POPAN and abundance estimation

[Bakere1]

I am a relative newcomer to MARK and am working with lake sturgeon, a long-lived iteroparous but intermittently spawning fish. We have 10 years of mark-recapture data from spawning fish collected at the only spawning habitat known for the population of interest. Over the 10 years we have marked nearly 850 unique individuals of known gender with PIT tags and have mulitple recapture events for many marked fish. We need to estimate abundance for the population to manage harvest and I've used POPAN to generate abundance estimates for males (approx 600) and females (also approx 600). However, I'm concerned about the accuracy of the estimates because of likely violations of the capture probability assumptions. Specifically, we know that most male lake sturgeon spawn on average every other year and females on average every third year so not all fish are equally likely to be captured every year (spawners are in the river, nonspawners stay in the lake). We are extremely efficient at capturing the spawning fish-in 2010 we captured a total of 219 fish in the spawning run and only 61 (28%) were new, unmarked individuals, suggesting we have a large majority of the population marked. Is there a better model to estimate abundance that I should use? I've considered a closed-captures model but am equally uncomfortable with those estimates because, although the population is spatially closed, the 10 year time span allows for additions and losses and the same catchability assumptions are in play for the closed-captures model. I've also considered a robust-design but we are treating each spawning-year as the sampling period and each fish is either captured or not seen.

Thanks in advance for your help.

-Ed

[dhewitt]

I'm not very proficient with abundance estimation, but this sounds like a problem for a multi-state model with an unobservable state (Bailey et al. 2004, Ecology 85:2456-). However, in the absence of a robust design sampling strategy (which so far as I can tell you don't have -- how does sampling occur during the spawning period?), I am not sure you can do much. I'm curious to hear what others say. My gut reaction is that with a population of manageable size (not tens of thousands or more) and recapture probs. as high as yours, you're in a decent spot, even if I can't tell you how to get there from here.

[jlaake]

I agree with most of Dave's comments. Robust design would be optimal. Not sure you would get too far with the multi-state approach without allowing for the structure to the transitions. One alternative would be to use CJS and use a time-dependent covariate that held for one year after capture for males and two years after capture for females. The time dependent covariate will allow for lower capture probability in the year or two proceeding a spawning event. If your p of spawners is quite high then this can capture most of the time-varying heterogeneity and will improve the survival rate estimate. But not sure how to proceed to abundance with that structure. Somehow you would have to derive an estimate of what fraction of the population (male and female separately) was spawning. Maybe that could be derived from your marked sample. Not sure.

--jeff

[Bill Kendall]

Under your circumstances your POPAN approach is estimating something larger than the number of individuals spawning in a given year and the total of spawners and skipped spawners. If you are interested in the number of spawners in a given year, then as Dave mentioned, set up a MS model with an observable state and one or more unobservable states (set p=0), depending on how you view the skipping process. Because you don't have robust design data, you will need more constraints on parameters than you would with the robust design (see Kendall and Nichols 2002, Ecology and Schaub et al. 2004, Ecology). If those constraints work for you then to get abundance for each sex just divide the number captured by the capture probability estimate for each for the observable state.

If you don't like the constraints required for the MS approach, then there is the alternative Jeff offered, using the CJS model. In the absence of an unbiased approach the question is how to make the inference with optimal combination of bias and precision.

[Fish_Boy]

I have been working with lake sturgeon and population estimation during the spawning period. In our case our field programs are scheduled for the onset of spawning and proceed through spawning and into the post-spawning period, such that the there are two 'natural' time periods during each survey. I used a robust design with closed captures and the results make intuitive sense with our acoustic tracking and floy-tag return data over the last 10 years. The main issues I have found with lake sturgeon is that you have to be consistent and religious about the effort as they are very habitual so the assumptions of the robust design are valid.