## Hassell's Orginal Type III pre-prey function.
# hassIII: The guiding function...
hassIII <- function(X, b, c, h, T) {
if(is.list(b)){
coefs <- b
b <- coefs[['b']]
c <- coefs[['c']]
h <- coefs[['h']]
T <- coefs[['T']]
}
#a <- (d+b*X)/(1+c*X) # From Julliano (2001), pg. 181: a = (d+bN)/(1+cN)
a <- (b*X)/(1+c*X) # From Hassell et al (1977)
#cat(mean(a), b, c, h, '\n')
return((a*X*T)/(1+a*X*h)) # Substituting into the code for hollingsII
#return((d*X*T+b*X^2*T)/(1+c*X+d*X*h+b*X^2*h)) # Direct from Julliano (2001), pg 181
}
# hassIII_fit: Does the heavy lifting
hassIII_fit <- function(data, samp, start, fixed, boot=FALSE, windows=FALSE) {
# Setup windows parallel processing
fr_setpara(boot, windows)
samp <- sort(samp)
dat <- data[samp,]
out <- fr_setupout(start, fixed, samp)
try_hassIII <- try(bbmle::mle2(hassIII_nll, start=start, fixed=fixed, data=list('X'=dat$X, 'Y'=dat$Y),
optimizer='optim', method='Nelder-Mead', control=list(maxit=5000)),
silent=T)
if (inherits(try_hassIII, "try-error")) {
# The fit failed...
if(boot){
return(out)
} else {
stop(try_hassIII[1])
}
} else {
# The fit 'worked'
for (i in 1:length(names(start))){
# Get coefs for fixed variables
cname <- names(start)[i]
vname <- paste(names(start)[i], 'var', sep='')
out[cname] <- coef(try_hassIII)[cname]
out[vname] <- vcov(try_hassIII)[cname, cname]
}
for (i in 1:length(names(fixed))){
# Add fixed variables to the output
cname <- names(fixed)[i]
out[cname] <- as.numeric(fixed[cname])
}
if(boot){
return(out)
} else {
return(list(out=out, fit=try_hassIII))
}
}
}
# hassIII_nll: Provides negative log-likelihood for estimations via bbmle::mle2()
hassIII_nll <- function(b, c, h, T, X, Y) {
if (h <= 0 || b <= 0) {return(NA)} # h and b estimates must be > zero
if (c < 0) {return(NA)} # c must be positive (can be negative)
prop.exp = hassIII(X, b, c, h, T)/X
# The proportion consumed must be between 0 and 1 and not NaN
# If not then it must be bad estimate of a and h and should return NA
if(any(is.nan(prop.exp)) || any(is.na(prop.exp))){return(NA)}
if(any(prop.exp > 1) || any(prop.exp < 0)){return(NA)}
return(-sum(dbinom(Y, prob = prop.exp, size = X, log = TRUE)))
}
# The diff function
hassIII_diff <- function(X, grp, b, c, h, T, Db, Dc, Dh) {
# a <- (b*X)/(1+c*X) # From Hassell et al (1977)
a <- ((b-Db*grp)*X)/(1+(c-Dc*grp)*X)
# return((a*X*T)/(1+a*X*h)) # Substituting into the code for hollingsII
return((a*X*T)/(1+a*X*(h-Dh*grp)))
}
# The diff_nll function
hassIII_nll_diff <- function(b, c, h, T, Db, Dc, Dh, X, Y, grp) {
if (h <= 0 || b <= 0) {return(NA)} # h and b estimates must be > zero
if (c < 0) {return(NA)} # c must be positive
prop.exp = hassIII_diff(X, grp, b, c, h, T, Db, Dc, Dh)/X
# The proportion consumed must be between 0 and 1 and not NaN
# If not then it must be bad estimate of a and h and should return NA
if(any(is.nan(prop.exp)) || any(is.na(prop.exp))){return(NA)}
if(any(prop.exp > 1) || any(prop.exp < 0)){return(NA)}
return(-sum(dbinom(Y, prob = prop.exp, size = X, log = TRUE)))
}
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