Use of the Weibull Function to Calculate Cardinal Temperatures in Faba Bean

Abstract

The onset of germination of faba bean seeds at constant temperature was progressively delayed as that temperature diverged from an optimum of 25.5 °C. At temperatures below 10 °C, or above 28 °C, the maximum germination percentage fell to below 90%. There was no germination at 39 °C. Positive and negative linear relationships were established between the constant temperatures and the rates of progress of germination to different percentiles, at sub-optimal and supra-optimal temperatures, respectively. Like germination rates, base temperature (T_b) declined from 3.71 to −0.83 °C as the percentile value increased from 10% to 80%. Caution was urged in extrapolating beyond the experimental data set. Differences in the ceiling temperature (T_c) with percentile could not be discerned. Cumulative germination progress curves at each temperature were modelled by the Weibull, logistic, and cumulative normal distribution functions. Cardinal temperatures (T_b and T_c) calculated from these data reasonably approximated the actual data. The Weibull function demonstrated a good approximation at all percentile levels, while the logistic and cumulative normal distribution functions, as a result of their inherent symmetry, deviated at the extreme percentiles. It was concluded that the Weibull function not only accurately modelled cumulative germination but could also be used in the calculation of cardinal temperatures.