rTPC (version 1.0.4)

modifiedgaussian_2006: Modified gaussian model for fitting thermal performance curves

Description

Modified gaussian model for fitting thermal performance curves

Usage

modifiedgaussian_2006(temp, rmax, topt, a, b)

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Arguments

temp

temperature in degrees centigrade

rmax

maximum rate at optimum temperature

topt

optimum temperature

a

related to full curve width

b

allows for asymmetry in the curve fit

Details

Equation: $$rate = r_{max} \cdot exp^{\bigg[-0.5 \left(\frac{|temp-t_{opt}|}{a}\right)^b\bigg]}$$

Start values in get_start_vals are derived from the data and gaussian_1987

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

References

Angilletta Jr, M. J. (2006). Estimating and comparing thermal performance curves. Journal of Thermal Biology, 31(7), 541-545.

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 = 'modifiedgaussian_2006')
# fit model
mod <- nls.multstart::nls_multstart(rate~modifiedgaussian_2006(temp = temp, rmax, topt, a, b),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'modifiedgaussian_2006'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'modifiedgaussian_2006'),
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()