Equilibrium, transient dynamics and sustainable reference points under age-specific natural mortality rates and varying levels of population productivity: The case of the Northern cod stock

Abstract

Scientific advisory bodies provide scientific advice for sustainable fisheries management based on the precautionary approach and maximum sustainable yield (MSY) reference points, such as spawning stock biomass (SSB) value Blim, and fishing mortality giving MSY, FMSY. The lack of a stock-recruitment function (SRF) to identify a clear breakpoint Blim has recently emerged in important stock collapses. It also precludes the use of equilibrium-based methods to analyze the sustainability of FMSY. Considering a hockey stick (HS) SRF, we propose here an equilibrium-based method that characterizes the equilibriums, their stability properties, transient dynamics, and changes in productivity (including age-specific natural mortality rates). We show that these relevant factors, not taken into account in standard methods, should play a central role in fisheries management and conservation. Considering the Northern cod stock (NCS) (Gadus morhua) by way of illustration, we properly estimate the HS and its associated Blim. We find that the HS fitted by the Fisheries Library in R underestimates Blim. Additionally, we determine the levels of productivity (medium-low or medium-high), and their corresponding growth rates of the SSB, which are consistent with the observed population dynamics. We find that the NCS was managed during the 1980s under myopic (unsustainable) harvest control rules, neglecting high age-specific natural mortality rates. We also find that recovery of the NCS remains a distant prospect, despite the current stable, positive equilibrium (sustainable FMSY).