description of growth curves, multivariate exploratory data analysis, and graphical displays. This approach is useful for comparing growth curves fitted to a parametric model, and analysis is made easier by the choice of the model whose parameters have a meaning for the biologist. Growth curves were compared using principal component analysis (PCA) adapted to the table of estimated parameters. Growth curves of 120 fruits were fitted to a model that assumes two growth phases. The first one described the pit growth and the first part of the flesh growth. The second described the second part of the flesh growth. From PCA, firstly it was seen that fruit growth varied according to cumulated growth during both growth phases and to date of maximal absolute growth. Secondly, fruit growth varied according to cumulated growth and relative growth rates during each phase. Further examples are presented where growth curves were compared for varying fruit number per shoot and leaf: fruit ratio, and for different sources of variation (tree, shoot, and fruit). Growth of individual fruit was not related to fruit number per shoot or to leaf: fruit ratio. Growth variability was especially high between fruit within shoots.

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Mathura Thillainathan and George C.J. Fernandez

A user-friendly SAS statistical and graphical application to classify genotypes evaluated under multiple sites is presented. First, the test sites are classified into three environments, LOW [(\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{{\cdot}j}\) \end{document}) < Q1], MEDIUM [Q1< = (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{{\cdot}j}\) \end{document})< = Q3], and HIGH [(\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{{\cdot}j}\) \end{document}) >Q3] yielding environments, using the first (Q1) and third (Q3) quartile of the site mean yield (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{{\cdot}j}\) \end{document}) as the cutoff value. Then, in each environment, the genotypes are classified as low [L: (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{i{\cdot}}\) \end{document}) < (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{{\cdot}{\cdot}}\) \end{document})], medium [M: (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{i{\cdot}}\) \end{document}) = (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{{\cdot}{\cdot}}\) \end{document})], and high [H: (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{i{\cdot}}\) \end{document}) > (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{{\cdot}{\cdot}}\) \end{document})] yielding under each of the three environments, by comparing each genotype mean (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{i{\cdot}}\) \end{document}) with the overall genotypic mean (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\bar{Y}}_{{\cdot}{\cdot}}\) \end{document}) based on lsd 0.01 statistic computed from a separate two-way ANOVA models for LOW, MED, and HIGH yielding environments. Using the user-friendly SAS MACRO, EXPLORGE horticulturists can effectively and quickly perform genotype classification under multi-site evaluation. The steps involved in downloading the necessary MACRO-CALL file from the author's home page [http://www.ag.unr.edu/gf] and the instructions for running the SAS MACRO are presented. The features of this graphical method and the graphics produced by the EXPLORGE MACRO are demonstrated and validated by published data.

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Atsushi Kono, Akihiko Sato, Yusuke Ban and Nobuhito Mitani

Genetic structure and differentiation in cultivated grape, Vitis vinifera L Genet. Res. 81 179 192 Chambers, J.M. Cleveland, W.S. Kleiner, B. Tukey, P.A. 1983 Graphical methods for data analysis. Duxbury Press, Boston, MA Evans, 1971 Two new table grape

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Eugene K. Blythe and Donald J. Merhaut

remains advisable to run diagnostic procedures with new data to check for normality and validity of other model assumptions. Both graphical methods and formal statistical tests are available for this purpose ( Neter et al., 1996 ), including those