BuchananRM function to fit the Buchanan reduced growth model to a reduced 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- 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(N(t)).
References
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(4), 313-326. ISSN 0740-0020, doi:10.1006/fmic.1997.0125 , http://www.sciencedirect.com/science/article/pii/S0740002097901258.
Author
Vasco Cadavez, vcadavez@ipb.pt and Ursula Gonzales-Barron, ubarron@ipb.pt
Examples
## Example: Buchanan reduced model
library(gslnls)
data(growthred) # simulated data set.
initial_values = list(Y0=0, MUmax=1.7, lag=5) # define the initial values
fit <- gsl_nls(lnN ~ BuchananRM(Time, Y0, MUmax, lag),
data=growthred,
start = initial_values)
summary(fit)
#>
#> Formula: lnN ~ BuchananRM(Time, Y0, MUmax, lag)
#>
#> Parameters:
#> Estimate Std. Error t value Pr(>|t|)
#> Y0 0.05010 0.22810 0.22 0.833
#> MUmax 1.83840 0.04722 38.93 1.92e-08 ***
#> lag 5.04160 0.21567 23.38 4.02e-07 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.3951 on 6 degrees of freedom
#>
#> Number of iterations to convergence: 3
#> Achieved convergence tolerance: 2.269e-11
#>