Evaluation of estimators of population size based on simulation techniques

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Virginia Polytechnic Institute and State University

Estimating the size of an animal population has been a major problem for the biologist. Although a host of techniques and mathematical refinements of existing estimators have been developed, they fail to aid the investigator when the individuals in the population do not exhibit equal probability of capture. The present work has resulted in a computer simulation model which mimics typical mark-recapture experiments and allows one the ability to examine existing estimators, determine the effect of alterations in the usual trapping experiment, and develop new estimators.

Five mark-recapture estimators of population size were examined in an effort to determine their behavior when the assumption of equal probability of capture is satisfied. The Lincoln, Schnabel, and Schumacher-Eschmeyer estimators gave similar results and had the best statistical properties. However, the assumption of equal probability of capture is usually violated in nature and, thus, the estimators were also examined when the individuals possessed a bivariate normal utilization distribution with σₓ = 1 and σᵧ = 2, a random spatial pattern, and various trapping behaviors. Simulation experiments of 10-sample mark-recapture experiments were performed. The results indicate that large negative and positive sample biases result, respectively, when the animals are trap happy or trap shy. Often the estimators yielded values of one-half to two times that of the true population size. After evaluating the sample bias, variance, and mean square error of the five estimators, the non-parametric was selected as the most robust under the specific situation studied. In order to improve this estimator, regression techniques were used to develop two correction factor ratios: one for trap happy populations and one for trap shy. These correction factor ratios were functions of the initial average probability of capture and a parameter controlling the trapping behavior of the animals. The corrected non-parametric estimators were defined as the non-parametric estimator times the appropriate correction factor ratio. The performance of the corrected non-parametric estimators were tested with known values for the parameters and found to be quite accurate. Currently, the problem exists of developing estimators of the parameters from field data. When this is accomplished, the corrected non-parametric estimators may be suited to field studies.