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.

Zusammenfassung: The statistical model used is extended to estimate abundance from commercial catch-at-age data for many of the major commercial fish species in the world. The model combines commercial catch-at-age data and research survey estimates of fish abundance; extends the model to allow correlated errors among ages within a year for the survey estimates of fish abundance. Method is formulated for modeling the fishing mortality on the oldest ages of the fish caught. Estimates are obtained using maximum likelihood. The level of correlation among ages is sufficiently large to produce large biases in the standard methods for some stocks. The statistical model that includes correlated errors greatly reduces bias and increases efficiency if the correlation in the estimation error is large.

Zusammenfassung: The authors determined the statistical properties of the index of biotic integrity (IBI) from electrofishing samples collected from Ohio streams. Although IBI is widely used to evaluate the condition of water resources by biologists and resource managers, expanding its role as a regulatory tool depends on statistical validation of its precision and power. We addressed these issues by constructing an additive variance model for IBI and testing the assumptions of that model directly with a bootstrap resampling algorithm and simulations using field data. Statistical properties of IBI supported the use of standard analysis techniques such as ANOVA for hypothesis testing. We determined with power analysis that IBI can distinguish between five and six nonoverlapping categories of biotic integrity based on a model that includes the effects of measurement error, variability of fish assemblages through time, and statistical interaction of location and time.

Zusammenfassung: Estimation of von Bertalanffy growth parameters has received considerable attention in fisheries research. Since Sainsbury much of this research effort has centered on accounting for individual variability in the growth parameters. In this paper we demonstrate that, in analysis of tagging data, Sainsbury's method and its derivatives do not, in general, satisfactorily account for individual variability in growth, leading to inconsistent parameter estimates (the bias does not tend to zero as sample size increases to infinity). The bias arises because these methods do not use appropriate conditional expectations as a basis for estimation.