Probability of stochastic depletion: An easily interpreted diagnostic for stock assessment modelling and fisheries management

Abstract

Marine fish populations have high variation in cohort strength, and the production of juveniles (recruitment) may have persistent positive or negative residuals (autocorrelation) after accounting for spawning biomass. Autocorrelated recruitment will occur whenever average recruitment levels change between oceanographic regimes or due to predator release, but may also indicate persistent environmental and biological effects on shorter time-scales. Here, we use estimates of recruitment variability and autocorrelation to simulate the stationary distribution of spawning biomass for 100 real-world stocks when unfished, fished at FMSY, or fished following a harvest control rule where fishing mortality decreases as a function of spawning biomass. Results show that unfished stocks have spawning biomass (SB) below its deterministic equilibrium value (SB0) 58% of the time, and below 0.5SB0 5% of the time on average across all stocks. Similarly, stocks fished at the level producing deterministic maximum sustainable yield (FMSY) are below its deterministic prediction of spawning biomass (SBMSY) 60% of the time and below 0.5SBMSY 8% of the time. These probabilities are greater for stocks with high recruitment variability, positive autocorrelation, and high natural mortality-traits that are particularly associated with clupeids and scombrids. An elevated probability of stochastic depletion, i.e. biomass below the deterministic equilibrium expectation, implies that management actions required when biomass drops below a threshold may be triggered more frequently than expected. Therefore, we conclude by suggesting that fisheries scientists routinely calculate these probabilities during stock assessments as a decision support tool for fisheries managers.