[R-sig-eco] 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: sbonner6 at uwo.ca | Telephone: 519-661-2111 x88205 | Fax: 519-661-3813
Twitter: @bonnerstatslab | Website: http://simon.bonners.ca/bonner-lab/wpblog/