Study Design: Minimum # of Recaptures Needed?

[kate12]

I'm designing a study in which preliminary data suggests a relatively large open sea turtle population. Three years of tagging has yielded 150 new individuals and only 3 recaptures. What is a simple, yet appropriate way to estimate how many samples are needed in order to reliably estimate the population given the practically non existent level of recaptures? I've read different guidance- some say 4 M*C is a good way to go. Suggestions?

[cooch]

I'm designing a study in which preliminary data suggests a relatively large open sea turtle population. Three years of tagging has yielded 150 new individuals and only 3 recaptures. What is a simple, yet appropriate way to estimate how many samples are needed in order to reliably estimate the population given the practically non existent level of recaptures? I've read different guidance- some say 4 M*C is a good way to go. Suggestions?

If you can't increase your capture probability more than 3/150, you're going to have essentially no power for inference of any kind. A general rule of thumb is that a minimum capture probability of 10% is needed before you can do much of anything remotely interesting.

Keep in mind the 'big law' (D.R. Anderson pers comm.) -- all studies need to balance effort spent on marking new individuals against cost of increasing detection probability for those encountered. Quite often, effort should be focused more on the latter, than the former.

[murray.efford]

I think Evan's reply may lead us in the wrong direction when the goal is to estimate population size. Probably, D. R. Anderson was not talking about estimating population size by capture-recapture, which I would have thought relies on (more or less) equal effort for initial captures and recaptures. Removal methods, of course, can dispense with recaptures altogether. Assuming kate12's data are for a closed population, they may indicate a large population with low capture probability, an effect of marking, or some other sampling irregularity: possibly this can be resolved by thinking through the biology & survey design. Otherwise, it's just a matter of how precise you want your estimate.

Murray

[kate12]

Regarding our study population- capture shyness has not been reported for this species before and we don't think this is likely influencing the results (animals are captured by tangle nets, not "traps" per se). We suspect that the population is either very large or that the population is open. Preliminary data hasn't excluded either hypothesis. This project will be long term in nature, so we expect that eventually we will have improved abundance estimates as time goes on. However there is some pressure from federal funding agencies to provide ballpark estimates sooner rather than later (in addition to better data in the future).

[murray.efford]

'Open' could mean that the population may be subject to turnover (births, deaths or migration) during sampling, or that animals have stationary home ranges distributed across an area that is sampled only in a spotty way. If the latter, (i) the relative locations of detectors (tangle nets) are an important part of the design that affects the ratio of captures to recaptures, (ii) you may find use for spatially explicit CR methods, and (iii) you need to worry not just about the total number of recaptures, but also about recaptures in a different detector if you are to estimate the scale of detection. Possibly not relevant, but just in case...
Murray

[cooch]

I think Evan's reply may lead us in the wrong direction when the goal is to estimate population size. Probably, D. R. Anderson was not talking about estimating population size by capture-recapture, which I would have thought relies on (more or less) equal effort for initial captures and recaptures. Removal methods, of course, can dispense with recaptures altogether. Assuming kate12's data are for a closed population, they may indicate a large population with low capture probability, an effect of marking, or some other sampling irregularity: possibly this can be resolved by thinking through the biology & survey design. Otherwise, it's just a matter of how precise you want your estimate.

Murray

Murray's point is well-taken, but I would add the the general admonition still stands -- even for abundance estimation -- with the condition that Murray notes. Yes, you *can* estimate abundance even with extremely low recapture rates, but the estimates will be of such low precision that -- rather that not being 'interesting' (as per my original post -- you could substitute the word 'useful' or 'informative)'.

For example, I simulated some data under true generating model M(t) (i.e., N, c(t)=p(t)). 5 occasions, true N=250. No heterogeneity (basic closed captures model). I set p=c=0.05 for each occasion (which is still higher than 3 out of 150, but will suffice to make the point). Simulating 10000 populations, I get 95% coverage (based on the distribution of estimated N for each simulation) of 133 <-> 832 (note the asymmetry wrt to the true population size of N=250). Perhaps there is some information in an estimate with a precision that ranges from about 50% of 'truth' to 332% of 'truth', but personally, I would probably plop this into the 'not particularly informative' pile. (Meaning, you might as well make a good guess as to abundance in this case).

Clearly, then, Murray's comments about design and such are entirely appropriate, since, in effect, what consideration of those factors will do is provide some guidance for improving realized encounter probability. Regardless of whether or not you're estimating abundance, or transition probabilities (survival, movement etc), I would submit that the basic admonition of the 'big law' still applies. Yes, "...it's just a matter of how precise you want your estimate.", but that is more or less the point -- unbiased but imprecise is still not particularly useful in many contexts. (Biased and imprecise is clearly cause for moving on to something else).

[kate12]

First off, thank you so much to everyone who has replied thus far. I really am grateful for all the input.

I suspect that Murray's point about stationary home ranges resulting in spotty sampling holds true for this site/species/study. If I had to guess, I would wager that some combination of the points brought up are in play : (1) large population, 2) spatially explicit to some degree (acoustic telemetry supports this to some degree), and 3) open population with respect to migration/recruitment (at least between field seasons). The study design is further complicated by competing ecological project goals that require a broader sampling strategy (i.e. not as site specific as I would like if my goal was only to estimate abundance) and an extremely remote field site which limits the duration of the field season. And this doesn't even account for the other logistical constraints like wrestling 300 lb animals from the ocean into a boat! But with so little recapture data it seems nearly impossible to ascertain which of these factors are most important. The project is further complicated by (as Murray suggests) different capture methodologies/detectors. We use both tangle nets and what is called "rodeo" capture (jumping off a boat onto the sea turtle), and capture data varies with each method (smaller animals are easier to catch with nets, larger animals, ironically, are easier to capture by rodeo because they are slower than zippy youngsters, and prelim data suggests some site preferences by size of animal). I do suspect however, that additional effort with collecting recaptures at specific sites, seems like a prudent next step. Now I just need to read up on site specific CR methods!