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Growth Curve Analysis of Temperature-Dependent Phenology Models¹

Much of the recent crop phenology research has involved estimation and comparison of crop growth curves for different treatments as a function of growing degree days. Usually, experimental units are set out in a certain type of design and repeatedly measured with approximately equal growing-degree-day intervals between measurements. The experiment is then analyzed as a split plot in time or as a repeated-measures multivariate analysis of variance (MANOVA). However, the assumptions underlying the analysis as a split plot in time require (i) homogeneity of error variance among growingdegree-day levels and (ii) identical correlations between measurements for any two periods. Both assumptions are unrealistic when considering plant growth. Also, the MANOVA requires more degrees of freedom for error than growing-degree-day levels, which may not hold when a large number of repeated measurements are made on each experimental unit. Growth curve analysis is useful when the split plot in time is inappropriate and a MANOVA is not possible. Growth curve analysis is carried out by fitting a polynomial regression of stage of plant growth on growing degree days for each experimental unit and performing a MANOVA on the resulting regression coefficients. Growth curve analysis is applied to a crop phenology field experiment in Zea mays L. to (i) develop temperature-dependent phenology models, (ii) test for coincidence of such models across treatments, and (iii) estimate confidence intervals for the final growth curves. It is concluded that growth curve analysis is a useful method in crop phenology modeling because the technique explicitly specifies the shape of the response profile, uses experimental information more efficiently, and is applicable to any type of experimental design.

Key Words: Growing degree days • Growth curve analysis • Phenology modeling • Repeated-measures multivariate analysis of variance

² Consultant, Biometrics and Information Systems Ctr., Univ. of Nebraska-Lincoln, Lincoln, NE 68583; and scientist, Int. Maize and Wheat Improvement Ctr., Londres 40, Mexico 6, D.F., Mexico, respectively.

Received for publication December 19, 1985.