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Time Distributions for Describing Appearance of Specific Culms of Winter Wheat¹

Cereal plants emerge and develop tillers in response to the field environment in which they are planted and grown. If the pattern of development of productive culms can be recognized and measured, impacts of different field conditions upon plants can be assessed. This study presents a method for describing emergence and tiller appearance patterns and illustrates the use of these patterns in comparing crop development responses to field environments. Desirable environments will produce uniform populations of culms with regularly spaced appearance patterns while stressful environments cause a variety of irregular patterns.

Characteristics of the populations of appearing culms can be described fundamentally by the logistic distribution function or can be approximated by the normal distribution function. The cumulative form of both functions is a sigmoid curve. The mean of the normal coincides with the 50% appearance time of the logistic. When the dispersion coefficient (s) of the normal function and the rate coefficient (k) of the logistic equation are related by ks = 1.69, the two curves differ by less than 1% of the final population size at any point. Culm appearance populations from good seedbeds appear as normal or logistic curves (considered to be the same curve) when appearances are timed by degree-days (3°C base). Fifty percent emergence for Stephens winter wheat (Triticum aestivum L.) occurs near 100 degree-days from planting, and tillers Tl, T2, and T3 occur at about 250, 300, and 375 degree-days, respectively, in a fertile seedbed with adequate water. Culm appearance data that are not normally distributed may be converted to normal form with transforms or population splitting procedures. The nature of the transformation required to normalize the data may help characterize the field condition causing non-normal appearance.

Key Words: Growth curves • Tillering • Tiller populations • Logistic function • Normal function • Degree-days • Degree-days • Development pattern • Triticum aestivum L. em. Thell.

² Soil scientist and plant physiologist, USDA, ARS, Columbia Plateau Conservation Research Center, Pendleton, OR 97801; associate professor of botany, Dep. Botany, Plant Pathology, and Microbiology, Auburn Univ., AL 36849.

Received for publication September 27, 1982.