Separating recruitment and mortality time lags for a delay-difference production model

Many fishery production models implicitly incorporate a single time lag for both recruitment and mortality despite the fact that in populations of breeding adults, deaths occur yearly while the entry of new adults comes from juveniles born potentially many years prior to adulthood. Models that do not account for this difference in timing will overestimate abundance for a decreasing stock and underestimate increases during a recovery period. We investigated the effect of incorporating unequal recruitment and mortality time lags into depletion-based stock reduction analysis (DB-SRA), a stock assessment method for data-poor species. Using both simulated data and catch series of Pacific rockfish (Sebastes spp.), we found that for declining stocks with no mortality delay and a recruitment time lag equal to age-at-maturity, estimated overfishing limits were up to 40% lower than those from the model with both time lags equal to age-at-maturity. Deviation between the two models' predictions increases with age-at-maturity and natural mortality rate, suggesting that time lag separation is most important for long-lived species. We propose a correction factor for net production models that eliminates stock overestimation due to implicitly equal time lags.