Model averaging N from closed models and POPAN

[stshroye]

I know this isn't normally done, but is there a legitimate way to model average N from closed-population models and POPAN? I have cases where both closed and open models fit about equally well. Closed-population models indicate trap shyness (Mb or Mbt) and open-population models indicate losses (phi < 1), so there is no basis for selecting closed vs. open. I would like to be able to determine AIC weights for closed vs. open models, or at least give them equal weight and account for model uncertainty of N. Thanks.

[murray.efford]

This can be handled in a fairly straightforward way in 'openCR' as variations on a robust design open model (below), and I imagine there is a MARK equivalent.
Murray

Code: Select all

library(openCR)
# use internal robust-design dataset FebpossumCH, ignoring space
# 'bsession' is a within-session learned response; there's no 'bt' model in openCR
# model JSSAN treats session-specific population size N as the recruitment parameter
# compare to JSSAf and JSSAb
fit0 <- openCR.fit(FebpossumCH, type = 'JSSAN', model=list(N~session, p~1, phi~session))
fit1 <- openCR.fit(FebpossumCH, type = 'JSSAN', model=list(N~session, p~bsession, phi~session))
AIC(fit0, fit1)
#                                 model npar rank    logLik      AIC     AICc  dAIC  AICwt
# fit1 p~bsession phi~session N~session   19   19 -6456.613 12951.23 12953.24 0.000 0.9437
# fit0        p~1 phi~session N~session   18   18 -6460.432 12956.86 12958.67 5.637 0.0563

# and some estimates...
predict(fit1,all=T)$p
predict(fit1)$phi
predict(fit0)$N
predict(fit1)$N

modelAverage(fit0, fit1)[,,'N']
#                                estimate SE.estimate       lcl      ucl
# stratum=1,session=1,bsession=0 142.6529    11.99950 121.00590 168.1724
# stratum=1,session=2,bsession=0 148.1942    12.24567 126.07064 174.2002
# stratum=1,session=3,bsession=0 156.0441    12.63713 133.17603 182.8390
# stratum=1,session=4,bsession=0 161.9422    13.10215 138.23081 189.7210
# stratum=1,session=5,bsession=0 145.6133    12.40088 123.26538 172.0130
# stratum=1,session=6,bsession=0 122.1193    11.33958 101.83898 146.4382
# stratum=1,session=7,bsession=0 152.0306    12.62211 129.23578 178.8461
# stratum=1,session=8,bsession=0 154.0359    12.70098 131.08567 181.0042
# stratum=1,session=9,bsession=0 118.6720    11.15610  98.74261 142.6238

[stshroye]

Murray,

Thanks for your prompt reply. I was not aware of openCR, but I have now read your openCR vignette and it looks very interesting. However, given my very limited understanding so far, I am not sure your suggestion will work for my dataset. I am attempting to estimate annual population size of Largemouth Bass in lakes sampled each spring for 9 years. Fish were captured and recaptured by electrofishing along the entire shoreline. Each year there were 3 - 8 electrofishing occasions spanning 8 - 37 days, with 3 - 13 days between occasions. My dataset would appear to be conducive to a robust design, except that there was likely substantial tag loss between primary sessions and I am therefore not attempting annual survival estimates (although I know it may be possible). My question refers to probable violations of closure within secondary sessions, mainly due to daily movement into or out of the narrow band of shoreline that was sampled by electrofishing. Assuming closure within a session, fish often appeared trap shy, but this could be due to net emigration from the electrofishing zone during a session.

Steve

[murray.efford]

My head hurts! If tag loss (not in your original post) invalidates a between-primary-session survival model then why trust a POPAN model at all? I'm happy to bow out of the discussion and leave it to those more familiar with tag loss & MARK's models for the robust design with (random or Markovian?) temporary (?) emigration.

Murray

[stshroye]

I am not using a robust design due to long-term tag loss, but tag loss is negligible within a secondary session. I am only using POPAN models within secondary sessions to account for potential violations of closure. I only want to model-average closed and open models within secondary sessions.