johnsonlewin_1946 {rTPC}

Johnson-Lewin model for fitting thermal performance curves

Description

Johnson-Lewin model for fitting thermal performance curves

Usage

johnsonlewin_1946(temp, r0, e, eh, topt)

Arguments

temp

temperature in degrees centigrade

r0

scaling parameter

e

activation energy (eV)

eh

high temperature de-activation energy (eV)

topt

optimum temperature (ºC)

Details

Equation:

rate= \frac{r_0 \cdot exp^{\frac{-e}{k\cdot (temp + 273.15)}}}{1 + exp^{-\frac{e_h -\big(\frac{e_h}{(t_{opt} + 273.15)} + k \cdot ln\big(\frac{e}{e_h - e}\big) \big) \cdot (temp + 273.15)}{k \cdot (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 difficult to fit.

References

Johnson, Frank H., and Isaac Lewin. The growth rate of E. coli in relation to temperature, quinine and coenzyme. Journal of Cellular and Comparative Physiology 28.1 (1946): 47-75.

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 = 'johnsonlewin_1946')
# fit model
mod <- suppressWarnings(
nls.multstart::nls_multstart(rate~johnsonlewin_1946(temp = temp, r0, e, eh, topt),
data = d,
iter = c(5,5,5,5),
start_lower = start_vals - 1,
start_upper = start_vals + 1,
lower = get_lower_lims(d$temp, d$rate, model_name = 'johnsonlewin_1946'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'johnsonlewin_1946'),
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()