spain_1982 {rTPC}

Spain model for fitting thermal performance curves

Description

Spain model for fitting thermal performance curves

Usage

spain_1982(temp, a, b, c, r0)

Arguments

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

Details

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.

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

BASIC Microcomputer Models in Biology. Addison-Wesley, Reading, MA. 1982

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 = '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()