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Comparison of Logistic and Weibull Functions: The Effect of Temperature on Cumulative Germination of Alfalfa

Dep. of Agronomy, The Pennsylvania State Univ., University Park, PA 16802

R. R. Hill, Jr. and R. A. Byers

USDA-ARS, U.S. Regional Pasture Res. Lab., University Park, PA 16802

^* Corresponding author.

The logistic and Weibull functions are mathematical equations that have been used to describe the characteristic curve of cumulative germination of plant seeds. The three objectives of this study were to determine (i) if either the logistic or Weibull function described the efffect of temperature on cumulative germination of alfalfa (Medicago sativa L.) seed; (ii) if the parameters of the equations could distinguish differences in germination among seed sources; (iii) and if either equation was predictive. ‘Saranac AR’ alfalfa seed was germinated at 5, 15, 25, or 35 °C over a period of 14 d in petri dishes containing filter paper saturated with distilled water. The logistic and Weibull functions both fit the curves generated by the four temperatures. Validation was accomplished by repeating the germination procedure described above at 10 and 20 °C with a germination period of 10 d and seed lots of six alfalfa cultivars. Parameters were estimated for the validation data set and prediction of the validation data set occurred using parameters estimated from the original data set. Both the Weibull and logistic functions gave satisfactory fits to the validation data set, but more accurate predictions of the validation data set were obtained with the Weibull than with the logistic equation derived from the original data set. The shape and scale Weibull parameters indicated that temperature and cultivar affected the rate of germination or vigor of the cultivars. However, the rate parameter of the logistic equation did not indicate any difference between the varieties. Therefore, use of the Weibull parameters increased the amount of information available for selecting for vigorous germination.

Received for publication December 28, 1987.