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Statistical evaluation of mathematical models for microbial growth
S López1, M Prieto, J Dijkstra
1Department of Animal Production, University of León, E-24071 León, Spain. dp1slp@unileon.es
International Journal of Food Microbiology
|September 30, 2004
Summary
This study evaluated mathematical models for microbial growth curves, finding Baranyi, three-phase linear, Richards, and Weibull models superior to Gompertz. These models offer better fits for bacterial and fungal growth data analysis.
Area of Science:
- Microbiology
- Mathematical Modeling
- Biostatistics
Background:
- Accurate modeling of microbial growth curves is crucial for understanding bacterial and fungal dynamics.
- Various nonlinear mathematical functions are employed to describe microbial growth, but their suitability varies.
- The Gompertz model is commonly used, yet its performance may not be optimal for all experimental data.
Purpose of the Study:
- To assess the performance of nine nonlinear mathematical functions in describing microbial growth curves.
- To compare the goodness-of-fit and residual analysis of different models using diverse experimental datasets.
- To identify superior models for microbial growth curve analysis, potentially challenging the widespread use of the Gompertz model.
Main Methods:
- Evaluated nine nonlinear functions: three-phase linear, logistic, Gompertz, Von Bertalanffy, Richards, Morgan, Weibull, France, and Baranyi.
- Utilized two datasets: optical density measurements (21 curves) and plate counts of Yersinia enterocolitica (34 curves) under varied conditions.
- Assessed model performance using statistical criteria including residual analysis and goodness-of-fit tests (e.g., AIC, F-test).
Main Results:
- The Baranyi, three-phase linear, Richards, and Weibull models demonstrated the best overall performance.
- The Baranyi model exhibited the best behavior across various criteria for the studied growth curves.
- Richards model excelled for optical density data, while the three-phase linear model showed limitations with optical density but performed well with plate counts.
Conclusions:
- The Baranyi, three-phase linear, Richards, and Weibull models are recommended over the Gompertz model for describing microbial growth.
- The choice of model may depend on the type of data (e.g., optical density vs. plate counts).
- Critical re-evaluation of the common use of the Gompertz model is warranted based on superior alternatives identified in this study.