deutsch_2008 {rTPC} | R Documentation |
Modified deutsch model for fitting thermal performance curves
Description
Modified deutsch model for fitting thermal performance curves
Usage
deutsch_2008(temp, rmax, topt, ctmax, a)
Arguments
temp |
temperature in degrees centigrade |
rmax |
maximum rate at optimum temperature |
topt |
optimum temperature (ºC) |
ctmax |
critical thermal maximum (ºC) |
a |
related to the full curve width |
Details
Equation:
\textrm{if} \quad temp < t_{opt}: rate = r_{max} \cdot exp^{-\bigg(\frac{temp-t_{opt}}{2a}\bigg)^2}
\textrm{if} \quad temp > t_{opt}: rate = r_{max} \cdot \left(1 - \bigg(\frac{temp - t_{opt}}{t_{opt} - ct_{max}}\bigg)^2\right)
Start values in get_start_vals
are derived from the data.
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 easy to fit.
References
Deutsch, C. A., Tewksbury, J. J., Huey, R. B., Sheldon, K. S., Ghalambor, C. K., Haak, D. C., & Martin, P. R. Impacts of climate warming on terrestrial ectotherms across latitude. Proceedings of the National Academy of Sciences, 105(18), 6668-6672. (2008)
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 = 'deutsch_2008')
# fit model
mod <- nls.multstart::nls_multstart(rate~deutsch_2008(temp = temp, rmax, topt, ctmax, a),
data = d,
iter = c(4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'deutsch_2008'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'deutsch_2008'),
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()