Carle & Strub
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This method was developed by Carle & Strub (1978) and is also called the Maximum weighted likelihood method. It was developed for use with catch data that is poor and fails to provide valid estimates using the maximum likelihood method.
The parameter M is calculated using:
where k is the number of samples taken, and ui the number of animals caught in the ith sample.
The population size, N is estimated as the smallest integer greater than the total catch, T, that satisfies the inequality
The above inequality is an approximation of a summation, and can fail for samples when k=2. The standard error is calculated as described for the maximum likelihood (Zippin's) method.
You should only use this method when the Constant probability and variable probability models have failed to give sensible results. This will normally occur when your data do not show a steady decline in the numbers caught with the number of samples.