Experimental design and parameter estimation for threshold models in seed germination

Abstract

SummaryHydrotime 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.

Bayesian approach for analysis of time-to-event data in plant biology

“…Thus, each of the parameters is assigned a prior distribution which quantifies our degree of belief in the parameter's values. Since alpha must lie in the interval [0,1], we assume its prior distribution to be the beta distribution, e.g., with the parameters [1,9]. B and C are assumed to have a Gaussian prior with mu B = 2, std B = 0.5, and mu C = 5, std C = 2.…”

“…However, growth curve fitting by means of nonlinear regression is not appropriate for time-to-event data because the regression models assume a different underlying mechanism (see the Additional file 1 for a full explanation). Several authors noticed the inadequacy of nonlinear regression for growth models, most notably [7][8][9][10].…”

Predicting field weed emergence with empirical models and soft computing techniques

“…Onofri et al . (, , ) presented new developments that maintain the positive features of parametric approaches, and Cao et al . () described a nonparametric approach as a very flexible tool to model weed emergence.…”

A comparative study between nonlinear regression and nonparametric approaches for modelling Phalaris paradoxa seedling emergence

“…Moreover, statistical goodness-of-fit techniques need to be applied to check the validity of the model used. However, these issues are not usually considered explicitly in the weed science literature, where fitting the model is the goal regardless of whether the statistical analysis is appropriate or not (Onofri et al, 2010(Onofri et al, , 2014Cao et al, 2011;Mesgaran et al, 2013). In order to cope with such limitations, different modelling approaches have been proposed, including techniques that account for censoring (Onofri et al, 2010(Onofri et al, , 2011, genetic algorithms (Haj Seyed-Hadi & Gonzalez-Andujar, 2009;Blanco et al, 2014) and artificial neural networks (Chantre et al, 2012).…”