Warren-Dreyer model for fitting thermal performance curves

Usage

warrendreyer_2006(temp, rmax, topt, a)

Arguments

temp: temperature in degrees centigrade
rmax: maximum performance/value of the trait
topt: temperature of max performance (ºC)
a: shape parameter

Value

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

Details

Equation: $$rate = R_{\text{max}} \cdot \exp{\left[-0.5 \cdot \left(\frac{\ln{\frac{T}{T_{\text{opt}}}}}{a}\right)^2\right]}$$

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 derived from the data or based extreme values that are unlikely to occur in ecological settings.

Note

Generally we found this model easy to fit.

References

Warren, C. R. & Dreyer, E. Temperature response of photosynthesis and internal conductance to CO2: results from two independent approaches. J. Exp. Bot. 57, 3057–3067 (2006).

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 = 'warrendreyer_2006')
# fit model
mod <- nls.multstart::nls_multstart(rate~warrendreyer_2006(temp = temp, rmax, topt, a),
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 = 'warrendreyer_2006'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'warrendreyer_2006'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)
#> 
#> Formula: rate ~ warrendreyer_2006(temp = temp, rmax, topt, a)
#> 
#> Parameters:
#>      Estimate Std. Error t value Pr(>|t|)    
#> rmax  1.46485    0.22630   6.473 0.000115 ***
#> topt 35.35356    1.31116  26.963 6.43e-10 ***
#> a     0.20583    0.04062   5.068 0.000674 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.3732 on 9 degrees of freedom
#> 
#> Number of iterations to convergence: 29 
#> 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()

# }