Simplified Brière II model for fitting thermal performance curves

Usage

briere2simplified_1999(temp, tmin, tmax, a, b)

Arguments

temp: temperature in degrees centigrade
tmin: low temperature (ºC) at which rates become negative
tmax: high temperature (ºC) at which rates become negative
a: scale parameter to adjust maximum rate of the curve
b: shape parameter to adjust the asymmetry of the curve

Value

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

Details

Equation: $$rate=a \cdot (temp - t_{min}) \cdot (t_{max} - temp)^{\frac{1}{b}}$$

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

Brière, J.F., Pracros, P., Le Roux, A.Y., Pierre, J.S., A novel rate model of temperature-dependent development for arthropods. Environmental Entomololgy, 28, 22–29 (1999)

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 = 'briere2simplified_1999')
# fit model
mod <- nls.multstart::nls_multstart(rate~briere2simplified_1999(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 = 'briere2simplified_1999'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'briere2simplified_1999'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)
#> 
#> Formula: rate ~ briere2simplified_1999(temp = temp, tmin, tmax, a, b)
#> 
#> Parameters:
#>       Estimate Std. Error t value Pr(>|t|)    
#> tmin 16.942850   2.344665   7.226 9.01e-05 ***
#> tmax 49.107438   0.730641  67.211 2.67e-12 ***
#> a     0.013094   0.008992   1.456   0.1834    
#> b     1.605833   0.719933   2.231   0.0563 .  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.3926 on 8 degrees of freedom
#> 
#> Number of iterations to convergence: 35 
#> 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()