Hydrotime Analysis of Yellow Sweetclover (Melilotus officinalis (L.) Lam.), Wild Mustard (Sinapis arvensis L.) and Barley (Hordeum vulgare L.) Seed Germination

Seed germination is one of the key stages in the life cycle of plants that can ultimately affect their fitness in the environment. The temporal pattern of seed germination is extremely depended on the soil water potential (Ψ) of the germination medium, as this determines the equilibrium water content of the seed. As for temperature, there is a minimum Ψ that must be exceeded in order for seeds complete germination, and seeds in a population vary in the value of this minimum or base Ψ. The germination of a seed population in response to the reduced water potential is modeled using the hydrotime model. According to this model, the time to germination for a given seed fraction (g) is inversely related to the difference between the current seed Ψ and the base water potential (Ψb) for that fraction (Ψb(g)). The hydrotime model functions are well in matching both the timing and the percentage of germination of seed populations in relation to their Ψ environment. In addition, the model outputs which are significant physiologically and ecologically and the parameters of the model can be used to characterize the properties of seed populations. Normal distribution of Ψb among seeds within a population is one of the assumptions of the hydrotime model. However, this assumption may not be met in many species and thus can result in poor predictions. We tried to investigate empirically the validity of this assumption, to compare the fit of alternative distributions and make recommendations to improve germination modeling procedures.
Seed germination of Melilotus officinalis, Sinapis arvensis and Hordeum vulgare were tested across a range of water potentials (0, -0.2, -0.4, -0.6 and -0.8 MPa for M. officinalis and S. arvensis and 0, -0.3, -0.6, -0.9, -1.2 and -1.5 MPa for H. vulgare) and germination responses were described by the hydrotime models based on twelve statistical functions including Normal, Beta, Gamma, Loglogistic, Weibull, Gumbel, Birnbaum-Saunders, Inverse-normal, Log-normal, logistics, Rayleigh and Inverse-gamma. Four replicates of 50 seeds were spread evenly within 9-cm-diameter Petri dishes, each containing a Whatman No 1 filter paper. Each filter paper was moistened with 6 mL of polyethylene glycol (PEG) solutions or distilled water (0 MPa). Osmotic solutions were prepared by dissolving PEG 6000 in distilled water according to the Michel (1983) equation. Germinated seeds (radicle protrusion of>2 mm) were counted daily two or three times for 20 days. All distributions, having been formulated into the hydrotime model, were fitted to data using the PROC NLMIXED procedure of SAS, with the default optimization technique of dual quasi-Newton algorithm.
The results showed that the estimated parameters of the hydrotime model developed on the basis of Beta distribution had more certainty than the other distributions (AICc=-556.60 for M. officinalis, AICc=-847.70 for S. arvensis and AICc=-1034.20 for H. vulgare). Based on the Beta hydrotime model, values of the hydrotime constant (θH) and water potential threshold for beginning of M. officinalis seed germination (δ) were estimated to be 14.01 MPa h and -0.85 MPa, respectively. For S. arvensis, θH and δ estimated to be 22.23 MPa h and -0.98 MPa, respectively. Estimated θH and δ for H. vulgare was 48.69 MPa h and -2.47 MPa, respectively. Results of this research are in contrast to assumption of a normal distribution of base water potential of a seed population. Hence, before using a hydrothermal time model to make predictions, the distribution of base water potential within a seed sample should be examined and an appropriate equation should be selected.. The results indicated that among all three species, the Beta distribution resulting in more accurate predictions than the other distributions. The hydrotime model based on Beta distribution predicts an actual value for the phase of delay germination. In fact, less skewed in predicted germination using beta model can be related to more accurately of this function to predict the onset of germination. Shape parameter gives high flexibility to this model and allows more accurate prediction of delayed germination phase. In addition, the hydrotime model based on Beta distribution was able to prediction germination of species for which the base water potential distribution is symmetrical or unsymmetrical.
In this paper, a model based on the beta distribution is proposed which is not only more biologically relevant, but also provides better predictions of germination compared to the conventional model.