In a pickle

questions concerning analysis/theory using program MARK

In a pickle

Postby EricM » Mon Apr 12, 2010 11:06 am

OK, I am in a pickle here and pretty much Program MARK illiterate.

I am in the final year of my nesting and brood rearing success study on American woodcock in southeastern PA. I have 11 nests located so far and think I can pick up a few more. Part of the study design calls for tracking radio marked hens and their broods to measure brooding success. My dilemma is that I only have 5 radio marked hens. I lost communication with 3 others and am frantically trying to relocate them. A colleague mentioned doing a "power anaylsis" in program MARK to see what number of radio marked hens I need to be statistically significant. I know of the Lucaks model but am not sure of how to do a power analysis to see what numbers of broods tracked I need to be significant. Thank you!

Eric Miller
Wildlife Biologist
PA Game Commission
homiller@state.pa.us
EricM
 
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Re: In a pickle

Postby sbonner » Tue Apr 13, 2010 2:16 pm

Hi Eric,

One way to conduct a power analysis would be to use the simulation capacity of MARK. Essentially, make a guess at the parameter values (survival probabilities for the known fate model), simulate many data sets for many different values of n (the number of marked individuals), and compute the proportion that meet your "significance" requirement for each value of n. This will give you a rough idea of how many individuals you will need to mark, and you can vary the parameter values to see how sensitive the choice. Simulations in MARK are discussed in Appendix 1 of the GIM http://www.phidot.org/software/mark/docs/book/pdf/app_1.pdf.

You will need to think carefully about what you mean by "significance" as it doesn't sound like you have a hypothesis to test. Do you just mean that you want good estimates of the survival probabilities? In this case, you'll have to quantify what good means in terms of the size of the standard errors (equivalently, the width of the confidence intervals) for the survival probabilities or the corresponding beta parameters.

Of course, if your question is whether or not 5 marked individuals is sufficient then you probably don't need to go through all of this. If you simply wanted to estimate the survival probability over a fixed period of time and could assume that the individual all have the same probability of survival, phi, then the number that survive would have a binomial distribution with probability of success phi. The standard error for phi would then be sqrt(phi.hat * (1-phi.hat)/5), where phi.hat is the estimate of phi. In the worst case, if phi.hat=.5 then the se would be .22 and a (very) approximate 95% CI for phi would be (.06,.94), covering almost the entire real line. The situation improves somewhat if phi.hat is close to 0 or 1. E.g., if 4 of 5 birds survived and phi.hat=.8 then the se would be .18 and an approximate 95% CI for phi would be (.44,1.00), but this is still very wide. These calculations are rough because the normal approximation to the binomial is not accurate for such a small sample, but they give the general idea that any estimates of survival will be very imprecise with only 5 marked individuals.

Hope that helps.

Cheers,

Simon
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Re: In a pickle

Postby cooch » Tue Apr 13, 2010 3:13 pm

EricM wrote:OK, I am in a pickle here and pretty much Program MARK illiterate.

I am in the final year of my nesting and brood rearing success study on American woodcock in southeastern PA. I have 11 nests located so far and think I can pick up a few more. Part of the study design calls for tracking radio marked hens and their broods to measure brooding success. My dilemma is that I only have 5 radio marked hens. I lost communication with 3 others and am frantically trying to relocate them. A colleague mentioned doing a "power anaylsis" in program MARK to see what number of radio marked hens I need to be statistically significant. I know of the Lucaks model but am not sure of how to do a power analysis to see what numbers of broods tracked I need to be significant. Thank you!

Eric Miller
Wildlife Biologist
PA Game Commission
homiller@state.pa.us


Simon has done a great job answering this question (not surprisingly).

I would point out that a search for "power analysis" on the forum would have directed you to several threads which consider the "simulation" approach. More directly, if had searched the PDF for the "Gentle Introduction" for the phrase "power analysis", you would have been taken directly to Appendix A. In a bit of self-criticism, I see that "power analysis" is not an item in the index - it should be. Next time I recompile said book.
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