Dear Severine,

There are tables  which will guide you through choosing sample. One of the best is Krejcie and Morgan Sampling table. And also there are more that you can choose which to use depending on your usage. 

Best regards,

This book by S. Sampath is helpful in sampling, sample size and estimating population size. You can download the book in PDF form. (see pp. 4-5).

http://www.math.hcmus.edu.vn/~tdkhanh/Sampling_theory/Reference/S.%20Sampath-Sampling%20theory%20and%20methods-CRC%20Press%20(2001).pdf

There is also an article at SSRN:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1478759

http://www.math.hcmus.edu.vn/~tdkhanh/Sampling_theory/Reference/S.%20Sampath-Sampling%20theory%20and%20methods-CRC%20Press%20(2001).pdf

All samples are wrong - some more than others.  In simple terms the standard error (SE) is proportional to 1/square root(n) where n is the number of measurements, experiments, numbers.  Usually we cannot sample the entire population to get the 'truth' and we have to take samples from the whole.  The larger the sample is then the closer we'll get (statistically speaking) to the true value.  The SE is that measure of potential closeness to the true mean.  So first you have to decide how close you want to get to the 'truth'.  For a standard error of 10% you'll need 100 random measurements or number in the sample.  50 in the sample then the SE is 1/root50 or about 14%.  A smaller sample of 10 will have an SE of 1/root10 or ~ 32%.  Samples this size really need evaluating with Students T-test - the potential variation is huge with small numbers.  In the extreme with 1 measurement only then the result is perfect!  With 3 measurements, throw out the 2 outliers and again be left with a perfect result!

I'm not aware of any sample size-related biases from the estimators used in NeEstimator (in other words, as far as I know, they do not systematically under- or over-estimate depending on sample size).  NeEstimator provides confidence intervals for Ne (asymptotic and jackknife) and one way of considering the adequacy of the sample size would be to ask if you're happy with this level of precision.  Speaking loosely, would you interpret the lower limit, Ne, and the upper limit differently or would they give you a similar interpretation?  If the former was the case, your sample size would appear to be too low for what you want to do.

Andrew hit the nail on the head "one way of considering the adequacy of the sample size would be to ask if you're happy with this level of precision"....