I am helping to analyze a data set made of resightings of already marked birds in a stopover area. I would like to use the approach described in an Ecological Applications paper where the authors (Guerín et al. 2017*) use three models to estimate stopover duration and testing hypotheses on p of recruiting and p of staying in the stopover area (in that case a pond with ampibians). Very nice paper!

Here it is a brief summary of the paper for those who do not have read it yet.

For all the three models there are three states that are: not yet arrived, arrived, departed. There are just two events: 0 (not detected), 1 (detected).

The first model they use is a time-dependent CJS-like model that was first proposed by Schaub et al. 2001**. This model is pretty flexible in terms of hypotheses testing on p of recruiting and p of staying but it relies on an assumption that in several biological cases may be unrealistic: the p of staying depends on date but not on the time since arrival.

The second model, a Markovian Time Since Arrival (M-TSA), takes into account that the p of staying depends also on the time already spent in the stopover site (Pradel 2009***). This is achieved by dividing the state “present in the area” into several states that are “just arrived”, “arrived 1 occasion before”, “arrived 2 occasions before”, and so on. This maintains a good flexibility in terms of hypotheses testing but tends to be easily overfitted because of a huge number of parameters to be estimated.

The third model, recently proposed by Choquet et al. 2014****, is a Semi-Markovian Time Since Arrival (SM-TSA) and accounts for the effect of time already spent in the site on the p of staying by means of an hazard function. This way the model has far fewer parameters with respect to the M-TSA and has therefore less problems of parameter identifiability. The negative aspect is that, until now, it is not possible to account for covariate effects (e.g. differences between sexes on stopover duration).

All these models may be run in E-SURGE and, as stated by Guérin et al. 2017, at some time there should be the possibility of using covariates also for the SM-TSA.

This is our case study:

We are considering 30 consecutive weeks (the first being added with zero individuals observed as described in the paper). Actually, data proceed from 5 consecutive years but I have pooled them into one to increase the sample size and by assuming that patterns of stopover in our study area are very similar among years (we have reasons to think that). We suspect that there are individuals that pass by the stopover site at some time during the first half of the study period, go away, and after come back at some time in the second half of the study period. Other individuals are likely to stop in the stopover site without travelling farther than that: these individuals would have a very long stopover. Our idea is therefore that there is a mixture of individuals with different use of the stopover duration.

There are at least two very clear peaks of abundance in the area (see this figure) and this is how the m-array looks like: see here. The first peak may be due to lot of individuals coming to exploit a period that is especially favorable for feeding.

Questions

I have run a unistate GOF with U-CARE and have found a strong transient effect and trap-happiness. I suspect that this may be due to the above mentioned heterogeneity of classes (some individuals with long stopover and others with short), is that reasonable?

In that case, is it possible to run a model with heterogeneity of classes on p of staying? I guess it is easy to be done in the time-dependent approach but is it possible for the M-TSA and SM-TSA?

Also, I was thinking about adding a ghost-state to account for those individuals that temporary emigrate from the stopover area. Would that be feasible for these type of models?

Any suggestion is very welcome.

* Guérin S, Picard D, Choquet R, Besnard A. 2017. Advances in methods for estimating stopover duration for migratory species using capture-recapture data. Ecol. Appl. 38:42–49.

** Schaub M., Pradel R., Jenni L., Lebreton J-D. (2001) Migrating bird stopover longer than usually thought: an improved capture-recapture analysis. Ecology 82(3), 852-859.

*** Pradel, R. (2009) The Stakes of Capture–Recapture Models with state uncertainty. In: Thomson, D.L., Cooch, E.G., Conroy, M.J. (Eds.), Modeling Demographic Processes in Marked Populations, Springer, Berlin, Germany, pp. 781-795.

**** Choquet R, Béchet A, Guédon Y. 2014. Applications of hidden hybrid Markov/semi-Markov models: from stopover duration to breeding success dynamics. Ecol. Evol. 4:817–826.