quadratic_2008 {rTPC}

Quadratic model for fitting thermal performance curves

Description

Quadratic model for fitting thermal performance curves

Usage

quadratic_2008(temp, a, b, c)

Arguments

temp

temperature in degrees centigrade

a

parameter that defines the rate at 0 ºC

b

parameter with no biological meaning

c

parameter with no biological meaning

Details

Equation:

rate = a + b \cdot temp + c \cdot temp^2

Start values in get_start_vals are derived from the data using previous methods in the literature

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

Montagnes, David JS, et al. Short‐term temperature change may impact freshwater carbon flux: a microbial perspective. Global Change Biology 14.12: 2823-2838. (2008)

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 = 'quadratic_2008')
# fit model
mod <- nls.multstart::nls_multstart(rate~quadratic_2008(temp = temp, a, b, c),
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 = 'quadratic_2008'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'quadratic_2008'),
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()