rTPC (version 1.0.4)

sharpeschoolhigh_1981: Sharpe-Schoolfield model (high temperature inactivation only) for fitting thermal performance curves

Description

Sharpe-Schoolfield model (high temperature inactivation only) for fitting thermal performance curves

Usage

sharpeschoolhigh_1981(temp, r_tref, e, eh, th, tref)

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Arguments

temp

temperature in degrees centigrade

r_tref

rate at the standardised temperature, tref

e

activation energy (eV)

eh

high temperature de-activation energy (eV)

th

temperature (ºC) at which enzyme is 1/2 active and 1/2 suppressed due to high temperatures

tref

standardisation temperature in degrees centigrade. Temperature at which rates are not inactivated by high temperatures

Author

Daniel Padfield

Details

Equation: $$rate= \frac{r_{tref} \cdot exp^{\frac{-e}{k} (\frac{1}{temp + 273.15}-\frac{1}{t_{ref} + 273.15})}}{1 + exp^{\frac{e_h}{k}(\frac{1}{t_h}-\frac{1}{temp + 273.15})}}$$

where k is Boltzmann's constant with a value of 8.62e-05.

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

References

Schoolfield, R. M., Sharpe, P. J. & Magnuson, C. E. Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. J. Theor. Biol. 88, 719-731 (1981)

Examples

# load in ggplot
library(ggplot2)
library(nls.multstart)

# 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 = 'sharpeschoolhigh_1981')
# fit model
mod <- nls_multstart(rate~sharpeschoolhigh_1981(temp = temp, r_tref, e, eh, th, tref = 20),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'sharpeschoolhigh_1981'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'sharpeschoolhigh_1981'),
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()