Robust Design Closed Captures

[Fish_Boy]

What would be literal interpretation for gamma in the following results?

Are we estimating the abundance of individuals "inside the samplig area at time t"? and if so does this mean that the larger 'superpopulation' is many times greater than the local popualtion?

1 S 1.00 0.00 1.00 1.00
2 S 0.97 0.01 0.95 0.98
3 S 1.00 0.00 1.00 1.00
4 S 0.98 0.01 0.95 0.99
5 gamma 0.91 0.03 0.83 0.95
6 p 1 0.11 0.03 0.06 0.18
7 c 1 0.02 0.00 0.01 0.02
8 N 1 2268 583 1438 3809
9 N 2 3653 934 2320 6121
10 N 3 3575 914 2271 5992
11 N 4 4463 1139 2837 7473
12 N 5 3662 936 2326 6137

[Bill Kendall]

I assume you only have one type of gamma because you set gamma"=gamma'. This model assumes completely random emigration, and therefore (1-gamma) for a given year becomes effectively the probability of availability, or the proportion of the superpopulation that is present in the study area for that primary period. For the first and last time periods it cannot be estimated. For the last time period the last gamma and last survival parameters are confounded. Under this model, where parameters are estimable, to get superpopulation size you divide N-hat by (1-gamma). Your estimates of gamma are pretty extreme, yet you appear to have good estimated precision.

[Fish_Boy]

Bill,

This is the project we discussed for the Barker Robust Design, however, we got only a single confirmed dead recovery and three confirmed trapped tags in pools. The Barker Robust models had too many instances of bounding zero for the beta estimates, which as I understand it not good. I think the superpopulation has to be saturated with tags in order to get the Barker Version to work for this particular example.

GIven what you stated regarding gamma and the closed with hetero is ~10x's for N^ the interpretation of gamma in the version I displayed makes good sense. There definitely is no shortage of fish the average day is 300-400 fish with 2% recaps. But the closed captures seems to make more biological sense to me.

FYI the gamma for the most constrained version of the Barker Robust provides the same N^ values, but gamma is ~0.09 and F is high 0.90. BUt there are too many problems with the time varying r and R bounding zero. I take this as indicating the encounter histories have insufficient recoveries to estimate r properly.