Description Usage Details Value Author(s) References Examples

Formulas of primary growth models used in predictive microbiology to model the simultaneous growth of two competitive bacterial flora assuming a Jameson effect

1 2 3 |

These models describe the simultaneous evolution of the decimal logarithm of
the microbial
counts of two flora (LOG10N) as a function of the time (t) and of the flora (flora)
coded as 1 for counts of flora 1 and 2 for counts of flora 2. These three
models assume independent lag and growth parameters for flora 1 and 2, except for
the saturation which is supposed to be governed by the Jameson effect and modelled
by a common parameter (tmax) which represents the time at which both flora stop to
multiply. Modelling the simultaneous saturation by this way enables the model
to be fitted by `nls`

, as an analytical form of the model is available.

`jameson_buchanan`

is based on the model of Buchanan et al. (1997) for lag phase modelling
and is characterized by seven parameters
(LOG10N0_1, mumax_1, lag_1, LOG10N0_2, mumax_2, lag_2 and the common saturation
time tmax). This model was described and used in Vimont et al. (2006).

`jameson_baranyi`

is based on the model of Baranyi and Roberts (1994) for lag phase modelling
and is characterized by seven parameters
(LOG10N0_1, mumax_1, lag_1, LOG10N0_2, mumax_2, lag_2 and the common saturation
time tmax)

`jameson_without_lag`

is based on the exponential model without lag phase
and is thus characterized by five parameters
(LOG10N0_1, mumax_1, LOG10N0_2, mumax_2 and the common saturation time tmax)

A formula

Florent Baty [email protected]

Marie-Laure Delignette-Muller [email protected]

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.

Vimont A, Vernozy-Rozand C, Montet MP, Lazizzera C, Bavai C and Delignette-Muller ML (2006) Modeling and predicting the simultaneous growth of Escherichia coli O157:H7 and ground beef background microflora in various enrichment protocols.
*Applied and Environmental Microbiology* **72**, 261-268.

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options(digits=3)
### Example 1: fit of model jameson_buchanan
data(competition1)
nls1 <- nls(jameson_buchanan, competition1,
list(lag_1 = 2, mumax_1 = 1, LOG10N0_1 = 1, tmax = 12,
lag_2 = 2, mumax_2 = 1, LOG10N0_2 = 4))
overview(nls1)
# Plot of theoretical curves with data
twocolors <- c("red","blue")
npoints <- 100
seq.t <- seq(0,max(competition1$t),length.out=npoints)
prednls1.1 <- predict(nls1,data.frame(t=seq.t,flora=rep(1,npoints)))
prednls1.2 <- predict(nls1,data.frame(t=seq.t,flora=rep(2,npoints)))
plot(competition1$t,competition1$LOG10N,col=twocolors[competition1$flora],xlab="t",ylab="LOG10N")
lines(seq.t,prednls1.1,col=twocolors[1])
lines(seq.t,prednls1.2,col=twocolors[2])
### Example 2 : fit of model jameson_baranyi
data(competition1)
nls2 <- nls(jameson_baranyi, competition1,
list(lag_1 = 2, mumax_1 = 1, LOG10N0_1 = 1, tmax = 12,
lag_2 = 2, mumax_2 = 1, LOG10N0_2 = 4))
overview(nls2)
plotfit(nls2)
# Plot of theoretical curves with data
twocolors <- c("red","blue")
npoints <- 100
seq.t <- seq(0,max(competition1$t),length.out=npoints)
prednls2.1 <- predict(nls2,data.frame(t=seq.t,flora=rep(1,npoints)))
prednls2.2 <- predict(nls2,data.frame(t=seq.t,flora=rep(2,npoints)))
plot(competition1$t,competition1$LOG10N,col=twocolors[competition1$flora],xlab="t",ylab="LOG10N")
lines(seq.t,prednls2.1,col=twocolors[1])
lines(seq.t,prednls2.2,col=twocolors[2])
### Example 3: fit of model jameson_without_lag
data(competition2)
nls3 <- nls(jameson_without_lag, competition2,
list(mumax_1 = 1, LOG10N0_1 = 1, tmax = 12,
mumax_2 = 1, LOG10N0_2 = 4))
overview(nls3)
plotfit(nls3)
# Plot of theoretical curves with data
twocolors <- c("red","blue")
npoints <- 100
seq.t <- seq(0,max(competition2$t),length.out=npoints)
prednls3.1 <- predict(nls3,data.frame(t=seq.t,flora=rep(1,npoints)))
prednls3.2 <- predict(nls3,data.frame(t=seq.t,flora=rep(2,npoints)))
plot(competition2$t,competition2$LOG10N,col=twocolors[competition2$flora],xlab="t",ylab="LOG10N")
lines(seq.t,prednls3.1,col=twocolors[1])
lines(seq.t,prednls3.2,col=twocolors[2])
``` |

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