Qualified estimation of two measures of diversity within populations

Abstract

Estimation of diversity within populations is a major concern in population genetics. An approach in the framework of hypothesis testing is developed, in which all hypothetical population frequencies that are not rejected on the basis of the sample frequencies define a confidence region. The test criterion requires that the sample be drawn according to a method of investigation that is qualified a priori, meaning that the probability of obtaining a sample with discrepancy not less than a given critical discrepancy from the true population frequencies not be greater than a given level of significance. Since a descriptor, such as diversity, is always a characteristic of the base population, confidence limits for the descriptor should be derived as the range of the descriptor throughout the confidence region or, by the duality between the non-rejected hypotheses and the confidence region of a sample, as the range of the descriptor for all non-rejected base populations. A table of minimal sample sizes for qualification is given. Geometric representations of the limits of confidence regions in S-3 and S-4 are shown for the absolute distance measure do of the discrepancy between frequency distributions. This method is applied to two measures of diversity commonly used in population genetics. Bounds on their derived confidence intervals are inferred. The computer program DIVSTAT used for calculations is introduced.