sharpeschoolfull_1981 {rTPC}

Full Sharpe-Schoolfield model for fitting thermal performance curves

Description

Full Sharpe-Schoolfield model for fitting thermal performance curves

Usage

sharpeschoolfull_1981(temp, r_tref, e, el, tl, eh, th, tref)

Arguments

temp

temperature in degrees centigrade

r_tref

rate at the standardised temperature, tref

e

activation energy (eV)

el

low temperature de-activation energy (eV)

tl

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

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 either high or low temperatures

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_l}{k}(\frac{1}{t_l} - \frac{1}{temp + 273.15})} + 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.

Value

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

Note

Generally we found this model easy to fit.

Author(s)

Daniel Padfield

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. Journal of Theoretical Biology 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 = 'sharpeschoolfull_1981')
# fit model
mod <- nls_multstart(rate~sharpeschoolfull_1981(temp = temp, r_tref, e, el, tl, eh, th, tref = 20),
data = d,
iter = c(3,3,3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'sharpeschoolfull_1981'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'sharpeschoolfull_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()