Population Estimation from Mark-Recapture Experiments Using a Sequential Bayes Algorithm

Abstract

Traditional analyses (e.g., Schnabel 1938 or Chapman 1954) of sequential mark—recapture experiments (Petersen and Schnabel type) yield population estimates with substantial negative bias and overly large confidence intervals if the combination of the number of animals marked and examined falls too low. To address these problems, sequential mark—recapture experiments are cast into a Bayesian framework using a "noninformative" discrete uniform improper prior (a priori theoretical) distribution. Some properties of the posterior distribution (probability of each population size given the data) are briefly and informally discussed (inference, convergence, mean, mode, median, and treatment of nuisance parameters). A sequential Bayes computational algorithm, suitable for microcomputers, is given. Several examples are presented as a practical guide to computing estimates. For relatively small sample sizes, the Bayesian approach yields larger mean abundance estimates than traditional methods. There is little difference in these estimates for larger sampling efforts. Advantages of the approach include the following: the probability of observing the data at all feasible population sizes is calculated exactly; the method works for all cases regardless of sample size or sampling procedure; a plot of successive posterior distributions can be used as a visual diagnostic of conformity with basic assumptions; and finally, inferences can be made directly, since the end product completely describes the uncertainty of the population size given the data.