growthmodels {nlstools} | R Documentation |
Formulas of primary growth models commonly used in predictive microbiology
baranyi baranyi_without_Nmax baranyi_without_lag buchanan buchanan_without_Nmax buchanan_without_lag gompertzm
These models describe the evolution of the decimal logarithm of the microbial count (LOG10N) as a function of the time (t).
baranyi
is the model of Baranyi and Roberts (1994) with four parameters (LOG10N0, mumax, lag, LOG10Nmax)
baranyi_without_Nmax
is the model of Baranyi and Roberts (1994) with three parameters (LOG10N0, mumax, lag), without braking
baranyi_without_lag
is the model of Baranyi and Roberts (1994) with three parameters (LOG10N0, mumax, LOG10Nmax), without lag
buchanan
is the three-phase linear model proposed by Buchanan et al. (1997)
buchanan_without_Nmax
is the two-phase linear model with three parameters (LOG10N0, mumax, lag), without braking
buchanan_without_lag
is the two-phase linear model with three parameters (LOG10N0, mumax, LOG10Nmax), without lag
gompertzm
is the modified Gompertz model introduced by Gibson et al. (1988) and reparameterized by Zwietering et al. (1990)
A formula
Florent Baty florent.baty@unibas.ch
Marie-Laure Delignette-Muller ml.delignette@vet-lyon.fr
Baranyi J and Roberts, TA (1994) A dynamic approach to predicting bacterial growth in food, International Journal of Food Microbiology, 23, 277-294.
Buchanan RL, Whiting RC, Damert WC (1997) When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves. Food Microbiology, 14, 313-326.
Gibson AM, Bratchell N, Roberts TA (1988) Predicting microbial growth: growth responses of salmonellae in a laboratory medium as affected by pH, sodium chloride and storage temperature. International Journal of Food Microbiology, 6, 155-178.
Zwietering MH, Jongenburger I, Rombouts FM, Van't Riet K (1990) Modeling of the bacterial growth curve. Applied and Environmental Microbiology, 56, 1875-1881.
# Example 1 data(growthcurve1) nls1 <- nls(baranyi, growthcurve1, list(lag=4, mumax=1, LOG10N0 = 4, LOG10Nmax = 9)) nls2 <- nls(gompertzm,growthcurve1, list(lag = 4, mumax = 1, LOG10N0 = 4, LOG10Nmax = 9)) nls3 <- nls(buchanan, growthcurve1, list(lag = 4, mumax = 1, LOG10N0 = 4, LOG10Nmax = 9)) def.par <- par(no.readonly = TRUE) par(mfrow = c(2,2)) plotfit(nls1, smooth = TRUE) plotfit(nls2, smooth = TRUE) plotfit(nls3, smooth = TRUE) par(def.par) # Example 2 data(growthcurve2) nls4 <- nls(baranyi_without_Nmax, growthcurve2, list(lag = 2, mumax = 0.4, LOG10N0 = 7.4)) nls5 <- nls(buchanan_without_Nmax,growthcurve2, list(lag = 2, mumax = 0.4, LOG10N0 = 7.4)) def.par <- par(no.readonly = TRUE) par(mfrow = c(2,1)) plotfit(nls4, smooth = TRUE) plotfit(nls5, smooth = TRUE) par(def.par) # Example 3 data(growthcurve3) nls6 <- nls(baranyi_without_lag, growthcurve3, list(mumax = 1, LOG10N0 = 0, LOG10Nmax = 5)) nls7 <- nls(buchanan_without_lag, growthcurve3, list(mumax = 1, LOG10N0 = 0, LOG10Nmax = 5)) def.par <- par(no.readonly = TRUE) par(mfrow = c(2,1)) plotfit(nls6, smooth = TRUE) plotfit(nls7, smooth = TRUE) par(def.par)