Experimental design and parameter estimation for threshold models in seed germination

Hydrotime threshold models are used to describe the dynamics of seed germination in response to reduced water availability. Although these models provide several biologically relevant parameters, it is unclear which statistical technique is best suited to their estimation. Most commonly, these models are fitted to the observed cumulative proportions of germinated seeds, using nonlinear regression. However, this approach has been questioned, due to its inability to account for some characteristics of data sets obtained from germination assays, such as interval censoring and correlated observations. We used Monte Carlo simulations to determine the bias and precision of nonlinear regression estimators for a wide range of experimental designs and hypothetical plant species. Results showed that point estimates of model parameters were almost unbiased, while standard errors obtained from nonlinear regression were on average 3-4 times smaller than the Monte Carlo precision. Standard errors obtained by nonparametric resampling methods were comparable to Monte Carlo precision and provided good coverage (very close to the nominal 95% value), with at least 4-8 treatments by four replicates and 50 seeds per Petri dish. With 10 seeds per Petri dish, a higher number of replicates were necessary to achieve good coverage. In particular, good results were obtained with the grouped jackknife (delete-a-Petri-dish), which accounts for repeated observations on the same Petri dish. It is suggested that nonlinear regression may be used to fit the hydrotime model, in association with resampling methods, particularly when the purpose is to compare hydrotime' parameters across treatments or plant species.