Abstract
Logistic, Gompertz, Richards and Weibull growth curves were evaluated for their suitability as mathematical and empirical models to represent cumulative germination. By avoiding the limitations associated with the method of moments and single-value germination indices, the fitted models provided superior description of the time course of germination. The four-parameter Weibull model gave the best fit across a relatively wide range of seed species and germination conditions, and the resulting parameter estimates reflected identifiable aspects of the germination process. The nonlinear estimation of the germination response included a parameter summary, together with their asymptotic standard errors and correlation matrix, along with an approximate band for the expectation function, pairwise plots of the parameter inference region, and profile t plots. Evaluation of the fitted models also included information on lack of fit and residual structure. Empirical results and hypothesis testing were demonstrated with reference to a replicated experiment designed to determine the effects of reduced water potential on germination of onion seeds.
Keywords
Nonlinear regression, cumulative germination, growth curves, Weibull model.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Shafii, Bahman; Price, William J.; Swensen, Jerry B.; and Murray, Glen A.
(1991).
"NONLINEAR ESTIMATION OF GROWTH CURVE MODELS FOR GERMINATION DATA ANALYSIS,"
Conference on Applied Statistics in Agriculture.
https://doi.org/10.4148/2475-7772.1415
NONLINEAR ESTIMATION OF GROWTH CURVE MODELS FOR GERMINATION DATA ANALYSIS
Logistic, Gompertz, Richards and Weibull growth curves were evaluated for their suitability as mathematical and empirical models to represent cumulative germination. By avoiding the limitations associated with the method of moments and single-value germination indices, the fitted models provided superior description of the time course of germination. The four-parameter Weibull model gave the best fit across a relatively wide range of seed species and germination conditions, and the resulting parameter estimates reflected identifiable aspects of the germination process. The nonlinear estimation of the germination response included a parameter summary, together with their asymptotic standard errors and correlation matrix, along with an approximate band for the expectation function, pairwise plots of the parameter inference region, and profile t plots. Evaluation of the fitted models also included information on lack of fit and residual structure. Empirical results and hypothesis testing were demonstrated with reference to a replicated experiment designed to determine the effects of reduced water potential on germination of onion seeds.
