View source: R/ratkowsky_1983.R
ratkowsky_1983 | R Documentation |
Ratkowsky model for fitting thermal performance curves
ratkowsky_1983(temp, tmin, tmax, a, b)
temp |
temperature in degrees centigrade |
tmin |
low temperature (ºC) at which rates become negative |
tmax |
high temperature (ºC) at which rates become negative |
a |
parameter defined as sqrt(rate)/(temp - tmin) |
b |
empirical parameter needed to fit the data for temperatures beyond the optimum temperature |
Equation:
rate = (a \cdot (temp-t_{min}))^2 \cdot (1-exp(b \cdot (temp-t_{max})))^2
Start values in get_start_vals
are derived from the data and previous values 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.
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.
Ratkowsky, D.A., Lowry, R.K., McMeekin, T.A., Stokes, A.N., Chandler, R.E., Model for bacterial growth rate throughout the entire biokinetic temperature range. J. Bacteriol. 154: 1222–1226 (1983)
# 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 = 'ratkowsky_1983')
# fit model
mod <- nls.multstart::nls_multstart(rate~ratkowsky_1983(temp = temp, tmin, tmax, a, b),
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 = 'ratkowsky_1983'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'ratkowsky_1983'),
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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