Resumen de New non-linear model for the study and the exploitation of fishery resources = Nuevo modelo no-lineal para el estudio y la explotación de recursos pesqueros
A new non-linear model 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): the proposed system which consists of a dynamical continuum governed by a variable carrying capacity with local dynamics in different orbits of stability. The author is first to formalize in the scientific literature on population dynamics in aquatic environments and fisheries the concepts of variable carrying capacity, dynamical continuum, multiple, linked orbits of stability and seudo-equilibria, and dynamical similarity at several spatio-temporal scales. The proposed model has been the first approach which could link all of the known population mechanics (that is, density-dependent, density-independent 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 cause/consequence of stable, periodic, multi-periodic and chaotic dynamics. The proposed framework offers several conceptual and practical advantages over the classical models and it may allow to do a more realistic assessment in stock dynamics. Some of the key concepts spinning off the model are as follows: (i) the persistency and plasticity of the population system, that is the ability of the stock to withstand both environmental perturbations and high fishing mortality and rehabilitate from low orbits of stability; (ii) the differential effects of fishing mortality during density-dependent and density-independent compensations and depensations; (iii) the understanding of (a) population collapses due to the effects from density-independent depensations combined to high fishing mortality and (b) density-dependent and density-independent mechanisms may induce the rehabilitation of the stock towards higher orbits of stability; (iv) the short and medium term estimation of recruitment due to trends (slopes and temporal evolution) in external "best descriptor" variables (such as Sea Surface Temperature, SST, SST Anomaly, SSTA, North Atlantic Oscillation, NAO, upwelling strength, among others and climate proxies); (v) the explanation of the high variability in the data and determination of how combined, multivariate correspondences, memory effects, time lags, periodic oscillations, noise and sensivity to external conditions may affect the population system; (vi) the existence of dynamical similarity at several spatio-temporal scales and extrapolation of trends between different scales. Furthermore, new concepts are proposed on (a) global and local dynamics; (b) residuals, signal, noise and dispersion in the data; (c) harvesting in systems with multiple orbits of stability; (d) conditions which may lead to the extinction of the commercial fishery; (e) forward and backwards bending nature of catches, fishing effort, and abundance; (f) incorporation of multivariate perturbations and (g) approximations to the multi-oscillatory model by different curve fitting methods and (h) autocorrelated residuals and population systems with strong dependencies on wave-like external variables. The author validates the proposed framework in five case studies on baltic and Icelandic cods, skipjack tuna and the common Octopus in FAO fishing Area 34 (Centra Eastern Atlantic) and a historical, tuna oriented Spanish almadraba fishery (years 1525-1756): it is shown that the dynamical patterns in the different cases consist systems with multiple orbits of stability and that population trends are due to the combined effects from internal population mechanics as well as the external environment and fishing mortality. Furthermore, sub-models are put forward for variables such as the North Atlantic Oscillation, Sea Surface Temperature, SST, and SST anomaly upon the dynamics of the populations and fisheries. Finally, several of the new dynamical concepts of the framework are discussed and an appendix on the use of catches as a proxy for abundance is put forward.
