RichardsNLM function to fit the Richards no lag growth model to an incomplete 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
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
Richards JF (1959). “A flexible growth function for empirical use.” J Exp Bot, 1(10), 290-310.
Author
Vasco Cadavez, vcadavez@ipb.pt and Ursula Gonzales-Barron, ubarron@ipb.pt
Examples
## Example: Richards no lag model
library(gslnls)
data(growthnolag) # simulated data set.
initial_values = list(Y0=0, Ymax=22, MUmax=1.7)
## Fitting the function to the experimental data
fit <- gsl_nls(lnN ~ RichardsNLM(Time, Y0, Ymax, MUmax),
data=growthnolag,
start = initial_values)
summary(fit)
#>
#> Formula: lnN ~ RichardsNLM(Time, Y0, Ymax, MUmax)
#>
#> Parameters:
#> Estimate Std. Error t value Pr(>|t|)
#> Y0 1.75827 0.36368 4.835 0.00189 **
#> Ymax 21.13234 0.24673 85.650 7.79e-12 ***
#> MUmax 1.85922 0.06619 28.091 1.86e-08 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.4896 on 7 degrees of freedom
#>
#> Number of iterations to convergence: 5
#> Achieved convergence tolerance: 1.326e-12
#>