ZwieteringFM function to fit the Zwietering full growth model to a complete microbial growth curve.
Returns the model parameters estimated according to data collected in microbial growth experiments.
Arguments
- t
is a numeric vector indicating the time of the experiment
- Y0
is the natural logarithm of the initial microbial concentration (
ln(N0)) at time=0- Ymax
is the natural logarithm of the maximum concentration (
ln(Nmax)) reached by the microorganism- MUmax
is the maximum specific growth rate given in time units
- lag
is the duration of the lag phase in time units
Details
Model's inputs are:
t: time, assuming time zero as the beginning of the experiment.
Y(t): the natural logarithm of the microbial concentration (ln(N(t)) measured at time t.
Users should make sure that the microbial concentration input is entered in natural logarithm, Y(t) = ln(X(t)).
References
Zwietering MH, Jongenburger I, Rombouts FM, van't Riet K (1990). “Modeling of the Bacterial Growth Curve.” Applied and Environmental Microbiology, 56(6), 1875-1881. ISSN 0099-2240, https://aem.asm.org/content/56/6/1875.
Author
Vasco Cadavez vcadavez@ipb.pt and Ursula Gonzales-Barron ubarron@ipb.pt
Examples
## Example: Zwietering full model
library(gslnls)
data(growthfull) # simulated data set.
initial_values = list(Y0=0, Ymax=22, MUmax=1.7, lag=5) # define the initial values
fit <- gsl_nls(lnN ~ ZwieteringFM(Time, Y0, Ymax, MUmax, lag),
data=growthfull,
start = initial_values)
summary(fit)
#>
#> Formula: lnN ~ ZwieteringFM(Time, Y0, Ymax, MUmax, lag)
#>
#> Parameters:
#> Estimate Std. Error t value Pr(>|t|)
#> Y0 0.01863 0.47551 0.039 0.97
#> Ymax 22.14679 0.60152 36.818 3.99e-11 ***
#> MUmax 2.29185 0.18848 12.160 6.88e-07 ***
#> lag 5.85464 0.48451 12.084 7.26e-07 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.7826 on 9 degrees of freedom
#>
#> Number of iterations to convergence: 7
#> Achieved convergence tolerance: 9.199e-11
#>