Mathematical model for sustainable fisheries resource management accounting for size spectrum

This paper proposes a novel modelling and control framework for growth models that incorporate a size spectrum in conjunction with numerical computation and extensive field surveys. In fisheries management, the size spectrum, characterized by individual differences in body weight and length, is a critical factor, as it influences the physiology and ecology of fish, as well as the preferences of anglers. However, a comprehensive theoretical framework for fisheries modelling and management that accounts for the size spectrum has yet to be established. We apply a growth model that considers the size spectrum to Plecoglossus altivelis altivelis (Ayu), an important inland fisheries resource in Japan. Additionally, we introduce a novel stochastic control theory for the resource management of Ayu, taking its size spectrum into account. The growth model is calibrated using data collected annually from a river system in Japan. Our control problem addresses the size spectrum of fishing benefits and terminal utility (nonlinear expectation) for sustainability, resulting in a nonstandard problem to which the dynamic programming principle does not apply. We address this difficulty using a time-inconsistent formalism, where solving the control problem is reduced to finding an appropriate solution to a system of nonlinear partial differential equations. We numerically compute the system using the finite difference method and explore the fisheries management of Ayu at the study site.