pawar_2018 | R Documentation |
Pawar model for fitting thermal performance curves
pawar_2018(temp, r_tref, e, eh, topt, tref)
temp |
temperature in degrees centigrade |
r_tref |
rate at the standardised temperature, tref |
e |
activation energy (eV) |
eh |
high temperature de-activation energy (eV) |
topt |
optimum temperature (ºC) |
tref |
standardisation temperature in degrees centigrade. Temperature at which rates are not inactivated by high temperatures |
This model is a modified version of sharpeschoolhigh_1981
that explicitly models the optimum temperature.
Equation:
rate= \frac{r_{tref} \cdot exp^{\frac{-e}{k} (\frac{1}{temp + 273.15}-\frac{1}{t_{ref} + 273.15})}}{1 + (\frac{e}{eh - e}) \cdot exp^{\frac{e_h}{k}(\frac{1}{t_opt + 273.15}-\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.
a numeric vector of rate values based on the temperatures and parameter values provided to the function
Generally we found this model easy to fit.
Daniel Padfield
Kontopoulos, Dimitrios - Georgios, Bernardo García-Carreras, Sofía Sal, Thomas P. Smith, and Samraat Pawar. Use and Misuse of Temperature Normalisation in Meta-Analyses of Thermal Responses of Biological Traits. PeerJ. 6 (2018),
# 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 = 'pawar_2018')
# fit model
mod <- nls_multstart(rate~pawar_2018(temp = temp, r_tref, e, eh, topt, 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 = 'pawar_2018'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'pawar_2018'),
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()
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