Analysis of retrospective error in an adaptive frame work for virtual population analysis

Abstract

Retrospective problem (RP) in an adaptive framework for virtual population analysis (ADAPT) is based on the observation that in some fisheries retrospective error in current stock size estimates (REs) in successive yearly assessments display a trend rather than a random pattern. I have investigated the likelihood of occurrence of the RP resulting from chance in the presence of random variation of "realistic" (lognormal) errors in "input data" in the use of ADAPT. Both simulation and analytical methods were used. It was found that the RP occurs with high likelihood by chance alone in a fishery. In combination with positive mean and median bias in REs, a random-walk property in time series estimates of REs that gives false impressions of trends (generated by non-drift random variations of errors in "input data") creates a RP. I have also explored the fundamental causal factor and the casual mechanism of the RP using an explanatory mathematical model. The REs was fundamentally explained by a function of temporal difference in ratios of abundance-index and cohort-size, which is ADAPT regression-independent. This explanatory model was based on the finding that in the overall regression, residuals of each age class are added to near zero. The REs forms temporal trends caused by changes in the biases of factors that influence the above difference, thereby creating a RP. It was also found that series of positive REs generated by temporal increase in the proportion of underestimated catch might not be "true" overestimations. This reality in the ADAPT implies that RP evident in fisheries may also be "illusionary" and may not always require corrective treatment.