An investigation of stratified population estimates

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Kirby, Christopher William
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This thesis presents the results of a comparative study of the two most commonly used two-sample, mark-recapture population estimators: the unstratified pooled Petersen estimator, and the stratified Darroch estimator. The primary focus of this thesis is the study of the estimators as they are applied to temporally stratified, migrating salmon populations. The study consists of applying the estimators to a series of hypothetical populations representative of those seen in migrating salmon populations. The study focuses on the asymptotic relative bias, the coefficient of variation (CV), the bias relative to the CV (effective bias), and the root mean-square error. It is determined that using a stratified estimator, such as the Darroch, can provide large improvements, in terms of reducing bias, over the unstratified pooled Petersen. As well, it is determined that while the Darroch offered improvements in bias over the pooled Petersen, the Darroch exhibited much larger CVs than the pooled Petersen. The much larger CVs of the Darroch lead to a study of the practice of pooling rows and columns of mark-recapture data to increase the precision of the Darroch estimate. These experiments yield two results: the first is that there exists no clear optimum level of pooling for the populations studied, and the second is a heuristic that can be used to determine when data have been over-pooled. A simulation study is conducted to examine the properties of the estimators' standard error estimates. It is determined that the standard error estimate for the pooled Petersen estimator is both unbiased and precise. Similarly, it is determined that standard error estimate for the Darroch estimator can exhibit the undesirable properties of high bias and low precision. Finally, a software package developed to produce the results for the study, is presented and discussed. (Abstract shortened by UMI.)