joehnk_2008 {rTPC}

Jöhnk model for fitting thermal performance curves

Description

Jöhnk model for fitting thermal performance curves

Usage

joehnk_2008(temp, rmax, topt, a, b, c)

Arguments

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

Details

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.

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

Joehnk, Klaus D., et al. Summer heatwaves promote blooms of harmful cyanobacteria. Global change biology 14.3: 495-512 (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 = '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()