Hydrotime modeling of Phalaris minor, Amaranthus retroflexus and A. blitoides seed germination

Seed germination has been modeled extensively using hydrotime and hydrothermal time models. Variation in time to germination arises from variation in base water potential within a seed population that typically is modeled by a normal distribution. Here, the assumption of normality in the distribution of base water potential was examined by germinating seed of Phalaris minor, Amaranthus retroflexus and A. blitoides across a range of constant water potential (0, -0.2, -0.4, -0.6 and -0.8 MPa). Three statistical distributions of Normal, Weibull and Gumbel were compared to illustrate the relative variation of base water potential. The results showed that the estimated parameters of the hydrotime model developed on the basis of Weibull distribution had more certainty than other distributions (AICc=-322.2 for P. minor, AICc=-262.8 for A. retroflexus and AICc=-507.9 for A. blitoides). Values of shape parameter suggest that the base water potential is right skewed for three species (λ=0.93 for P. minor, λ=1.75 for A. retroflexus and λ=2.21 for A. blitoides). Based on the Weibull hydrotime model, values of the hydrotime constant and water potential threshold for onset of P. minor seed germination were estimated to be 106.64 MPa h and -1.52 MPa, respectively, for A. retroflexus 20.47 MPa h and -0.86 MPa, respectively and for A. blitoides as 76.61 MPa h and -1.07 MPa, respectively. 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.