hinshelwood_1947 {rTPC} | R Documentation |
Hinshelwood model for fitting thermal performance curves
Description
Hinshelwood model for fitting thermal performance curves
Usage
hinshelwood_1947(temp, a, e, b, eh)
Arguments
temp |
temperature in degrees centigrade |
a |
pre-exponential constant for the activation energy |
e |
activation energy (eV) |
b |
pre-exponential constant for the deactivation energy |
eh |
de-activation energy (eV) |
Details
Equation:
rate=a \cdot exp^{\frac{-e}{k \cdot (temp + 273.15)}} - b \cdot exp^\frac{-e_h}{k \cdot (temp + 273.15)}
where k
is Boltzmann's constant with a value of 8.62e-05
Start values in get_start_vals
are taken from the literature.
Limits in get_lower_lims
and get_upper_lims
are based on extreme values that are unlikely to occur in ecological settings.
Value
a numeric vector of rate values based on the temperatures and parameter values provided to the function
Note
Generally we found this model difficult to fit.
References
Hinshelwood C.N. The Chemical Kinetics of the Bacterial Cell. Oxford University Press. (1947)
Examples
# load in ggplot
library(ggplot2)
# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)
# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'hinshelwood_1947')
# fit model
mod <- nls.multstart::nls_multstart(rate~hinshelwood_1947(temp = temp,a, e, b, eh),
data = d,
iter = c(5,5,5,5),
start_lower = start_vals - 1,
start_upper = start_vals + 1,
lower = get_lower_lims(d$temp, d$rate, model_name = 'hinshelwood_1947'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'hinshelwood_1947'),
supp_errors = 'Y',
convergence_count = FALSE)
# look at model fit
summary(mod)
# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)
# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()