Maturity dispersion, stock auto-correlation, and management strategy in exploited populations

Fishery management policies need to be based on historical summaries of stock status which are well correlated with the size of the group of individuals who will be affected by any harvest. This paper is motivated by the problem of managing stocks of Atlantic salmon, which can be accurately monitored during the riverine stages of their life-history, but which spend a lengthy period at sea before returning to spawn. We begin by formulating a minimal stochastic model of stock-recruitment driven population dynamics, which linearises to a standard ARMA form. We investigate the relation between maturity dispersion and the auto-covariance of stock fluctuations driven by process noise in the recruitment process and/or random variability in survival from recruitment to spawning. We demonstrate that significant reductions in fluctuation intensity and/or increases in long-run average yield can be achieved by controlling harvesting in response to the value of a historical summary focussed on lags at which the uncontrolled population dynamics produce strong correlations. We apply our minimal model to two well-characterised Atlantic salmon populations, and find poor agreement between predicted and observed stock fluctuation ACF. Re-examination of the ancilliary data available for one of our two exemplary systems leads us to propose an extended model which also linearises to ARMA form, and which predicts a fluctuation ACF more closely in agreement with that observed, and could thus form a satisfactory vehicle for policy discussion.