Statistical analysis of growth curves in plant breeding

Abstract

Growth curves, measuring growth (design), multivariate analysis of variance (MANOVA), SUMMARY In the first part of this paper some experimental conditions necessary for a valid statistical analysis of differences in growth curves are discussed .Next the multivariate character of growth curves is considered . Data on the growth curves of three genotypes of an experiment with tomatoes of the IVT are used for illustrating the computational procedure and some aspects of interpretation .The growth curves of log dry leaf weight for each plot could be described by a quadratic function of time and were characterised by three components : mean level m, slope 1(linear component) and curvature q (quadratic component) .Univariate analyses of variance (ANOVA) showed significant differences between cultivars for each growth component ; however, this is only part of the information as the correlation between the components is not involved. From a multivariate analysis of variance (MANOVA) it appeared that in this experiment the differences in growth between the cultivars were best expressed by using mean level m only .An estimate of the final (reduced) statistical model underlying the tomato example is derived . It is advised to split up growth into different phases of development each with its own analysis . At least four harvest dates for every phase seem desirable.

The parameters of grain filling and yield components in common wheat (Triticum aestivum L.) and durum wheat (Triticum turgidum L. var. durum)

“…Since all three variables define the shape of each growth curve, the stepwise MANOVA method described by [10] was considered to be a more appropriate one than ANOVA for comparisons of growth curves. The procedure was used in order to determine which of the estimated variables (W, R, T) were most important in assessing the grain filling curves.…”

“…If this λ-value was significant, the importance of adding the next variable (R) can be determined by calculating the λ-value for R after removal of the effects of W and T: λ(R\WT)=λ(WRT)/λ(WT) [3]. All calculations, including explanations regarding degrees of freedom given in various tables, were described in details together with a numerical example in [10].…”

“…Logistic models were found to be more appropriate in describing wheat grain growth [9]. Therefore, stepwise multivariate analysis-MANOVA of nonlinear regression estimated grain filling parameters was proposed as the most suitable statistical method [3,10]. Univariate analysis of variance (ANOVA) is sometimes used to differentiate among growth curves, but, MANOVA proved to be more appropriate for analyzing growth curve parameters.…”

“…This study was undertaken in order to compare grain filling patterns between groups of common and durum wheat genotypes, and investigate relationships among grain filling parameters, yield components and yield. To detect genotypes suitable for further breeding programs, growth analysis may provide important information [10].…”

Analysis of variance of primary data on plant growth analysis

“…The functional approach has some problems related to the choice of the appropriate function and to the statistical comparison of growth rates (Hunt, 1982;Poorter, 1989). Although the statistical comparison of curves fitted to the primary data is feasible (Neter et al, 1990), the statistical comparison of derived rates is a complex task, which has not been solved satisfactorily by some attempts (Hughes & Freeman, 1967;Hunt & Parsons, 1974;Hunt & Evans, 1980;Keuls & Garretsen, 1982;Garretsen & Keuls, 1986;Poorter & Lewis, 1986).…”