spain_1982 | R Documentation |
Spain model for fitting thermal performance curves
spain_1982(temp, a, b, c, r0)
temp |
temperature in degrees centigrade |
a |
constant that determines the steepness of the rising portion of the curve |
b |
constant that determines the position of topt |
c |
constant that determines the steepness of the decreasing part of the curve |
r0 |
the apparent rate at 0 ºC |
Equation:
rate = r_0 \cdot exp^{a \cdot temp} \cdot (1-b \cdot exp^{c \cdot temp})
Start values in get_start_vals
are derived from the data or plucked from thin air.
Limits in get_lower_lims
and get_upper_lims
are derived from the data or plucked from thin air.
a numeric vector of rate values based on the temperatures and parameter values provided to the function
Generally we found this model easy to fit.
BASIC Microcomputer Models in Biology. Addison-Wesley, Reading, MA. 1982
# 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 = 'spain_1982')
# fit model
mod <- nls.multstart::nls_multstart(rate~spain_1982(temp = temp, a, b, c, r0),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 1,
start_upper = start_vals + 1,
lower = get_lower_lims(d$temp, d$rate, model_name = 'spain_1982'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'spain_1982'),
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()
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