secondary {nlstools} | R Documentation |
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 florent.baty@unibas.ch
Marie-Laure Delignette-Muller ml.delignette@vet-lyon.fr
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)