Zusammenfassung: This paper is concerned with certain computational aspects of estimating the mean fecundity of a single age-class of a population of fish. Four computational methods for estimating mean fecundity are compared by Monte Carlo simulation. One of the four methods is the simple expedient of estimating fecundity at sample mean length, a method known to be downwardly biased. The Monte Carlo study shows that the other three methods reduce bias and provide worthwhile efficiency gains. For small samples, the most efficient of the four methods is a “bias adjustment”, proposed here, that uses easily calculated sample statistics. For large samples, a numerical integration method has the highest efficiency. The fourth method, a “direct summation” procedure which can be done easily in many statistical or spreadsheet programs, performs well for all sample sizes.

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.