Classical Data on the Growth of Maize: Curve Fitting With Statistical Analysis

SUMMARY A new method of fitting curves to long sequences of data from successive harvests from populations of growing plants is applied to the classical data of Kreusler and his co‐workers on the growth of maize, carried out near Bonn in 1875 to 1878. The method effectively divides the data into phases, which are fitted by splined cubic polynomials meeting in‘knots’where adjacent curves agree in position, slope and rate of change of slope, thus ensuring smooth transitions and minimizing loss of degrees of freedom. The phases can be chosen on some physiological or morphological criteria, or (as here) best positions for knots can be determined statistically by a method which minimizes sums of squares of deviates. The curves are fitted to the natural logarithms of the primary data on dry wt and leaf area, and relative growth rates, leaf area ratios and unit leaf rates are derived by manipulating the equations of the original fitted curves. All these curves are presented for five varieties grown in 1875 and one variety grown from 1875 to 1878. A full statistical apparatus gives confidence limits for all the interpolated points along all these curves. The variances are homogeneous along any one of the sixteen original fitted curves, and taken as a whole the data show remarkable statistical uniformity, reflecting great credit on the experimental planning and execution a century ago. The fitted curves and their derivates show a large measure of agreement on common developmental progressions, with differences from variety to variety and year to year. Detailed examination shows that a number of these differences, particularly cases involving only a short sequence of harvests, were almost certainly due to deficiencies in the original data, the fitted curves and their associated statistics being valuable in detecting these. At the same time no serious example was detected of the fitting program injecting features not present in the primary data; but one minor example, not affecting specific conclusions, shows how necessary it is always to be on guard.