Importance of distribution function selection for hydrothermal time models of seed germination

Summary The germination of a population of seeds was modelled using the concept of hydrotime or hydrothermal time. Typically, a Normal distribution for base water potential (Ψb(g)) was used within these models to relate variation in Ψb(g) to the variation in time to germination of a given fraction of seeds. We sought to examine empirically the validity of this assumption, to compare the fit of alternative distributions and make recommendations for improved germination modelling procedures. Eight statistical distributions (Gumbel, Weibull, Normal, Log‐Normal, Logistic, Loglogistic, Inverse Normal and Gamma) were fitted to data for four weed species Hordeum spontaneum, Phalaris minor, Heliotropium europaeum and Raphanus raphanistrum. Methods for incorporating each of these distributions into hydrotime are presented. For three species (H. spontaneum, P. minor and H. europaeum), the Normal distribution gave the worst fit (with AIC values: −124.2, −296.9 and −264.5, respectively) and would lead to biased predictions, whereas the Loglogistic distribution consistently provided the best explanation of Ψb(g) variation in these species (with AIC values: −188.6, −326.2 and −272.1 respectively). All distributions failed to provide an unbiased description of the observed distribution of Ψb(g) in R. raphanistrum. The Normal distribution is not necessarily the best function for base water potential in hydrothermal models and, indeed, may give much more biased predictions than alternative functions. The ‘best’ distribution may vary with species. The distribution of Ψb(g) within a seed sample should therefore be examined and an appropriate equation selected, before using a model to make predictions.