joehnk_2008 | R Documentation |
Jöhnk model for fitting thermal performance curves
joehnk_2008(temp, rmax, topt, a, b, c)
temp |
temperature in degrees centigrade |
rmax |
the rate at optimum temperature |
topt |
optimum temperatute (ºC) |
a |
parameter with no biological meaning |
b |
parameter with no biological meaning |
c |
parameter with no biological meaning |
Equation:
rate=r_{max} \bigg(1 + a \bigg(\bigg(b^{temp-t_{opt}} -1\bigg) - \frac{ln(b)}{ln(c)}(c^{temp-t_{opt}} -1)\bigg)\bigg)
Start values in get_start_vals
are derived from the data or sensible values 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.
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.
Joehnk, Klaus D., et al. Summer heatwaves promote blooms of harmful cyanobacteria. Global change biology 14.3: 495-512 (2008)
# 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 = 'joehnk_2008')
# fit model
mod <- nls.multstart::nls_multstart(rate~joehnk_2008(temp = temp, rmax, topt, a, b, c),
data = d,
iter = c(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 = 'joehnk_2008'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'joehnk_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()
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