`panel4pt1.fn` <-
function(y,J=11,nsites=50,Nmax=100){
# This is the R construction of the likelihood for the Royle-Nichols
# model (Panel 4.1), and R commands for obtaining the MLEs and summarizing 
# the output.
    ####
    lik<-function(parms){
         r<-expit(parms[1])
         lambda<-exp(parms[2])
         pvec<-1-(1-r)^(0:Nmax)
         gN<-dpois(0:Nmax,lambda)
         gN<-gN/sum(gN)
         lik<-rep(NA,nsites)
         for(i in 1:nsites){
            lik[i]<-sum(dbinom(y[i],J,pvec)*gN)
         }
        -1*sum(log(lik))
       }
    ####

  tmp<-nlm(lik,c(0,0),hessian=TRUE)
  ests<-tmp$estimate
  aic<-tmp$minimum*2 + 2*length(ests)
  se<- sqrt(diag(solve(tmp$hessian)))
  list(ests=ests,se=se,aic=aic)
  }