POPAN groups

[angieluis]

Hi. I am running POPAN models in RMark. I have 4 different groups (2 sex and 2 sites). For the models that I specify not to group animals (eg Phi.month, p.month, pent.month, N~1) (not including sex or site), when I look at the derived estimates in the output file, there are 4 estimates for N*-hat (I'm assuming for each of the 4 groups) and 4 groups of Nhat. But the beta parameters don't include the groups (only 1 N, only 1 set of pent). This doesn't make sense to me. I don't know where the derived estimates are getting the group information when it's not specified. Can someone enlighten me?

Thanks!
angie

[jlaake]

Once you specify groups in a POPAN model, it will produce an abundance estimate for each group regardless of the model for N. The model for N is actually a model for f0 which is the number never seen. N=n+f0 where n is the number seen. When you specify ~1 for N that means it will fit a single parameter for the 4 groups and the value of f0 is the same across groups but you'll still get 4 estimates of N and they will differ unless the number seen in each group was the same.

N1=n1+f0
N2=n2+f0
N3=n3+f0
N4=n4+f0

If you specify N~group then there are 4 different f0 values

N1=n1+f0_1
N2=n2+f0_2
N3=n3+f0_3
N4=n4+f0_4


--jeff

[harding]

Thank you for answering this. I had wondered about it as well. Just to make sure I understand completely - if you ran a model N(site), you get N-hat values, which are really f0, by site and session. To get an actual abundance estimate for each site in each session, you would add the N-hat values to the number of animals caught in each site in each session. Is this correct?

Is this unique to POPAN or do other models which estimate abundance, like the robust design, operate in the same way (i.e., is an N-hat value in the output of a robust design model actually f0 as well, or is it really the final abundance estimate)?

Thanks!

[jlaake]

Thank you for answering this. I had wondered about it as well. Just to make sure I understand completely - if you ran a model N(site), you get N-hat values, which are really f0, by site and session. To get an actual abundance estimate for each site in each session, you would add the N-hat values to the number of animals caught in each site in each session. Is this correct?

No in the POPAN model there is one f0 for each group as the estimate of N is super-population size which is the number of animals that were ever in the population (group) and the pent parameter describes their entry into the population across time. I suggest that you read the chapter 13 in the MARK book with particular emphasis on 13.3.2

Is this unique to POPAN or do other models which estimate abundance, like the robust design, operate in the same way (i.e., is an N-hat value in the output of a robust design model actually f0 as well, or is it really the final abundance estimate)?

I've not used all of the models in MARK but it is my understanding that they do all work this way. If I'm wrong about that maybe some one will correct me.

--jeff

[JeffHostetler]

Hello,

A few of us were concerned when we saw these posts because we wanted to make sure we were using population size estimates from POPAN correctly in a recently accepted paper (not too late for edits, though). I've looked into this with our data now and everything Jeff said is confirmed. However, the "Population Estimates" group of derived parameters (estimated population size by site and occasion) is often less than the number captured for both N(~1) and N(~group) models (we are running a reduced group model for Phi and reduced time models for p and pent). I looked in the MARK help files and saw this passage:

The number of animals in the population on occasion 1 is N(1) = pent(0) times N. The number of new animals (births, B) entering the population prior to occasions i = 2, 3, ..., t is B(i) = pent(i - 1) times N. The population size on occasion i = 2, 3, ..., t is N(i) = (N(i - 1) - losses on capture) times phi(i - 1) + B(i). Estimates of the B(i) and N(i) are provided as derived parameters from models with the POPAN data type.

I also tested this with our data and results and it fits too. So while the super-population size estimate for group g is equal to the total number of individuals captured in group g plus exp(N beta), the derived estimate N-hat(i,g) is based on the estimates of pent, super-population size, Phi, and losses on capture, and not specifically on the number captured at i.

Our question is: is it okay to use these derived population estimates, even if we know that some of them are too low (because they're less than the number captured)? Would it be more appropriate to bump those estimates up to the number captured?

Thanks,

Jeff

[cooch]

I'd suggest a careful reading of Carl Schwartz & Neil Arnason's 'JS' chapter (chapter 13) in the MARK book.