Persistence index for harvested populations

Fish stocks face both anthropogenic and environmental pressures, which can drastically reduce population sizes and threaten species' survival. While some species can persist and recover from such disturbances, others require careful management to prevent collapse. We introduce a new, biologically intuitive, measure of persistence, the number of eggs produced by an individual fish over its lifetime (NEL) under a harvest policy. Additionally, we demonstrate the relationship between NEL and other candidate indices such as the inherent net reproductive rate, biomass, number of spawners, and dominant eigenvalue of the Jacobian. We show that, NEL inherits a desirable monotonicity property with respect to harvest survival probabilities. That is, NEL (persistence) is higher when survival is higher. If persistence were measured by the dominant eigenvalue of the Jacobian, we show that this property is violated. Hence, NEL offers a valuable and easily computable index for managers to assess persistence under alternative harvest policies.