Evaluating the effect of temperature on microbial growth rate--the Ratkowsky and a Bělehrádek-type models

The objective of this paper to conduct a parallel comparison of a new Bělehrádek-type growth rate (with an exponent of 1.5, or the Huang model), Ratkowsky square-root, and Ratkowsky square equations as secondary models for evaluating the effect of temperature on the growth of microorganisms. Growth rates of psychrotrophs and mesophiles were selected from the literature, and independently analyzed with the 3 models using nonlinear regression. Analysis of variance (ANOVA) was used to compare the means of growth rate (μ), estimated minimum temperature (T(min) ), approximate standard errors (SE) of T(min) , model mean square errors (MSE), accuracy factor (A(f) ), bias factor (B(f) ), relative residual errors (δ), Akaike information criterion (AICc), and Bayesian information criterion (BIC). Based on the estimated T(min) values, the Huang model distinctively classified the bacteria into 2 groups (psychrotrophs and mesophiles). No significant difference (P > 0.05) was observed among the means of the μ values reported in the literature or estimated by the 3 models, suggesting that all 3 models were suitable for curve fitting. Nor was there any significant difference in MSE, SE, δ, A(f) , B(f) , AICc, and BIC. The T(min) values estimated by the Huang model were significantly higher than those estimated by the Ratkowsky models, but were in closer agreement with the biological minimum temperatures for both psychrotrophs and mesophiles. The T(min) values estimated by the Ratkowsky models systematically underestimated the minimum growth temperatures. In addition, statistical estimation showed that the mean exponent for the new Bělehrádek-type growth rate model may indeed be 1.5, further supporting the validity of the Huang model.