Local influence diagnostics for the retrospective problem in sequential population analysis

Abstract

Abstract The retrospective problem involves systematic differences in sequential population analysis (SPA) estimates of stock size or some other quantity in a reference year. The differences occur as successively more data are used for estimation, and they appear to be structural biases caused by a mis-specification of the SPA. In some cases the retrospective problem is so severe that the SPA is considered to be too unreliable for stock assessment purposes. There are many possible sources of retrospective patterns, and it is usually difficult in practice to determine which are more likely. We propose diagnostics to help determine the more likely causes. We use local influence diagnostics to investigate whether small changes or perturbations to SPA input components such as catches or natural mortalities can remove or reduce retrospective patterns. We show, for the fall-spawning herring stock in the southern Gulf of St. Lawrence SPA, that relatively small age- and year-specific changes to the SPA assumptions about the proportional relationship between an abundance index and stock size can result in greatly reduced retrospective patterns. We therefore conclude primafacie that these assumptions are a plausible source of the retrospective pattern. Larger changes to catches, natural mortality assumptions, or estimation weights are required to reduce the retrospective pattern. These other factors seem to be less plausible sources of the retrospective pattern, although this is best assessed by the herring stock experts who are more knowledgeable about the fishery and other scientific information for this stock.