Cardinal model for temperature

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

Usage

CMTI(x, Tmax, Tmin, MUopt, Topt)

Arguments

x

is a numeric vector indicating the temperature of the experiment

Tmax

maximum temperature for growth

Tmin

is minimum temperature for growth

MUopt

is the optimum growth rate

Topt

is optimum temperature for growth

Value

A numeric vector with the fitted values

Details

The model's inputs are:

x: Temperature

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(salmonella)
initial_values <- list(Tmax = 42, Tmin = 1, MUopt = 1.0, Topt = 37)
fit <- gsl_nls(sqrtGR ~ CMTI(Temp, Tmax, Tmin, MUopt, Topt),
  data = salmonella,
  start = initial_values
)
summary(fit)
#> 
#> Formula: sqrtGR ~ CMTI(Temp, Tmax, Tmin, MUopt, Topt)
#> 
#> Parameters:
#>       Estimate Std. Error t value Pr(>|t|)    
#> Tmax  49.03256    0.13336  367.68  < 2e-16 ***
#> Tmin   5.02679    0.37058   13.56 1.51e-10 ***
#> MUopt  0.75206    0.01156   65.05  < 2e-16 ***
#> Topt  40.36709    0.24985  161.56  < 2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.01718 on 17 degrees of freedom
#> 
#> Number of iterations to convergence: 44 
#> Achieved convergence tolerance: 7.98e-17
#> 

plot(salmonella$Temp, salmonella$sqrtGR^2)
lines(salmonella$Temp, fitted(fit)^2, col = "green")

plot(salmonella$Temp, salmonella$sqrtGR)
lines(salmonella$Temp, fitted(fit), col = "red")