Comment on elementary operations of sequential population analysis

Abstract

I wish to comment on the recent article by Evans (1996), which was a provocative analysis of the retrospective problem in fisheries assessments. Evans proposed the use of untuned sequential population analysis (SPA) to reveal the underlying inconsistencies in fishery assessment data. He then presented a metric of this inconstancy, based on the ratio of two estimates of the population numbers at age. He concluded that the retrospective problem was inherent in the data for the stocks he analyzed. I submit that his proposed metric is neither the result of elementary operations nor easily related to traditional assessment practice. The paper’s title refers to “elementary operations of sequential population analysis.’’ The first of these is described in his equation (1) as the accumulation of deaths over the life of a cohort. Unfortunately, there is some confusion concerning how these deaths are to be estimated. Assuming that some aspect of natural mortality is included in the number of deaths at each age in a cohort, the statement in the Discussion that “there is no need of simplifying assumptions about how fishing pressure is distributed over the year’’ is hard to reconcile. Pope’s (1972) cohort analysis, which the author used, applies corrections for the time of year when the deaths due to fishing are assumed to take place. The problem of estimating the number of deaths is mentioned (Evans 1996, p. 240), but it is not commonly assumed that “... standard assessment practice treats deaths, D(y, a), as known ...,’’ as he asserts. In fact, the SPA assumptions relating to natural mortality are probably the most tenuous. SPA converts the numbers of fish in the catch into estimated population numbers at age by accumulating the catch down cohorts after correcting for natural mortality. Traditionally these numbers are tuned to some index of abundance or fishing effort (Mohn and Cook). The tuning is based on what I would consider the second elementary operation which is linking the population numbers, N(y, a) of cohort y at age a, to an abundance index, u(y, a):