mitchell_2009: Mitchell Angilletta model for fitting thermal performance...

In padpadpadpad/rTPC: Fitting and Analysing Thermal Performance Curves

Mitchell Angilletta model for fitting thermal performance curves

Description

Mitchell Angilletta model for fitting thermal performance curves

Usage

mitchell_2009(temp, topt, a, b)

Arguments

temp	temperature in degrees centigrade
topt	optimum temperature (ºC) where rate is maximal
a	scale parameter to convert the value of the cosine density to the appropriate magnitude
b	parameter dictating the performance breadth

Details

Equation:

rate=\frac{1}{2 \cdot b} \cdot (1 + cos(\frac{temp - t_{opt}}{b} \cdot \pi)) \cdot a

When temperatures fall below topt - b or above topt + b, rates are set to 0 to prevent multimodality.

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 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 easy to fit.

Author(s)

Daniel Padfield

References

Mitchell, W. A., & Angilletta Jr, M. J. (2009). Thermal games: frequency-dependent models of thermal adaptation. Functional Ecology, 510-520.

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 = 'mitchell_2009')
# fit model
mod <- nls.multstart::nls_multstart(rate~mitchell_2009(temp = temp, topt, a, b),
data = d,
iter = c(3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'mitchell_2009'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'mitchell_2009'),
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.