Despite the extensive literature on fisheries economics, there is a lack of knowledge of ecosystem processes where the intrinsic growth rate at low stock levels is affected by demographic uncertainty. They propose a multidisciplinary project in mathematical bioeconomic and population dynamics modeling of collapsed fisheries. We aim to build stochastic mathematical models to i) analyze the population dynamics of collapsed species by using advanced mathematical tools: a spline parameterization method and the ensemble Kalman filter and smoother, ii) test the limit reference points proposed by fishery scientists, and iii) develop bioeconomic stochastic dynamic optimization models to provide scientifically sound management strategies ensuring long term sustainability. The NSSH stock is among the largest and biologically most productive fishery resources in the world. This is the reason why this species has been extensively analyzed by the Norwegian research team (NRT) by acquiring much technical and scientifically knowledge which will benefit to the Spanish’s research team (SRT) in order to detect depensatory population dynamics.
Summary of project results
The aim of this project is to develop a discretization method of CM (DCM), based on the fourth order Runge-Kutta method (RKM), which allows us to construct a bridge between CM and DM by overcoming the biological and economic weakness and by preserving the strengths of both approaches. Specifically, in the DCM developed in this project, a CM is thought of as the limiting case of a DM in which the interval between times in the discrete time frame becomes vanishingly small. This allows for increments in time less than one year and consequently it allows us to analyze seasonal fisheries. Using the NEAC by way of illustration, the main contributions of this project include: First, in contrast to the LG used in CM, which is often estimated in discrete-time, a proper continuous-time LG, which is a differential equation, is estimated by using data assimilation methods. In particular, researchers use the EnK and EnKS to show that the proper LG estimated in continuous-time is quite different to that estimated in discrete-time. Second, using the RKM, a proper discrete-time LG is obtained by using an appropriate discretization of the LG estimated above in a continuous-time setting. In contrast to the LG estimated in DM, researchers show that the discretized LG obtained by the DCM is non-decreasing at high population sizes by properly reflecting the natural behaviour (without harvest) of fish stocks. Third, researchers show that if DM do not take into account the discretized LG obtained by the DCM then such an approach would lead to erroneous (suboptimal) policy advice with the consequent implications for sustainability of fish stocks. Consequently, they show that the DM obtained by the DCM is the appropriate model for management advice. Fourth, the team show that, at least for the NEAC fishery, seasonal harvesting is a win-win optimal solution. In particular, they analyze both the case of quarterly harvest and the case of monthly harvest, and compare these to the case of annually harvest. Next, researchers show that the DCM described above is able to deal with both strong seasonal variations over the year in economic parameters (economic seasonality), and seasonal regulatory measures (seasonal regulation).
Summary of bilateral results
Both research teams have taken an active part in seminars organized by both universities, Norwegian School of Economics (NHH) and University Complutense of Madrid (UCM). In a coordinated way, each research team decided to hold periodic meetings and seminars in their own university in order to follow up the joint work agenda. In addition, it was decided to hold at least one seminar in the host university during each research stay in order to discuss the progress made in the implementation of the Project. This Project has established a fruitful collaboration among both individuals and institutions. In particular, Maroto and Morán are members of a Research Council of Norway (NFR) project: “A General Age-structured Model for Ecosystem Management (AGAMEM)” leaded by Stein I. Steinshamn. They are also members of a Spanish Ministry of Economy and Competitiveness project: “Optimalidad en modelos bioeconomicos estructurados por edades” leaded by Maria Jose Gutierrez. Apart from University Complutense of Madrid, it involves the University of the Basque Country (Spain), the University of Vigo (Spain), Norwegian University of Science and Technology (Norway), and University of Helsinki (Finland). They are also members of IMI-Interdisciplinary Mathematical Institute (UCM). The results obtained in this project have attracted great interest from researches at the Spanish Oceanographic Institute (IEO) in Vigo due to the fact that they are just now estimating relevant fisheries seasonal data that will be used by the European Union to establish Total Allowable Catches (TACs) for the 2016 management advice. As described below, the results obtained in this project have also attracted great interest from researches who attended the international seminar held at UCM. On the other hand, it is expected that the results obtained in this project will be of great interest to both other researches and institutions which are located outside of Norway and Spain.