Temporary emigration versus heterogeneity

[Todd]

I've got a heuristic question that I can't seem to satisfactorily intuit.

I am analyzing data collected in a robust design form with 10 primary periods and 81 total occasions with two groups: males and females.

In preliminary analyses of the separate closed periods using program CAPTURE, I've found that there is evidence of heterogeneity (Mh) rather than the null model or other combinations more than half the time.

Thus, when using the robust design models in MARK, I've chosen the Huggins Full Heterogeneity model with two mixtures (one pi for each primary period and sex).

The problem becomes that there is never any support for temporary emigration (or estimates of gamma" and gamma' are near 0). However, in collecting the data, we are well aware that some animals are captured in some months and then disappear for a short period before reappearing in traps again in later primary periods. This sounds like the perfect stereotype of temporary emigration. When I constrain the pi's to "1" and remove the double p's (to effectively eliminate the heterogeneity from the model), gamma estimates become 0.42, which we find very credible. However, this model with no heterogeneity receives no support (AIC) compared to models with heterogeneity, despite having many fewer parameters. Although confidence intervals and standard errors suggest the models are doing a decent job, I simply cannot believe that the "best" models show no evidence for temp. emigration.

How does the model know to distinguish between temporary emigration versus heterogeneity? Although I'm familiar with the descriptions of heterogeneity and temporary emigration, after seeing these results and ruminating on it, I'm not convinced the program can really distinguish them, possibly because capture probabilities (p) are often 0.1-0.2.

Perhaps this is a question best presented to some of the RD folks (Kendall, Pollock, Bailey, et al.) but I figured I would start with the MARK community before pestering other individuals.

Thank you for any insight.

-Brian

[Bill Kendall]

I wrote a longer response but the system timed me out. So I'll go with a shorter one. The easy answer is that temporary emigration and heterogeneity models predict different patterns of recaptures, despite the fact that both predict animals being missed for periods of time. Therefore in theory they should be able to distinguish if one or the other, or both, are operating. However, with a small data set it might be more difficult to distinguish. The fact that in MARK membership in a given mixture for an individual is not modeled over time (i.e., membership is not assigned and which mixture an individual is in at time t is independent of the mixture it is in at time t+1) might make it easier for temporary emigration to look like heterogeneity (I'm waving my hands at this point).

Bottom line: in theory one should be able to distinguish between the two. In practice, especially with small data sets, there is no guarantee the model selection process will choose the most appropriate model.