Tomlinson-Phillips model for fitting thermal performance curves

Usage

tomlinsonphillips_2015(temp, a, b, c)

Arguments

temp: temperature in degrees centigrade
a: parameter similar to R at Tmin
b: shape parameter indicating the slope of the upwards part of the curve
c: peak position parameter, similar to Topt

Value

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

Details

Equation: $$rate = a \cdot [\exp{(b \cdot T) - \exp{(T-c)}}]$$

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.

Note

Generally we found this model somewhat difficult to fit.

References

Tomlinson, S. & Phillips, R. D. Differences in metabolic rate and evaporative water loss associated with sexual dimorphism in thynnine wasps. J. Insect Physiol. 78, 62–68 (2015).

Author

Francis Windram

Examples

# \donttest{
# 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 = 'tomlinsonphillips_2015')
# fit model
mod <- nls.multstart::nls_multstart(rate~tomlinsonphillips_2015(temp = temp, a, b, c),
data = d,
iter = c(3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'tomlinsonphillips_2015'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'tomlinsonphillips_2015'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)
#> 
#> Formula: rate ~ tomlinsonphillips_2015(temp = temp, a, b, c)
#> 
#> Parameters:
#>   Estimate Std. Error t value Pr(>|t|)    
#> a  0.32024    0.26234   1.221    0.253    
#> b  0.02922    0.02230   1.310    0.223    
#> c 47.66374    1.21665  39.176 2.29e-11 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.5378 on 9 degrees of freedom
#> 
#> Number of iterations to convergence: 81 
#> 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()

# }