A delay-differential model for representing small pelagic fish stock dynamics and its application for assessing alternative management strategies under environmental uncertainty

Abstract

We present a novel adaptation of the classic discrete delay-difference model, a continuous delay-differential model (cDDM), which can adequately represent population dynamics of stocks that turn over rapidly and continuously over time (e.g., small pelagic fish, small tunas, and shrimps). We used the Northern-Central Peruvian anchoveta stock (Engraulis ringens, Engraulidae) as a case study for implementing the cDDM and conducted a management strategy evaluation (MSE) through stochastic optimization in policy space (SOPS). Our results showed that cDDM integrated with SOPS efficiently searches optimum and near-optimum harvest control rules (HCR) and is an alternative to pre-setting arbitrary HCRs as in traditional MSE. The cDDM showed comparable stock biomass and recruitment estimate reconstructions to more complex stock assessment models described for anchoveta. We concluded that the anchoveta stock is sustainably managed and is an example of adaptive fisheries management under high ocean-climate variability and uncertainty. Contrary to fishery textbooks, the anchoveta's collapse was not entirely due to the 1972 El Niño (EN) but a recruitment failure preceding EN. Our reconstructions revealed that low recruitment (or recruitment failure) could still occur at high stock biomass. Anchoveta's stock biomass is larger than pre-collapse, likely due to favourable environmental conditions (a cooling trend) and management, despite more frequent and stronger EN events. SOPS quickly revealed that harvest strategies with large base biomass (>5 mmt) lead to higher interannual stock variability and would not produce substantial increases in long-term yield. Alternative HCRs with lower base biomass, while adjusting for productivity regimes, have similar long-term yields without affecting the long-term average stock.