Zusammenfassung: Leslie's removal method, which is used to estimate the initial population size and the removal ratio simultaneously, is modeled in terms of the product of binomial distributions. The approximation of these binomial distributions to the standard normal distribution presents a new method which has no bias for estimators. This is an improvement over the maximum likelihood method and the likelihood ratio test, and is essentially equivalent to a standard goodness-of-fit test. The confidence region on the 2-dimensional plane defined by the initial population size and the removal ratio gives each confidence interval. This region is defined by the chi-square distribution with 2 degrees of freedom.

Zusammenfassung: In mathematics, the age-length key method is an estimating method for the ratio of each distribution in a mixture of distributions. Although the maximum likelihood method is the principle of this estimation, this model is a nonlinear model with a restrictive condition. At first, Hasselblad solved this model by using a new iteration method with a computer. Although his method was regarded as the steepest descent method or EM algorithm, it is proved to be an application of Lagrange's indeterminate multiplier method to the iteration method. Nowadays, there are other useful algorithms of optimization, especially Marquardt's method, for this estimation.

Zusammenfassung: A microcomputer system that weighs and measures fish and records the data on a computer file was tested at two hatcheries. The device produced fairly accurate lengths and might save labor and reduce transcription errors.

Zusammenfassung: Pacific salmon (Oncorhynchus spp.) escapements in natural streams are often determined by conducting fence counts in conjunction with mark-recapture operations. Typical field conditions are characterized by protracted floods, undetected immigration, variation in sampling rates, mortality during the census periods, small sample sizes, and few successive recaptures. Closed population models tend to overestimate escapement under such conditions, and traditional open population models cannot always be relied on due to the lack of sufficient data. A likelihood-based estimation method was specifically designed for such conditions. A distinguishing feature of this model is that individual recapture histories are not required for parameter estimation. The model is also structured to incorporate ancillary data in the estimation process to improve the precision and accuracy of the estimates. The model is described in detail, and suggestions are made to facilitate its application.