growthmodels {nlsMicrobio}

Bacterial growth models

Description

Formulas of primary growth models commonly used in predictive microbiology

Usage

  baranyi
  baranyi_without_Nmax
  baranyi_without_lag
  buchanan
  buchanan_without_Nmax
  buchanan_without_lag
  gompertzm

Details

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)

Value

A formula

Author(s)

Florent Baty, Marie-Laure Delignette-Muller

References

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.

Examples

# 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)