New non-linear model for the study and the exploitation of fishery resources

Abstract

A novel modeling approach is put forward in which recruitment (to the population, area and fishery) is regarded as a system or summation of non-linear functions with dynamic features ranging from chaos (the ceiling, when external conditions are extremely benign), going through a range of relatively stable, converging cycles (as external stress increases), to a quasi-standstill state with no clear oscillations (when the minimum viable population is being approached). A system which consists of a dynamical continuum governed by a variable carrying capacity with local dynamics in different orbits of stability is proposed. The author is first to formalize in the scientific literature the concepts of variable carrying capacity, multiple, linked orbits of stability and seudo-equilibria, and dynamical similarity at several spatiotemporal scales, as well. The model has been the first which could link all of the known population mechanics (that is, density-dependent, densityindependent and inverse-density-dependence processes) in a relatively simple equation. This system model which is limited by a maximum carrying capacity and an overall minimum viable population is highly flexible as it has the capacity to, persistently, evolve and return within a range of dynamical states allowing for the description of multi-oscillatory population systems with features which may be caused by stable, periodic, multi-periodic and chaotic dynamics...