eubank_1973: Eubank model for fitting thermal performance curves

In padpadpadpad/rTPC: Fitting and Analysing Thermal Performance Curves

Eubank model for fitting thermal performance curves

Description

Eubank model for fitting thermal performance curves

Usage

eubank_1973(temp, topt, a, b)

Arguments

temp	temperature in degrees centigrade
topt	optimum temperature (ºC)
a	scale parameter defining the height of the curve
b	shape parameter of the curve

Details

Equation:

rate = \frac{a}{(T-T_{\text{opt}})^2+b}

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.

Author(s)

Francis Windram

References

Eubank, W. P., Atmar, J. W. & Ellington, J. J. The significance and thermodynamics of fluctuating versus static thermal environments on Heliothis zea egg development rates. Environ. Entomol. 2, 491–496 (1973).

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 = 'eubank_1973')
# fit model
mod <- nls.multstart::nls_multstart(rate~eubank_1973(temp = temp, topt, a, b),
data = d,
iter = 200,
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'eubank_1973'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'eubank_1973'),
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()

padpadpadpad/rTPC documentation built on Feb. 21, 2025, 5:30 a.m.