basic sample size/precision question

[Amurskaya Meghan]

While not a question exclusive to MARK per se, I thought I'd check to see if anyone has insight into this:

For capture-recapture analyses aimed at estimating abundance, how does one calculate the sample size required to meet a given power (X) with a given alpha (Y) at a specified effect size (Z)?

In other words, what equation would one use to determine the number of captures and recaptures needed to be able to detect, say, a 10% change in abundance for specific power and alpha values?

Thanks for any and all help...

[cschwarz@stat.sfu.ca]

For a simple Petersen experiment, Seber (1982) and other books have nomograms available. As a rough and ready estimate, the relative se of N-hat is approximately equal to 1/sqrt(marks back). So, 100 marks back give a relative se of about 10%. There are lots of combintions of marks put out and recaptures that would give the same number of marks back.

Pollock et al (1982?) monograph on capture-recapture and Otis et al (1982) monograph have planning studies for estimating abundance to certain levels of precision.

You can also investigate using simulation tools of MARK. I would generate the expected counts for the histories, and analyze the expected counts to see what level of precision you get.

Detecting change is another issue. This will depend on the time frame (e.g. a 10% change over 10 years? over 5 years? over 3 years?)? Are you planning two petersen experiments or a real continuous mark-recapture experiment? If the population suffers mortality, do you want to estimate simply mortality or do you want the net of immigration/recruitment and death/emigration? Can you do a robust design, a simple JS, a combined JS + dead recovery model?

We will need more details.

[ganghis]

Hi,

This is a great question to ask before doing an experiment, but has a lot to do with what the underlying mechanisms that affect detection probability. Your best bet is to employ simulation based on what you think is going on (heteroneity will tend to make things a bit more out of control than otherwise). Gary has some pretty neat tools in MARK to do this - not sure how documented they are at this point.

Paul

[cooch]

Hi,

This is a great question to ask before doing an experiment, but has a lot to do with what the underlying mechanisms that affect detection probability. Your best bet is to employ simulation based on what you think is going on (heterogeneity will tend to make things a bit more out of control than otherwise). Gary has some pretty neat tools in MARK to do this - not sure how documented they are at this point.

Paul

The simulation tools in MARK are documented in Appendix A.

[SBeatham]

Hi,

I have a similar question concerning power analysis and the poisson log normal model. I have read through appendix 1 of 'A Gentle Introduction' and I'm finding it difficult to apply the process of assigning beta parameters to my mark-resight data and how to choose the link functions. I am looking at the sample size required to detect a change in population between a control group and treated group of individuals over three years (the treated would be expected to decline by approximately 20% per year). I have run the models for the first two years worth of data so I have alpha, sigma and U estimates for the two populations. I want to see if it is worth doubling the sample size for further studies.

Hope you can help,

Best regards

Sarah

[bmcclintock]

Hi Sarah,

To my knowledge, one can simply use the identify link function under the True Model specification and then enter the real parameter values under the Beta Values specification. The Beta Values for U do not matter because U is determined by the Releases and Known Marks specification (i.e. U = N - n), as well as the open population parameters (if there are multiple primary sampling occasions). I'm not sure what the default link functions are for the Estimation Models, so the safest bet would be to use the Parm-Specific link function (which allows one to manually assign the appropriate link function to each parameter). The appropriate link function for alpha, sigma, and U is the log link. The appropriate link function for phi, gamma'', and gamma' is the logit link.

Happy simming!

Brett

[SBeatham]

Hi Brett,

Thank you for your speedy reply. I just have a couple more queries.

1) When you said enter the real parameters under the beta values specification, did you mean the real parameter estimates that were produced from modelling my existing data? If not how do you decide what values to use for the beta values?

2) In the example in appendix 1 of 'A gentle introduction' to determine whether a change in survival could be detected you simply had to compare the true model assuming survival varied between groups to a reduced model where it did not and then use the LRT method to check for a significant difference. I'm interested in how sample size affects the abundance estimates, and therefore the ability to detect a 25% drop in population for one group compared to no change in a second group. In the poisson log normal model I have used 8 groups, four sampling occasions for each of the two groups. As abundance is a derived estimate I'm not sure how I can compare change in abundance over time for both groups and for significant differences between sample sizes as I am using the same models each time rather than comparing a true model to a reduced model so the LRT method would not be suitable.

I hope I'm making sense here and I hope you can decipher what I mean and put me right!

Best wishes

Sarah

[bmcclintock]

Hi Sarah,

See below.

Brett


1) When you said enter the real parameters under the beta values specification, did you mean the real parameter estimates that were produced from modelling my existing data?

Yes. Otherwise enter whatever values you think they should be.

2) In the example in appendix 1 of 'A gentle introduction' to determine whether a change in survival could be detected you simply had to compare the true model assuming survival varied between groups to a reduced model where it did not and then use the LRT method to check for a significant difference. I'm interested in how sample size affects the abundance estimates, and therefore the ability to detect a 25% drop in population for one group compared to no change in a second group. In the poisson log normal model I have used 8 groups, four sampling occasions for each of the two groups. As abundance is a derived estimate I'm not sure how I can compare change in abundance over time for both groups and for significant differences between sample sizes as I am using the same models each time rather than comparing a true model to a reduced model so the LRT method would not be suitable.

I don't fully follow you here, but I don't see any reason why one couldn't use a similar approach: for each sample size, compare true model(s) with treatment/time effects to reduced model(s) without treatment/time effects. I fail to see how abundance being a derived parameter could have any effect on one's ability to use the LRT (or any other) method. Note this is not the only way to conduct a power analysis using Monte Carlo simulation. Some of the material is a bit dated now, but some "early" papers by a young hotshot named Len Thomas (and references therein) might be worth going over (in addition to Appendix A of The Book):

Thomas, L and J Francis. 1996. The importance of statistical power analysis: an example from Animal Behaviour. Animal Behaviour 52, 856–859.

http://www.creem.st-and.ac.uk/len/paper ... SA1997.pdf

[SBeatham]

Hi Brett,

Sorry for not being clearer about this and thank you for the paper and your patience! Can I just check I have this straight? My most parsimonious model for my real data assumes alpha and U vary over group and time while sigma only varies across groups. This is my true model. To test the power of detection for abundance decline between the two groups I intend to do the following; For group 1 set N as x for year 1 and x - 25% in year 2, for group 2 set N as x for both years. Then compare estimation models that assume U varies only over time or only between groups with the true model and do this for increasing values for x. The known marks will be set as the % of N from the existing data. I am concerned that I am testing detection of U rather than abundance, even though abundance is derived from U. Am I missing the point here?

Hope you can put me straight one last time!

Best wishes

Sarah

[SBeatham]

P.S. I am entering the values for alpha and sigma. For increasing sample sizes will these values change? I thought they were probabilities so would not change but I notice from my real parameter estimates that alpha is not on a scale of 0 to 1.

Hope you can help (again)

Thank you

Sarah