Analytis-Kontodimas model for fitting thermal performance curves

Usage

analytiskontodimas_2004(temp, a, tmin, tmax)

Arguments

temp: temperature in degrees centigrade
a: scale parameter defining the height of the curve
tmin: low temperature (ºC) at which rates become negative
tmax: high temperature (ºC) at which rates become negative

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Details

Equation: $$rate = a \cdot \left(T - T_{\text{min}}\right)^2 \cdot \left(T_{\text{max}} - T\right)$$

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 based on extreme values that are unlikely to occur in ecological settings.

Note

Generally we found this model easy to fit.

References

Kontodimas, D. C., Eliopoulos, P. A., Stathas, G. J. & Economou, L. P. Comparative temperature-dependent development of Nephus includens (Kirsch) and Nephus bisignatus (Boheman) (Coleoptera: Coccinellidae) preying on Planococcus citri (Risso) (Homoptera: Pseudococcidae): evaluation of a linear and various nonlinear models using specific criteria. Environ. Entomol. 33, 1–11 (2004).

Author

Francis Windram

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 = 'analytiskontodimas_2004')
# fit model
mod <- nls.multstart::nls_multstart(rate~analytiskontodimas_2004(temp = temp, a, tmin, tmax),
data = d,
iter = 200,
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'analytiskontodimas_2004'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'analytiskontodimas_2004'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)
#> 
#> Formula: rate ~ analytiskontodimas_2004(temp = temp, a, tmin, tmax)
#> 
#> Parameters:
#>       Estimate Std. Error t value Pr(>|t|)    
#> a    2.249e-04  7.640e-05   2.944 0.016381 *  
#> tmin 1.438e+01  2.763e+00   5.203 0.000562 ***
#> tmax 4.900e+01  9.767e-01  50.170 2.49e-12 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.3081 on 9 degrees of freedom
#> 
#> Number of iterations to convergence: 45 
#> Achieved convergence tolerance: 1.49e-08
#> 

# 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()