Threshold for sustainable exploitation of an age-structured fishery stock

Abstract

Assuming a discrete rate of variation of the total number of individuals equaling to zero in the long-term, as a population responds to exploitation with constant age-specific survival probabilities, it can be proved that a stable age structure exists. Such a stable structure does not depend on the recruitment process but on the survival probability from one age to another. It is not necessary to make any assumption on the recruit–reproductive biomass relationship or on depensation or compensation. The age structure is “filled” with the recruitment process and with the survival of individuals from one age to another. Besides assuming that the contribution of each age to determine future recruitment stabilizes through time, it can be proved that recruitment stabilizes and that a strong convergence of the vector of each population state to a stable state exists. All these results are general for population dynamics. The impact of exploitation varies according to ages and modifies the probabilities of survival. A threshold to separate sustainable from non-sustainable survival probabilities under exploitation can be established. This threshold depends only on biological-reproductive parameters. In fisheries stock assessment the age-specific survival probabilities show a functional relationship with age-specific fishing mortality rates. The combination of closed areas and selectivity of the fishing gear permit to put a limit to age-specific fishing mortality rates. Such regulations, and other complementary measures combined in a consistent manner allow to establish sustainable recovery and exploitation plans.