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McGinley, Ed

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Re: Question

Simon Bonner
Ed,

I've held off on replying to this post because I'm not familiar with
RCapture, but I thought I'd jump in as no one else.

The answer is that, yes, your sample size is too small. What is
happening is that the maximum likelihood estimates for the capture
probabilities lie on the boundary of the parameter space -- they are
exactly equal to one. Unfortunately, the approximate normality of
maximum likelihood estimates breaks down at this point, so the standard
errors don't make sense. Computing standard errors from the usual
approximation (inverse information matrix) results in standard errors of
0 for the capture probabilities -- suggesting that there is no
uncertainty. This in turn means that there is no uncertainty in
abundance. If the capture probabilities were truly 1 with no uncertainty
then you would definitely have captured every individual in the
population and you would know the abundance exactly. Clearly that's not
true.

The reason for this is that your sample is too small. Note that most of
the individuals were never recaptured and that there was never a gap
between captures -- individuals were recaptured on subsequent occasions
until they were never seen again. This is perfectly consistent with the
inference that capture is perfect and individuals are seen on every
occasion until they leave the population, which is what the results are
telling you.

My guess is that this may be close to the truth and, by chance with the
small sample, you have hit a data set that leads to boundary estimates.
Is it reasonable to believe that this species has a fairly short
life-span (relative to the time between captures) and that the capture
probability is high?

One solution is to use profile likelihood intervals to compute estimates
of uncertainty for the parameters on the boundary (the p's). Again, I
don't know about RCapture, but this is possible in Program MARK.
Alternatively, you could work with a Bayesian analysis using a prior
selected to keep the parameters away from the boundary.

I hope this helps.

Cheers,

Simon


On 2016-09-15 2:00 PM, McGinley, Ed wrote:

--
Simon Bonner
Assistant Professor of Environmetrics/Director MMASc
Department of Statistical and Actuarial Sciences/Department of Biology
University of Western Ontario

Office: Western Science Centre rm 276

Email: [hidden email] | Telephone: 519-661-2111 x88205 | Fax: 519-661-3813
Twitter: @bonnerstatslab | Website: http://simon.bonners.ca/bonner-lab/wpblog/

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