Thomas model (2017) for fitting thermal performance curves
Arguments
- temp
temperature in degrees centigrade
- a
birth rate at 0 ºC
- b
describes the exponential increase in birth rate with increasing temperature
- c
temperature-independent mortality term
- d
along with e controls the exponential increase in mortality rates with temperature
- e
along with d controls the exponential increase in mortality rates with temperature
Value
a numeric vector of rate values based on the temperatures and parameter values provided to the function
Details
Equation: $$rate = a \cdot exp^{b \cdot temp} - (c + d \cdot exp^{e \cdot temp})$$
Start values in get_start_vals are derived from the data.
Limits in get_lower_lims and get_upper_lims are derived from the data or based on extreme values that are unlikely to occur in ecological settings.
References
Thomas, Mridul K., et al. Temperature–nutrient interactions exacerbate sensitivity to warming in phytoplankton. Global change biology 23.8 (2017): 3269-3280.
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 = 'thomas_2017')
# fit model
mod <- nls.multstart::nls_multstart(rate~thomas_2017(temp = temp, a, b, c, d, e),
data = d,
iter = c(3,3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'thomas_2017'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'thomas_2017'),
supp_errors = 'Y',
convergence_count = FALSE)
# look at model fit
summary(mod)
#>
#> Formula: rate ~ thomas_2017(temp = temp, a, b, c, d, e)
#>
#> Parameters:
#> Estimate Std. Error t value Pr(>|t|)
#> a -1.074e+01 1.201e+06 0.000 1.000
#> b 7.475e-02 5.731e+01 0.001 0.999
#> c 1.342e+00 1.977e+01 0.068 0.948
#> d -1.135e+01 1.201e+06 0.000 1.000
#> e 7.370e-02 5.708e+01 0.001 0.999
#>
#> Residual standard error: 0.3609 on 7 degrees of freedom
#>
#> Number of iterations till stop: 96
#> Achieved convergence tolerance: 1.49e-08
#> Reason stopped: Number of calls to `fcn' has reached or exceeded `maxfev' == 600.
#>
# 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()
