Hydrothermal-time-to-event models for seed germination

Time-to-event methods have been proposed in the agricultural sciences, as one of the most suitable options for the analysis of seed germination data. In contrast to traditional linear/nonlinear regression, time-to-event methods can easily account for all statistical peculiarities inherited in germination assays, such as censoring, and they can produce unbiased estimates of model parameters and their standard errors. So far, these methods have only been used in combination with empirical models of germination, which are lacking biological underpinnings. We bridge the gap between statistical requirements and biological understanding by developing a general method that formulates biologically-oriented hydro time (HT), thermal time (TT) and hydrothermal time (HTT) models into a time-to-event framework. HT, TT, and HTT models are widely used for describing seed germination and emergence of plants as affected by the environmental temperature and/or water potential. Owing to their simplicity and the direct biological interpretation of model parameters, these models have become one of the most common tools for both predicting germination as well as understanding the physiology of germination responses to environmental factors. However, these models are usually fitted by using nonlinear regression and, therefore, they fall short of statistical rigor when inference about model parameters is of interest. In this study, we develop HT-to-event, TT-to-event and HTT-to-event models and provide a readily available implementation relying on the package “drc” in the R statistical environment. Examples of usage are also provided and we highlight the possible advantages of this procedure, such as efficiency and flexibility.