weibull_1995 {rTPC} | R Documentation |
Weibull model for fitting thermal performance curves
Description
Weibull model for fitting thermal performance curves
Usage
weibull_1995(temp, a, topt, b, c)
Arguments
temp |
temperature in degrees centigrade |
a |
scale the height of the curve |
topt |
optimum temperature |
b |
defines the breadth of the curve |
c |
defines the curve shape |
Details
Equation:
rate = a \cdot \bigg( \frac{c-1}{c}\bigg)^{\frac{1-c}{c}}\bigg(\frac{temp-t_{opt}}{b}+\bigg(\frac{c-1}{c}\bigg)^{\frac{1}{c}}\bigg)^{c-1}exp^{-\big(\frac{temp-t_{opt}}{b}+\big( \frac{c-1}{c}\big)^{\frac{1}{c}}\big)^c} + \frac{c-1}{c}
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 easy to fit.
References
Angilletta Jr, Michael J. Estimating and comparing thermal performance curves. Journal of Thermal Biology 31.7 (2006): 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 = 'weibull_1995')
# fit model
mod <- nls.multstart::nls_multstart(rate~weibull_1995(temp = temp, a, topt, b, c),
data = d,
iter = c(4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'weibull_1995'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'weibull_1995'),
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()