Iranian Journal of Seed Research

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Extended abstract
  Introduction: Numerous studies are being carried out to reveal the effects of different treatments on the germination of seeds from various plants. The most commonly used method of analysis is the nonlinear regression which estimates germination parameters. Although the nonlinear regression has been performed based on different models, some serious problems in its structure and results motivated researchers to investigate alternative approaches with higher accuracy and precision. The main purpose of the present research is to introduce the alternative parametric time to event model and comparing its reliability to the nonlinear regression in experiments carried out under different conditions.
  Materials and Methods:  The results of four different experiments were used here including the effect of Potassium cyanide on walnut seed germination, the effect of salinity on wheat seed germination, the effect of water potential on corn seed germination and the effect of temperature on cotton seed germination. The nonlinear regression and time to event methods were applied based on the Gompertz model. The obtained standard errors from the two models were further assessed using the Monte-Carlo method.
  Results: Both methods provided well-fitting models according to the MSE and R²   criteria. Although the germination parameters were approximately identical in both models, the standard error of parameters in nonlinear regression was significantly less than those of time to event method except for the experiments in which all tested seeds germinated within the time frame of study so that in the latter case the estimated standard errors in both models were identical. The Monte-Carlo method confirmed the results of the time to event model and reveals the underestimation of the nonlinear regression method in estimating the standard error of parameters.
  Conclusions: Generally, the results of this research showed that the time to event model can be trustfully utilized in seed germination studies under different conditions and treatments. This model, not only provides precise estimates of the germination parameters but also provides the precise standard error of parameters that have important roles in making inferences for parameters. The drc package in R software enables researchers to fit the different time to event models.

 
Highlights:

1. Using the time to the event model in estimation of seed germination parameters.
2. Comparing the time to event and nonlinear regression methods in different seed germination experiments.
3. Using the Monte-Carlo method for investigating the accuracy of results of the used methods.

 
 
 
 
 
 

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Objective: This study introduces functional analysis of variance as a method for comparing germination trends under different treatments over a given time interval. This approach not only enables the comparison of treatments over the entire time period but also allows for treatment comparisons at each specific moment in time. Moreover, it identifies critical time points at which the maximum significant difference between treatments occurs, which can serve as novel germination indices.
Method: In this study, real experimental data from four germination studies were analyzed: (1) the effect of temperature on Nigella sativa germination, (2) the effect of salinity stress on Zea mays seed germination, (3) the comparison of germination among different Triticum astivum cultivars, and (4) the effect of water stress on Brassica napus germination. Using spline functions, germination data from these experiments were modeled as a function of time. The results of functional analysis were then used to compare treatments in terms of both germination percentage and germination time across the four experiments.
Results: The results of the functional analysis demonstrated its high efficiency in detecting significant or non-significant differences between treatments throughout the germination period. Furthermore, this method enabled comparisons of germination percentages at any given time point, as well as comparisons of germination times at various germination percentiles, providing detailed insights into the nature of differences among treatments. This approach also facilitated the introduction of new germination indices applicable to different seed types.
Conclusions: Overall, the results of this study indicate that the stepwise functional analysis method introduced here is an effective and precise tool for comparing treatments in germination data. This approach not only enhances treatment comparisons but also provides detailed insights into the nature of differences between treatments. Moreover, it overcomes the limitations associated with using conventional germination indices for treatment comparisons.

Highlights

• Functional analysis was applied to compare treatments in germination percentage data.
• The method enabled treatment comparisons in terms of germination percentage at each moment in time, as well as comparisons of germination times at various percentiles.
• Critical germination times and percentiles at which the maximum differences between treatments occur were introduced as novel germination indices.