gaussian_1987 {rTPC}

Gaussian model for fitting thermal performance curves

Description

Gaussian model for fitting thermal performance curves

Usage

gaussian_1987(temp, rmax, topt, a)

Arguments

temp

temperature in degrees centigrade

rmax

maximum rate at optimum temperature

topt

optimum temperature (ºC)

a

related to the full curve width

Details

Equation:

rate = r_{max} \cdot exp^{\bigg(-0.5 \left(\frac{|temp-t_{opt}|}{a}\right)^2\bigg)}

Start values in get_start_vals are derived from the data

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

Lynch, M., Gabriel, W., Environmental tolerance. The American Naturalist. 129, 283–303. (1987)

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 = 'gaussian_1987')
# fit model
mod <- nls.multstart::nls_multstart(rate~gaussian_1987(temp = temp,rmax, topt,a),
data = d,
iter = c(4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'gaussian_1987'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'gaussian_1987'),
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()