Estimates of population parameters from multiple recapture data with both death and dilution—deterministic model

Abstract

A number of methods are available for estimating total populations, survival rates and emergence rates of mobile animal populations from capture-recapture data. Most assume a deterministic model in which each class in the population is assumed to be subject to exactly the same survival rate, and their methods differ mainly in the grouping of the data and in the type of estimates used. The animals captured on each occasion are assumed to be a random sample from the population. The two commonest methods of grouping are method A which amounts to recording total number of previous captures among the animals caught at each sampling, and method B in which only the last of the previous captures of a particular animal is counted and any earlier captures ignored. The earlier writers, Jackson (1939, 1948), and Fisher & Ford (1947) have grouped their data according to method A, and Bailey (1951) discusses the variances of the estimates these writers have used. Grouping according to method B was first introduced by Leslie & Chitty (1951), who give the maximum likelihood equations for both methods A and B for a chain of five successive samplings when the survival rate is assumed constant. The two methods are compared and it is shown that method A results in loss of information, whereas method B is fully efficient under the assumption of the deterministic model. These ideas are extended in Leslie (1952) to cover the more general case when the survival rate is not constant over the period of sampling and when dilution of the population may be occurring due either to fresh emergences or immigration into the area. Solution of the maximum likelihood equations, whether or not the survival rate is assumed constant, is done by iteration to give estimates of total populations, survival and dilution rates, the computation becoming somewhat laborious in the case of a long chain of samples. Leslie also gives a quick method of obtaining approximate estimates from a triangle of three entries in the table of recaptures. In an example of the practical application of estimating population parameters, Leslie, Chitty & Chitty (1953) derive their estimates by an improved approximate method utilizing data from two adjacent columns of their recapture table to provide estimates for any one sampling occasion. Moran (1952) discusses the theoretical aspects associated with the deterministic and other models. Hammersley (1953) and Darroch (1958, 1959) base their estimates on a fully stochastic model. Darroch has shown that in the three cases when the population is: (1) a closed one subject neither to death nor immigration, (2) subject to death only, (3) subject to immigration only, the population parameters can be very simply estimated together with their variances and covariances. In the more general case when both death and immigration are occurring, estimation equations are derived. A method is indicated for obtaining variances and covariances, but the procedure is complex and formulae are not given.