The value and application of growth curves to field plat experiments

Two years' growth data on cereal crops and flax are presented to show that the construction and analysis of growth curves may yield information that can be used to good advantage to supplement yield data from plat experiments, especially insofar as such curves may furnish an index on the basis of which the different seasons encountered in the course of the experiment may be evaluated. Growth curves were constructed from data obtained from weekly height measurements of winter wheat, spring wheat, oats, barley, and flax. The growth curves of the various crops grown were analyzed from the standpoints of (a) symmetry shown, (b) maximum height attained (c) interval of time from emergence to attainment of greatest height, and (d) on the basis of the generalized or average slope of the curves produced. Attempts were made to evaluate the slopes of the growth curves produced by the employment of Robertson's growth equation. It was found that the differences in the calculated values of K (the constant) in any variety, since all of the curves encountered deviated from the symmetrical, were so great that but little significance could be attached to the averages of the separate values obtained for different values of t (the time factor). The fitting of the growth data to straight line trends by the method of least squares gave the most reliable and workable means of expressing the general slope of growth curves of crop plants. By the employment of this method the growth curve of Turkey 144 showed an average slope of 4.50 for the unfavorable growing season of 1931 when it yielded but 2.9 bushels per acre as against a slope of 8.48 and a yield of 20.2 bushels in the more favorable season of 1932. The curve for Ceres, a spring wheat, showed slopes of 5.95 and 11.01 for these same respective seasons. The fact that the growth curves of all of the spring sown cereal crops measured exhibited very similar slopes for the respective seasons emphasizes the point that the values designating the slopes of the curves produced may be used to good advantage, if not for the direct evaluation of two or more seasons, then at least to supplement meteorological data of the seasons encountered in the course of particular field plat experiments. Since the compilation of growth data is completed in the cereal crops at or near the heading stage, it cannot provide an index of seasonal conditions during the ripening period, consequently a complete correlation between one value summarizing growth data and shaped especially during the vegetative period of development of the plant and final yield performance cannot be expected in all seasons. Nevertheless, the data presented show rather conclusively that the types of curves produced by plants with similar habits of growth, such as spring sown cereal crops, are more indicative of the seasonal conditions shaping such growth curves, especially those factors determining the slope of these curves, than of the genetic differences of the crops or varieties grown. The growth curves here dealt with and the equations given for the straight line trends were used strictly to give information to supplement yield data and as a means of expressing the general slope of the curves. They were not and should not be employed for purposes of predicting final yields or ultimate height of plants prior to the completion of growth. The primary object of this investigation was not to clothe the rather unsymmetrical growth curves produced with the dignity of a mathematical formula or to obtain a particularly close fit between the produced curves and an exponential equation involving two or more variables, but rather to express the general slope of these curves in an understandable and practical manner. Mathematically formulated curves, except where provisions are made to allow for the changing values of constants employed for the various phases of the growth cycle, are symmetrical. The processes concerned in organic growth are too complex to