A New Method for Estimating Population Size from Removal Data

The theory leading to the maximum likelihood (ML) estimation of population size from removal data is reviewed. The assumptions of the removal method are that changes in population size occur only through capture, and the probability of capture is equal for all individuals in a population during the removal sequence. A modification of the multinomial model is proposed and a new estimator developed. In the new model the likelihood density of the probability of capture is weighted with a beta prior. The case where α = β = 1 (uniform prior) is compared with ML estimation and found to have lower bias and variance. The new method, unlike previous methods, does not fail for any catch vector thus avoiding the substitution of the total catch for the estimate of N when infinite estimates occur. The assumptions that result from applying large sample theory while estimating the variance of ML estimates are reviewed, and a condition presented for the inadequacy of asymptotic variance formulae when using the weighted estimator (α = β = 1). Examples illustrating the use of the new method are given; one example illustrates the use of the new method when previous methods fail. Various assumption violations are investigated and the new method is found to be more robust against the violation of assumptions than previous methods.