partial census and censored individuals

[achatinella]

I have a question about dealing with censored observations in a mark-recapture analysis.

I am using mark-recapture methods to analyze data for a plant population sampled on three occasions (years). The objective is to estimate the abundance of reproductive adults, and to see if individual covariates influence capture probabilities. The plants can only be identified during ~3 days each year when they produce flowers.

Unfortunately, many of the individuals that were observed in years 1 and 2 were censored during the third occasion. Bad weather prevented us from sampling about half of the study area during the third year. This means that we have exhaustive censuses for years 1 and 2, but only a partial census for year 3.

Is there a rigorous way to deal with these censored observations in a mark-recapture analysis?

One idea I had was to analyze the data in two separate analyses: one for the individuals sampled on three occasions, and one for the individuals sampled on two occasions. I could get separate estimates of abundance for each area, and then add them together to get an aggregate estimate for my entire study site. I could calculate a variance using the delta method. I’d appreciate any comments or suggestions on this approach.

Jim

[ganghis]

Jim,

I'm guessing that you're using a closed captures model (no mortality or recruitment over the 3 years) and that you're using the Huggins model so that you can consider covariate effects on p.

You probably DON'T want to conduct 2 separate analyses as the amount of information to estimate p will be less and thus your abundance estimates will be less precise. Two thoughts come to mind: 1) Enter the individuals in locations that you can't survey in the 3rd year as a separate group, constraining capture probability in the last period to 0 for this group. In this case, you end up with 2 separate abundance estimates, but information on p is pooled between the 2 areas. You can use the delta method to get a combined estimate and variance for years 1 and 2 as you anticipated. 2) treat the ones you can't observe in the 3rd period as losses on capture. I'm not real sure how this works with closed models but is something worth looking into.

In either case, you'll only have an estimate for the area that you surveyed in the 3rd year.

Cheer, Paul Conn

[achatinella]

Jim,

I'm guessing that you're using a closed captures model (no mortality or recruitment over the 3 years) and that you're using the Huggins model so that you can consider covariate effects on p.

You probably DON'T want to conduct 2 separate analyses as the amount of information to estimate p will be less and thus your abundance estimates will be less precise. Two thoughts come to mind: 1) Enter the individuals in locations that you can't survey in the 3rd year as a separate group, constraining capture probability in the last period to 0 for this group. In this case, you end up with 2 separate abundance estimates, but information on p is pooled between the 2 areas. You can use the delta method to get a combined estimate and variance for years 1 and 2 as you anticipated. 2) treat the ones you can't observe in the 3rd period as losses on capture. I'm not real sure how this works with closed models but is something worth looking into.

In either case, you'll only have an estimate for the area that you surveyed in the 3rd year.

Cheer, Paul Conn

Paul,

Thanks for your thoughts. You're right, I am using Huggins closed capture models.

Your idea to use all individuals to estimate p for the areas that were surveyed in all three years sounds very good. But it seems harsh not to estimate abundance for the indiviudals that were only observed in two years, which is half my study site (~500 individuals). A precise estimate of N for a fraction of my study area is probably less useful to me than a less precise estimate for the whole area.

Why not do the following, which seems the best of both worlds? 1) Enter the individuals that were not surveyed in the third year as a separate group, as you described. Estimate abundance for the group surveyed in three years. Ignore the estimate of abundance for the censored area from this model (since it has zeros for the censored individuals in year 3). 2) Run a 2-occasion model for the individuals that were censored in year 3. 3) Use the delta method to get a combined estimate of abundance.

I think this would allow me to avoid losing the areas where I only have 2 years of data. It would also allow me to estimate N for the entire area. Finally, it would estimate p for censored and non-censored areas with all of the information available in each scenario, so my estimates of N will be more precise.

Would this approach be legitimate? Clearly the estimates would not be independent, because the censored individuals contribute to estimates of p in both analyses.

Jim

[ganghis]

Jim,

Sorry if the final sentence on my last reply was misleading. What I meant to say is "In both approaches you will get a combined estimate for abundance in years 1 and 2 (i.e. the whole study area), but in the third year you can only get an estimate for the area that you surveyed."

Cheers, Paul