secondary: Secondary growth models
In nlsMicrobio: Nonlinear Regression in Predictive Microbiology

Description Usage Details Value Author(s) References Examples

Formulas of secondary growth models commonly used in predictive microbiology

  cpm_T
  cpm_pH_4p
  cpm_pH_3p
  cpm_aw_3p
  cpm_aw_2p
  cpm_T_pH_aw

All the models describe the evolution of the square root of the maximum specific growth rate (sqrtmumax) as a function of one or more environmental factors among temperature (T), pH (pH) and water activity (aw). Each model must be fitted to a data frame including at least two columns, the last one named "sqrtmumax" and the first ones named "T", "pH" or "aw" according to the model.

cpm_T is the cardinal temperature model with inflection (Rosso et al., 1993) with four parameters (Tmin, Topt, Tmax,muopt)

cpm_pH_4p is the cardinal pH model (Rosso et al., 1995) with four parameters (pHmin, pHopt, pHmax, muopt)

cpm_pH_3p is a symetric cardinal pH model with three parameters (pHmin, pHopt, muopt), obtained by fixing pHmax to 2pHopt-pHmin in the cpm_pH_4p model

cpm_aw_3p is the cardinal aw model (Rosso and Robinson, 2001) with three parameters (awmin, awopt, muopt)

cpm_aw_2p is a simplified cardinal aw model (Rosso and Robinson, 2001) with two parameters (awmin, muopt) obtained by fixing awopt to 1 in the cpm_aw_3p model

cpm_T_pH_aw is the cardinal model based on the gamma concept (Pinon et al., 2004) with 9 parameters (Tmin, Topt, Tmax, pHmin, pHopt, pHmax, awmin, awopt, muopt)

A formula

Florent Baty, Marie-Laure Delignette-Muller

Pinon A, Zwietering M, Perrier L, Membr\'e J, Leporq B, Mettler E, Thuault D, Coroller L, Stahl V, Vialette M (2004) Development and validation of experimental protocols for use of cardinal models for prediction of microorganism growth in food products. Applied Environmental Microbiology, 70, 1081-1087.

Rosso L, Robinson TP (2001) A cardinal model to describe the effect of water activity on the growth of moulds. International Journal of Food Microbiology, 63, 265-273.

Rosso L, Lobry JR, Bajard S, Flandrois JP (1995) Convenient model to describe the combined effects of temperature and pH on microbial growth. Applied Environmental Microbiology, 61, 610-616.

Rosso L, Lobry JR, Flandrois JP (1993) An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model. Journal of Theoretical Biology 162, 447-463.

data(ross)

# Example for the cpm_T model

d1 <- subset(ross, author == "salter" & aw == 0.997, 
	select = c(T, sqrtmumax))
nls1 <- nls(cpm_T, d1, list(muopt = 1.7, Tmin = 4, Topt = 40, Tmax = 47))
plotfit(nls1, smooth = TRUE)
overview(nls1)

# Example for the cpm_pH_4p model

d2 <- subset(ross, author == "presser" & aw > 0.99, 
	select = c(pH, sqrtmumax))
nls2 <- nls(cpm_pH_4p, d2, list(muopt = 0.5, pHmin = 4, 
	pHopt = 6.5, pHmax = 9))
plotfit(nls2, smooth = TRUE)
overview(nls2)

# Example for the cpm_pH_3p model

d3 <- subset(ross, author == "presser" & aw == 0.997, 
	select = c(pH, sqrtmumax))
nls3 <- nls(cpm_pH_3p, d3, list(muopt = 0.5, pHmin = 4, pHopt = 6.5))
plotfit(nls3, smooth = TRUE)
overview(nls3)

# Example for the cpm_aw_3p model

d4<-subset(ross, author == "mellefont", select = c(aw, sqrtmumax))
nls4 <- nls(cpm_aw_3p, d4, list(muopt = 0.6, awmin = 0.95, awopt = 0.995))
plotfit(nls4, smooth = TRUE)
overview(nls4)

# Example for the cpm_aw_2p model

d5 <- subset(ross, author == "mellefont" & aw < 0.99, 
	select = c(aw, sqrtmumax))
nls5 <- nls(cpm_aw_2p, d5, list(muopt = 0.6, awmin = 0.95))
plotfit(nls5, smooth = TRUE)
overview(nls5)


# Examples for the cpm_T_pH_aw model

d6 <- subset(ross, select = c(T, pH, aw, sqrtmumax))
nls6 <- nls(cpm_T_pH_aw, d6, list(muopt = 2, Tmin = 4, Topt = 40, Tmax = 49, 
	pHmin = 4, pHopt = 6.5, pHmax = 9, awmin = 0.95, awopt = 0.995))
def.par <- par(no.readonly = TRUE)
par(mfrow = c(2, 2))
plotfit(nls6, variable = 1)
plotfit(nls6, variable = 2)
plotfit(nls6, variable = 3)
overview(nls6)
par(def.par)