inst/non_lin_models/Mod_chapman.R

In txm676/mmSAR2: Fit and Compare Species-Area Relationship Models Using Multimodel Inference

#Chapman–Richards 3 S = a [1 − exp(−bA)]c Flather (1996)
#note there was an error in our original formula (corrected
#Nov 2020)
model <- list(
  name = c("Chapman Richards"),
  formula = expression(S == d * (1 - exp(-z*A))^c),
  exp = expression(d * (1 - exp(-z*A))^c),
  shape = "sigmoid",
  asymp = function(pars)pars["d"],
  #limits for parameters
  parLim  =  c("Rplus","R","R"),
  #initials values function
  init = function(data){
    d=max(data$S) 
    Z=(-log((-data$S/(max(data$S)+1))+1))/data$A
    z = mean(Z)
    c(d,z,0.5)}
)