Innovative mathematical modeling of life history of migratory fishes for regeneration of river environment

2018 Fiscal Year Final Research Report

• Project/Area Number: 17K15345
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Rural environmental engineering/Planning
• Research Institution: Shimane University
• Principal Investigator: Yoshioka Hidekazu 島根大学, 学術研究院環境システム科学系, 助教 (70752161)
• Project Period (FY): 2017-04-01 – 2019-03-31
• Keywords: 魚類回遊 / アユ / 数理モデリング / 粘性解 / 有限差分法 / HJB方程式 / 確率制御理論 / 微分ゲーム

Outline of Final Research Achievements

We explored the optimality principle immanent in the diadromous fish Ayu. We firstly described the life history of the fish based on the stochastic control theory where the fish population dynamics is described with a system of stochastic differential equations. The problem ultimately reduces to solving the optimality equation, which is called Hamilton-Jacobi-Bellman (HJB) equation. We then performed mathematical and numerical analyses of the equation based on the concept of viscosity solutions (appropriate notion of solutions for the HJB equation). We also carried out the stochastic control modeling of river environmental management, focusing on Hii River, Shimane Prefecture, Japan. In addition, we could evaluate seasonal growth of Ayu in the river through field observations. We also evaluated individual difference of the fish growth in the river.

Free Research Field

生物資源科学

Academic Significance and Societal Importance of the Research Achievements

アユは，我が国における主要な内水面水産資源であるとともに，水圏生態系において欠かせない役割を担う魚種です．本研究を通し，アユの生活史や，アユを取り巻く河川環境に関する数理モデリングを大きく推進できました．いずれの課題も，これからの人間と環境の共生を考えていくうえで社会的に極めて高い重要性を有しています．とくに，HJB方程式に依拠するアユ生活史のモデリングは数理生物学的に新奇性が高く，その数理的な理解が進み，実現象への様々な示唆，および実際の水産資源管理や河川環境管理への示唆を得たことは，本研究の大きな学術的成果です．斐伊川という一河川についてですが，アユの成長を定量化できたことも貴重な成果です