Capture recapture for only two visit assuming a open population model?

Question

I have a study system where I’m doing a capture recapture analysis. I mark fish in one year and I’m recapturing a subset of them the next year. I only have 2 capture events. Since a lot of time has passed, relative to the fish, between the two episode of recapture, I cannot assume a closed population model. Is there an alternative? What mark-recapture model would be best for this situation given that I want to compute a recapture probability?

Answer 1

Good question!

Since you only have the two samples, your main options would be the Lincoln-Peterson or the Chapman estimator. If the proportion of tagged individuals captured in the second sample is small, you may want to select the Chapman.

In regards to the closed population assumption, there are no 2 capture event models that do not use the closed population assumption. With a 2 capture event mark-recapture study, you are pretty strictly only estimating abundance, since you don't have enough data to account for mortality, births or emigration. In order to model an open population and account for mortality, births and emigration/immigration, you would need at least 3 capture events and for some models uniquely identifiable individuals to make an encounter history.

A few things to keep in mind here:

1) Remember, all models are wrong, but some models are useful. Even if your two samples were only 1 week apart instead of a year, in a real experiment there would always be the possibility of an organism perishing, tags falling off (or healed if doing a method like fin clips), or individuals entering or leaving the study area. When checking assumptions, you are asking whether or not it is reasonable to assume a condition is met regardless of realistically what may or may not have occurred.

2) Thinking about what assumptions you'd need to meet for running particular models is an important part of study design once you start running your own experiments. If your two samples are a year apart, you will be a lot less confident in your estimate than if the samples were a month apart. The better the sample design, the more useful your models will be.

3) Depending on the study species and sampling strategy, you could argue that the closed population assumption was met. For example, if you were doing a mark-recapture of adult lake sturgeon with a survival rate of 99%, then for a one-year gap natural mortality could be considered negligible. Similarly, as recruitment rate to catchable size for your gear is low (in many cases <5%), we are regarding births/recruitment as negligible for this estimate (Because it's always just an estimate). And as long as no stocking has occurred and we consider the entire lake the study area then neither immigration nor emigration has occurred (let's say our study site has no inflow and outflow streams).