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

Marine fish populations have high variation in cohort strength, and the production of juveniles (recruitment)mayhave persistent positive or nega-tive residuals (autocorrelation) after accounting for spawning biomass. Autocorrelated recruitmentwill occurwhenever average recruitment levels changebetweenoceanographic regimes or due topredator release, butmayalso indicatepersistent environmental andbiological 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 below0.5SB0 5%of the timeon average across all stocks. Similarly, stocks fished at the level producing deterministicmaximumsustainable yield (FMSY) are below its deterministic prediction of spawning biomass (SBMSY) 60 % of the time and below 0.5SBMSY 8 % of the time. These prob-abilities 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 expect