Controlling effort, catch and biomass in models of the global marine fisheries

Abstract

The starting point is the reduced model of global marine fisheries designated by W-3. The main variables of an ordinary differential equation are: the stock of bioresource, its net natural increase, as well as the catch value, which linearly depends on exogenous effort and nonlinearly on available biomass. In W-4, the effort became endogenous as a result of its positive feedback from biomass.In both models, there are values of control parameters in the catch equations, in which the value of the latter can be maintained for a long time at the maximum stable level, with the exception of transition sections. The principle of necessary precaution is fulfilled for small fish stocks more reliably in W-4 than in W-3, thanks to the transformation of the saddle into an unstable node with a common stable node.For these one-dimensional models, the author proposed an original generalization - the R-1 model of two nonlinear ordinary differential equations. In the latter effort, a new phase variable appears, subordinated to proportional control and derivative regulation. Biomass serves as a “prey”, and the effort appears as a “predator”.For two key control parameters, areas of change were identified for which the target stationary state is a locally asymptotically stable node or focus in R-1. A policy has been proposed for the restoration of depleted fish stocks and a transition to a long-term maximum sustainable harvest has been determined.Optimization over a wide time frame (from 40 to 400 years) allows us to calculate the values of the selected control parameters for which the integral catch volume in R-1 is higher than in W-4 for the same initial values of stock, effort and catch. Social constraints from below on the magnitude of the effort, as well as the desired nature of the transition to the target stationary state, are taken into account. The danger of biomass collapse is overcome, unlike previous models.