beta_2012 {rTPC}

Beta model for fitting thermal performance curves

Description

Beta model for fitting thermal performance curves

Usage

beta_2012(temp, a, b, c, d, e)

Arguments

temp

temperature in degrees centigrade

a

dimensionless parameter

b

dimensionless parameter

c

dimensionless parameter

d

dimensionless parameter

e

dimensionless parameter

Details

Equation:

rate=\frac{a\left(\frac{temp-b+\frac{c(d-1)}{d+e-2}}{c}\right)^{d-1} \cdot \left(1-\frac{temp-b+\frac{c(d-1)}{d+e-2}}{c}\right)^{e-1}}{{\left(\frac{d-1}{d+e-2}\right)}^{d-1}\cdot \left(\frac{e-1}{d+e-2}\right)^{e-1}}

Start values in get_start_vals are derived from the data or sensible values from the literature.

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 difficult to fit.

Author(s)

Daniel Padfield

References

Niehaus, Amanda C., et al. Predicting the physiological performance of ectotherms in fluctuating thermal environments. Journal of Experimental Biology 215.4: 694-701 (2012)

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 = 'beta_2012')
# fit model
mod <- nls.multstart::nls_multstart(rate~beta_2012(temp = temp, a, b, c, d, e),
data = d,
iter = c(7,7,7,7,7),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'beta_2012'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'beta_2012'),
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()