Cardinal model for water activity

CMAW function to fit the water activity cardinal model (Rosso et al., 1993). Returns the model parameters estimated according to data collected in microbial growth experiments.

Usage

CMAW(x, AWmin, MUopt, AWopt)

Arguments

x

is a numeric vector indicating the water activity of the experiment

AWmin

is minimum water activity for growth

MUopt

is the optimum growth rate

AWopt

is optimum water activity for growth

Value

A numeric vector with the fitted values

Details

The model's inputs are:

x: Water activity

sqrtGR: the square root of the growth rate (\(h^{-1}\))

Users should make sure that the growth rate input is entered after a square root transformation, sqrGR = sqrt(GR).

References

Rosso L, Lobry J, Charles (Bajard) S, Flandrois J (1995). “Convenient Model To Describe the Combined Effects of Temperature and pH on Microbial Growth.” Applied and environmental microbiology, 61, 610–6. doi:10.1128/AEM.61.2.610-616.1995 .

Author

Vasco Cadavez vcadavez@ipb.pt and Ursula Gonzales-Barron ubarron@ipb.pt

Examples

library(gslnls)
data(aw)
initial_values <- list(AWmin = 0.89, MUopt = 1.0, AWopt = 0.98)
fit <- gsl_nls(sqrtGR ~ CMAW(aw, AWmin, MUopt, AWopt),
  data = aw,
  start = initial_values
)
summary(fit)
#> 
#> Formula: sqrtGR ~ CMAW(aw, AWmin, MUopt, AWopt)
#> 
#> Parameters:
#>       Estimate Std. Error t value Pr(>|t|)    
#> AWmin 0.771652   0.005203  148.30 6.34e-12 ***
#> MUopt 1.558631   0.060203   25.89 2.19e-07 ***
#> AWopt 0.946016   0.002955  320.16 6.27e-14 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.04824 on 6 degrees of freedom
#> 
#> Number of iterations to convergence: 9 
#> Achieved convergence tolerance: 4.337e-16
#>