Staggered entry of sites in CJS models

[Bryan Hamilton]

Hello,

I'm working through some CJS analysis. CMR was initiated at three sites in 2001 and at a fourth site in 2005.

Is this a problem for CJS analysis? I've recently read a paper where they conducted two separate analyses in similar situation. One analysis for sites monitored over the same time period and a second analysis for the site monitored over a shorter duration.

I've currently coded the capture histories for the fourth site with four leading zeros and analyzed all four sites together. This seems to be pushing down overall estimates of apparent survival early in study and site specific estimates for the site monitored for less time.

Staggered entry seems to be well documented for known fate models but less so for CJS models where actual sites, rather than individuals, are staggered. I appreciate any thoughts or comments on this.

[Dan_Gibson]

Hey Bryan,

Other people can jump in if I am wrong, but I believe in a perfect world the staggered site-entry you describe should not bias your parameter estimates. That being said, I imagine that if there is substantial amount of variation in detection or survival among sites and across time that is not being adequately accounted for with your model, you may observed the patterns you are describing.

Here is a little code that I had lying around that may help you come to a resolution about what is going on under the hood. As it stands, this simulates a capture history based on two sites, one of which entering in at the third year. The sim.data dataframe can be sent directly to rmark, or you can make a few modifications and export it into mark. I haven't spent too much time with it, but I was getting estimates that were in the ballpark for the few scenarios I cooked up.

-Dan

Code: Select all

library(RMark)
rm(list=ls())

#simulate CJS data for 1 group
simul.cjs<-function(phi,p,marked)
{
  n.occasions<-length(p)+1
  Phi<-matrix(phi,n.occasions-1,nrow=sum(marked),byrow=T)
  P<-matrix(p,n.occasions-1,nrow=sum(marked),byrow=T)
 
  #n.occasions<-dim(Phi)[2]+1
  CH<-matrix(0,ncol=n.occasions,nrow=sum(marked))
  #define a vector with marking occasion
  mark.occ<-rep(1:length(marked),marked[1:length(marked)])
  #fill in CH
  for (i in 1:sum(marked))
  {
    CH[i,mark.occ[i]]<-1
    if (mark.occ[i]==n.occasions) next
    for(t in (mark.occ[i]+1):n.occasions)
    {
      #survive?
      sur<-rbinom(1,1,Phi[i,t-1])
      if(sur==0) break #move to next
      #recaptured?
      rp<-rbinom(1,1,P[i,t-1])
      if(rp==1) CH[i,t]<-1
    } #t
  } #i
  return(CH)
}
###function to create capture history character strings (need for input to RMARK)
pasty<-function(x)
{
  k<-ncol(x)
  n<-nrow(x)
  out<-array(dim=n)
  for (i in 1:n)
  {
    out[i]<-paste(x[i,],collapse="")
  }
  return(out)
}

#call simulation for a 2-group example
n.occasions<-10
marked.1<-rep(50,n.occasions-1)               #Release individuals for first site
marked.2<-c(0,0,rep(50, n.occasions-3))       #Release individuals for second site starting in year 3
phi.1<-rep(0.8,n.occasions-1)                 #Mean phi for site 1
phi.2<-c(0,0,rep(.6, n.occasions-3))          #Mean phi for site 2
p.1<-rep(0.4,n.occasions-1)                   #Mean p for site 1
p.2<-c(1,1,rep(.4, n.occasions-3))            #Mean p for site 2
sim.1<-simul.cjs(phi.1,p.1,marked.1)
sim.2<-simul.cjs(phi.2,p.2,marked.2)
#put togther in format needed for RMark
first.hist<-data.frame(ch=pasty(sim.1),Site="A")
second.hist<-data.frame(ch=pasty(sim.2),Site="B")

sim.data<-rbind(first.hist,second.hist)
sim.processed=process.data(sim.data,model="CJS",groups="Site")
sim.ddl=make.design.data(sim.processed)


[Bryan Hamilton]

Thank you Dan. This is a big help.

The paper I just read about splitting sites into two modeling exercises had Gary White as a co-author:

Hansen, E. C., R. D. Scherer, G. C. White, B. G. Dickson, and E. Fleishman 2015. Estimates of Survival Probability from Two Populations of Giant Gartersnakes in California’s Great Central Valley. Copeia 103:1026-1036.

When I do split the sites into two modeling efforts, the parameters are very similar. Some subtle changes to detection probability and survival translate into stable lambda versus declining lambda, but overall the story is still pretty much the same. I prefer one modeling exercise for simplicity if its appropriate. I think you nailed the issue that some of the variation is not being accounted for. With all sites in a single model set, I can run more complex models and should be able to account for more of that variation.

Thank you again.