Zusammenfassung: The statistical model for the Petersen method is a hypergeometric distribution. Approximation to a binomial distribution has been used, and the usual method for this binomial model is based on approximation to a normal distribution. The Bayesian statistical model for a binomial distribution, which assumes that the prior distribution of parameters is uniform, corresponds well with the conventional method. However, the Bayesian statistical method for a hypergeometric distribution which assumes the uniform prior distribution is not feasible. The prior distribution according to the inverse squared parameter is natural for this model. Beta function and zeta function are important to understand these methods. This model is simpler to understand and easier to calculate by micro-computer than the conventional method.

Zusammenfassung: Multispecies virtual population analysis is an attempt to take species interactions into account when assessing the status of fish stocks. It was introduced primarily with the aim of lowering the uncertainty in the natural mortality rate as used in single species VPA and to take account of variability between years and ages by calculating inside the model the part of the mortality rate caused by predation. The output of the MSVPA is therefore – in addition to stock sizes and fishing mortality rates as in single species VPA and intraspecific – and possible species replacement are not considered and neither is predation on larvae and prerecruits. The potential relevance of multispecies models lies in long-term forecasts since short-term forecasts from multi- and single species models differ only slightly. In making long-term forecasts, predicting recruitment is of fundamental importance and the value of MSVPA in throwing light on the processes governing recruitment is limited. MSVPA is concerned primarily with calculating postrecruitment mortalities, and although in principle there is nothing to prevent prerecruitment predation mortalities being calculated, such estimates are not likely to be reliable or useful. Predation on the larval stages can be of major importance in determining recruitment but is not addressed in the MSVPA. Thus, it is quite possible that processes which are not dealt with in the MSVPA are much more important in determining the future of the fisheries. In view of all this uncertainty, it is inevitable that it will be questioned whether multispecies management advice is superior to single species advice.