Zusammenfassung: Leslie's method in removal methods is modeled into the joint of the binomial distributions. An interval estimation of p (removal ratio) and n (initial population size) based on the null hypothesis for p and n is easily obtained by the approximation of each binomial distribution to the normal distribution. The confidence region on the (p, n) plane is easily obtained by micro-computers. The maximum likelihood method for a point estimation and the convenient method on the curves of partial maximum likelihood for an interval estimation are also presented.

Zusammenfassung: A review is made of the literature on the back-calculation of fish body length from marks on scales or other hard parts (otoliths, vertebrae, fin rays, etc.). Though the technique is widely used it does not appear to be well understood. Regression methods are commonly used, apparently in ignorance of the more realistic proportional methods. It is not generally recognized that there are two equally plausible back-calculation hypotheses which can lead to significantly different back-calculated lengths. The Fraser-Lee equation, the most commonly used back-calculated formula, follows neither of these hypotheses but is based on a misuse of linear regression. It is recommended that back-calculation be restricted to procedures following one of the proportional hypotheses; that the difference between lengths calculated using the two hypotheses is a useful measure of the minimum uncertainty in back-calculation lengths; and that more attention be paid to validating back-calculation hypotheses by comparing observed and back-calculated lengths for individual fish. The pattern of heteroscedasticity in body length-scale radius plots is noted as a useful diagnostic in evaluating back-calculation hypothesis.