Estimating and Testing Differences between Population Levels by the Schnabel Estimation Method

Abstract

In the Schnabel method of estimating number of animals, the number of recaptures has been assumed to follow a Poisson distribution. This approximation is useful in testing differences in population levels when the Schnabel method is used for estimation, since the distribution of recaptures from one population, conditional on the total number of recaptures from both populations, is approximately binomial with parameters n and p, where p is a function of the parameters of the two Poisson distributions. Tests based on this conditional binomial distribution are described. Confidence limits of the population numbers have been considered and a stop rule developed for the Schnabel experiment used at the second stage of a paired comparison. The Schnabel method (Schnabel 1938) of estimating numbers of animals from tagrecapture data is widely used in fish and game population studies. This method is popular because (1) computations are simple, (2) daily estimates are a feature of this method, enabling the field worker to see his results as the work progresses, and (3) the method is flexible and can reasonably be expected to provide useful results over a wide range of capture conditions. However, there is some hesitancy about using the Schnabel method, since the variances of these estimates are difficult to estimate. In addition, it has not been made clear whether tests of differences between estimated populations can safely be based on such estimates of variance, as is also true for confidence intervals about an estimate. Simple straightforward tests of differences in population level, as well as confidence limits for the population estimate, are possible by using the knowledge that the number recaptured has approximately a Poisson distribution (Chapman 1954). To estimate population size by the Schnabel method, let x x-= number of recaptures, (1) A(n,M,), (2) 1=1