The simple ratio estimate of the total number of marked fish present in a catch is described and the variance estimates discussed. A maximum likelihood estimate of the total number of marks present in a catch is derived which combines both marks found in samples and marks voluntarily returned from the non-sampled portion of the catch. The use of this estimate is illustrated with data from the salmon sport fishery in Puget Sound.
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Daniel K. Kimura (1976) studied this question.