R/modifiedgaussian_2006.R

In padpadpadpad/rTPC: Fitting and Analysing Thermal Performance Curves

#' Modified gaussian model for fitting thermal performance curves
#'
#' @param temp temperature in degrees centigrade
#' @param rmax maximum rate at optimum temperature
#' @param topt optimum temperature
#' @param a related to full curve width
#' @param b allows for asymmetry in the curve fit
#' @return a numeric vector of rate values based on the temperatures and parameter values provided to the function
#' @details Equation:
#' \deqn{rate = r_{max} \cdot exp^{\bigg[-0.5 \left(\frac{|temp-t_{opt}|}{a}\right)^b\bigg]}}{%
#' rate = rmax.exp(-0.5.(abs(temp - topt)/a)^b)}
#'
#' Start values in \code{get_start_vals} are derived from the data and \code{gaussian_1987}
#'
#' Limits in \code{get_lower_lims} and \code{get_upper_lims} are based on extreme values that are unlikely to occur in ecological settings.
#'
#' @note Generally we found this model difficult to fit.
#' @references Angilletta Jr, M. J. (2006). Estimating and comparing thermal performance curves. Journal of Thermal Biology, 31(7), 541-545.
#' @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 = 'modifiedgaussian_2006')
#' # fit model
#' mod <- nls.multstart::nls_multstart(rate~modifiedgaussian_2006(temp = temp, rmax, topt, a, b),
#' data = d,
#' iter = c(3,3,3,3),
#' start_lower = start_vals - 10,
#' start_upper = start_vals + 10,
#' lower = get_lower_lims(d$temp, d$rate, model_name = 'modifiedgaussian_2006'),
#' upper = get_upper_lims(d$temp, d$rate, model_name = 'modifiedgaussian_2006'),
#' supp_errors = 'Y',
#' convergence_count = FALSE)
#'
#' # look at model fit
#' summary(mod)
#'
#' # 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()
#'
#' @export modifiedgaussian_2006

modifiedgaussian_2006 <- function(temp, rmax, topt, a, b){
  est <- rmax * exp(-0.5 * (abs(temp - topt)/a)^b)
  return(est)
}