library(RTMB)

turbot <- read.table("turbot.dat", head=FALSE)
dat <- list()
dat$pos <- turbot[,2]
dat$catch <- turbot[,3]
dat$N00 <- 3529
dat$w <- 4.5
dat$t <- 2

par <- list(alpha=0, logSigma=5, logitQ=0)

l <- function(par){
  getAll(par,dat) # now we can directly access everything in the two lists  
  sd <- exp(logSigma)*sqrt(t)
  q <- plogis(logitQ)
  C.bar <- q*N00*(pnorm((pos+w/2-alpha*t)/sd)-pnorm((pos-w/2-alpha*t)/sd))
  -sum(dpois(catch, C.bar, log=TRUE))
}

obj <- MakeADFun(l,par,silent=TRUE)

fit <- nlminb(obj$par,obj$fn, obj$gr)