Boatman model for fitting thermal performance curves

Usage

boatman_2017(temp, rmax, tmin, tmax, a, b)

Arguments

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

Value

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

Details

Equation: $$rate= r_{max} \cdot \left(sin\bigg(\pi\left(\frac{temp-t_{min}}{t_{max} - t_{min}}\right)^{a}\bigg)\right)^{b}$$

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

Boatman, T. G., Lawson, T., & Geider, R. J. A key marine diazotroph in a changing ocean: The interacting effects of temperature, CO2 and light on the growth of Trichodesmium erythraeum IMS101. PLoS ONE, 12, e0168796 (2017)

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 = 'boatman_2017')
# fit model
mod <- nls.multstart::nls_multstart(rate~boatman_2017(temp = temp, rmax, tmin, tmax, a, b),
data = d,
iter = c(4,4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'boatman_2017'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'boatman_2017'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)
#> 
#> Formula: rate ~ boatman_2017(temp = temp, rmax, tmin, tmax, a, b)
#> 
#> Parameters:
#>      Estimate Std. Error t value Pr(>|t|)    
#> rmax   1.5836     0.1969   8.044  8.8e-05 ***
#> tmin -50.0000   834.9816  -0.060  0.95392    
#> tmax  49.0000    11.8375   4.139  0.00435 ** 
#> a      6.1111    48.6868   0.126  0.90364    
#> b      1.9305     7.0634   0.273  0.79251    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.2739 on 7 degrees of freedom
#> 
#> Number of iterations to convergence: 78 
#> 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()