The multi-sample single recapture census

Abstract

The aim of this paper is to set up a capture-recapture method for estimating the population parameters for a population in which there is both 'immigration' (including birth) and 'death' (including emigration). The method used may be readily described as the multisample single recapture census as opposed to the multiple-recapture census which has been used in many previous papers on capture-recapture analysis (see Darroch, 1958, 1959) and which as yet has not been solved satisfactorily for the most general population where both immigration and death are taking place. Although the multiple-recapture method provides some very elegant estimates of the population parameters for populations in which there is either just death or immigration, it has two main disadvantages. First, as the captured individuals are returned to the population, the method has no use commercially. Secondly, careful attention must be given to the method of capture, for, if there is any slight deviation from the underlying assumption that marked and unmarked individuals have the same probability of being caught-which is the basis of all capture-recapture models-then this deviation will be multiplied by repeated recaptures. For example, trap shyness (Leslie, 1952, p. 385) would affect the results in the same way as immigration. Thus the main advantage of the model considered below is that the individuals are only recaptured once and are then removed from the population as, for example, in commercial fishing and trapping. The technique used for this single recapture census is as follows: The experimenter, using differentiated marking, releases batches of marked individuals of sizes a,, a2, ... into the population he is investigating, and after each batch a, is released, a commercial catch of size bi is made and the individuals are killed, thus giving the sequence a1 added, b, removed, a2 added, b2 removed, etc. The numbers of marked individuals from the different ai and unmarked individuals are noted for each catch bi and passed on to the experimenter. Ideally, the marked individuals which are to be released, should either be caught before the whole experiment and stored, or perhaps taken from a similar population not connected with the one under investigation. In actual practice, however, the experimenter could take the samples at from the population during the experiment, because, in general, the ai, although large, will be much smaller than the bi and therefore the recaptures in the successive al, a2, ... will be negligible. Also the overall reduction in the number of un-