Modeling Seed Germination of Ricinus communis Using Hydrothermal Time Model Developed on the Basis of Weibull Distribution

Temperature and water potential are two of the most important environmental factors regulating the seed germination. The germination response of a population of seeds to temperature and water potential can be described on the basis of hydrothermal time (HTT) model. Regardless of the wide use of HTT models to simulate germination, little research has critically examined the assumption that the base water potential within these models is normally distributed. An alternative to the normal distribution that can fit a range of distribution types is the Weibull distribution. Using germination data of Castor bean (Ricinus communis L.) over a range of water potential and sub-optimal temperature, we compared the utility of the normal and Weibull distribution in estimating base water potential (b). The accuracy of their respective HTT models in predicting germination percentage across the sub-optimal temperature range was also examined.

Castor bean seed germination was tested across a range of water potential (0, -0.3, -0.6 and -0.9 MPa) at the sub-optimal range of temperature (ranging from 10 to 35 ˚C, with 5 ˚C intervals). Osmotic solutions were prepared by dissolving polyethylene glycol 8000 in distilled water according to the Michel (1983) equation for a given temperature. Seed germination was tested on 4 replicates of 50 seeds in moist paper towels in the incubator. The HTT models, based on the normal and Weibull distributions were fitted to data from all combinations of temperatures and water potentials using the PROC NLMIXED procedure in SAS.

Based on both normal and Weibull distribution functions, hydrotime constant and base water potential for castor bean seed germination were declined by increasing the temperature. Reducing the values of base water potential showed the greater need to water uptake for germination at lower temperatures and reducing hydrotime constant indicated an increase in germination rate by increasing the temperature. Compared with hydrothermal time model based on the normal distribution, Weibull hydrothermal time model gave a better fit (RMSE=8.07%) and more accurate (AIC=-5801) to seed germination data of castor bean. Based on Weibull hydrothermal time model, base temperature and hydrothermal time constant were estimated to be 8.86 ˚C and 833/10 MPa h, respectively. The osmotic potential from which the germination begins was (μ) -1.71 MPa. The shape parameter (λ) of the Weibull hydrothermal time model implied asymmetry of base water potential data and skewness of distribution to the right. A right-skewed distribution of b(g) has important ecological implications, as it means that the seed population have a greater reserve of seeds with very high values of b(g) and are therefore slow in germination, even under optimal conditions. The HTT model assumes that the timing, rate and percentage of seed germination for a constant temperature to be controlled by the difference between water potential of the seedbed and the b for a given percentile (b(g)). Most previous studies have assumed that b(g) is normally distributed. Our results suggested that the Weibull distribution may be more suitable than the normal distribution for seed germination modeling of castor bean. Similar to the normal distribution model the parameters of the Weibull HTT model can be readily interpreted to yield information about the frequency distribution of population for b(g), enabling comparison of the germination behaviors in different seed populations. The location parameter of Weibull HTT model (μ) specifies the lowest b(g) possible value in the population ((b(0)) that cannot be derived from normal HTT model. The median (M) and mode (Mo) can be readily determined by equations of and, respectively, from the μ, scale (σ) and λ parameters. The median specifies the value of b(50) for the population and the mode will specify the location of the peak of the probability distribution function for b(g). Another advantage of the Weibull distribution in this application is that it can approximate a range of b(g) distributions through changing the shape parameter.

Results of this research were in contrast with the assumption of a normal distribution of base water potential of a seed population. Hence, before using a hydrothermal time model for predictions the distribution of base water potential within a seed sample should be examined and an appropriate equation be selected.. Due to the flexibility of the Weibull distribution, this model provides a useful method for predicting germination and determining the distribution of base water potential.