Conditions for estimating temporary emigration

[sixtystrat]

I am using a huggins heterogeneity model in a RD framework (4 primary and 8 secondary sessions) to estimate bear population size and trends. I am confused about the conditions under which one can estimate temporary emigration (gamma" and gamma'). In some papers it looks like capture heterogeneity can be estimated only in the case when emigration is random or zero (not markovian). What about time specific estimates of gamma" and gamma' if S is constant over time? My problem is that the top models are based on constant survival, time specific gammas, and a mixture effect and a covariate effect on p and c (p=c). Some of the gamma estimates are very low (near zero) and I don't trust them. When I take out the mixture effect, I get good estimates of gamma but then the models do not rank near the top. Do these low estimates of gamma signify estimation problems? If so, do I throw them out? Thanks for any help!
Joe