A mathematical model that uses Gaussian distribution to analyze the germination of Manfreda brachystachya (Agavaceae) in a thermogradient

Germination of nondormant seeds of Manfreda brachystachya (Agavaceae) was analyzed at temperatures ranging from 11–35°C. Maximum germination (95%) occurred at 25°C. An exponential sigmoid relationship was found between time and cumulative germination. Germination rate for every subpopulation (10–90% germination) was estimated by means of a normal distribution analysis. The kurtosis indicated die amplitude of the range of temperatures where the highest germination rates were concentrated, and the skew indicated sharply inhibitory temperatures in the range of temperatures used. Based on analysis of the normal distribution models for each subpopulation, we calculated a theoretical function which described germination rate over the temperature range considered: F(T,χ) = A × exp[−B(C−1)²], where A is the function that describes germination rate for each subpopulation (characterized by the percentage [χ] at optimal temperature); B is a shape parameter, 1/(σG²); and C is the ratio between each germination temperature (T) and the optimal germination temperature. The Gaussian curves were used to calculate thermal time, and base and ceiling temperatures. Germination thermal time ranged from 1 333 to 2 373°C h, and base and ceiling temperatures were 10.44 ± 0.7°C and 39.54 ± 0.7°C, respectively. There was a linear relationship between thermal time and cumulative percentage of germination of the subpopulations. Based on fitted curves for each subpopulation, the use of a general model for all the subpopulations has been proven: F8 = A × exp[−5.9437(C−1)²], where changes in the curves for each subpopulation depended on temperature only.