Mathematical and numerical modeling for migration of Plecoglossus altivelis considering uncertainties

• Project/Area Number: 15H06417
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Rural environmental engineering/Planning
• Research Institution: Shimane University
• Principal Investigator: Yoshioka Hidekazu 島根大学, 生物資源科学部, 助教 (70752161)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: アユ / 回遊 / 最適制御理論 / ハミルトン・ヤコビ・ベルマン方程式 / 粘性解 / 斐伊川 / 魚群回遊 / 遡上 / 動的計画原理 / HJB方程式 / 有限要素法 / 魚類回遊 / 生物物理学 / 確率制御理論 / 河川水系 / 回遊魚 / 河川回遊 / 内水面漁業 / 非線型偏微分方程式系 / 有限体積法

Outline of Final Research Achievements

We developed a new mathematical model for describing fish migration along 1-D rivers or connected graphs based on the optimal control theory. We showed that the derivation of the migration strategy reduces to finding a solution to a Hamilton-Jacobi-Bellman equation: a nonlinear degenerate parabolic partial differential equation. We also showed that the equation admits a viscosity solution and discussed its practical implications. Accurate numerical schemes for stable computation of the HJB equation has also been developed in the project. In addition, macroscopic mathematical models for population dynamics of Plecoglossus altivelis (Ayu) in river environment was established and applied to finding cost-effective management of the fish population.

Research Products

• [Journal Article] Cost-minimizing upstream migration strategy of isolated and schooling fishes in 1-D open channel flows (2017)
  • Author(s): Yoshioka H., Shirai T., and Tagami D.
  • Journal Title: 土木学会論文集B1 Volume: 73
  • NAID: 130006406205
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 1次元局所慣性方程式に対する摩擦項を考慮した数値安定性解析 (2017)
  • Author(s): 田中 智大，吉岡 秀和，木村 匡臣，山崎 大
  • Journal Title: 土木学会論文集B1 Volume: 73
  • NAID: 130006406281
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Optimization model to start harvesting in stochastic aquaculture system (2017)
  • Author(s): Yoshioka H. and Yaegashi Y.
  • Journal Title: Applied Stochastic Models in Business and Industry Volume: in press Issue: 5 Pages: 1-18
  • DOI: 10.1002/asmb.2250
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] An optimal management strategy for stochastic population dynamics of released Plecoglossus altivelis in rivers (2017)
  • Author(s): Yaegashi Y., Yoshioka H., Unami K., and Fujihara M.
  • Journal Title: International Journal of Modeling, Simulation, and Scientific Computing Volume: 8, No.1750039 Issue: 02 Pages: 1-16
  • DOI: 10.1142/s1793962317500398
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Numerical simulation of a Hamilton-Jacobi-Bellman equation for optimal management strategy of released Plecoglossus altivelis in river systems (2016)
  • Author(s): Yaegashi Y, Yoshioka H, Unami K, Fujihara M
  • Journal Title: Communications in Computer and Information Science Volume: 603 Pages: 91-101
  • DOI: 10.1007/978-981-10-2158-9_8
  • ISBN: 9789811021572, 9789811021589
  • Peer Reviewed
• [Journal Article] Application of stochastic control theory to biophysics of fish migration around a weir equipped with fishways (2016)
  • Author(s): Yoshioka H, Yaegashi Y, Unami K, Fujihara M
  • Journal Title: Communications in Computer and Information Science Volume: 645 Pages: 190-200
  • DOI: 10.1007/978-981-10-2669-0_21
  • ISBN: 9789811026683, 9789811026690
  • Peer Reviewed
• [Journal Article] Mathematical analysis and validation of an exactly solvable model for upstream migration of fish schools in one-dimensional rivers (2016)
  • Author(s): Yoshioka H.
  • Journal Title: Mathematical Biosciences Volume: 281 Pages: 69-84
  • DOI: 10.1016/j.mbs.2016.09.014
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Finding the optimal opening time of harvesting farmed fishery resources (2016)
  • Author(s): Yoshioka H. and Yaegashi Y.
  • Journal Title: Pacific Journal of Mathematics for Industry Volume: 8(6) Issue: 1 Pages: 1-6
  • DOI: 10.1186/s40736-016-0025-9
  • NAID: 40021103709
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 斐伊川中流域における内水面漁業の現状とその展望 (2016)
  • Author(s): 吉岡 秀和，吉井 傅，八重樫 優太
  • Journal Title: 島根大学生物資源科学部研究報告 Volume: 21 Pages: 23-28
  • NAID: 120005853190
  • Acknowledgement Compliant
• [Journal Article] Identifying the cost function for upstream migration of individual fishes in 1-D open channels based on an optimal control theory (2016)
  • Author(s): Yoshioka H., Yaegashi Y., Unami K., and Fujihara M.
  • Journal Title: 土木学会論文集B1分冊 (水工学特集号) Volume: 72
  • NAID: 130005311929
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Optimal strategies for harvesting and predator extermination to sustain Plecoglossus altivelis (Ayu) population in stochastic river environment (2016)
  • Author(s): Yaegashi Y., Yoshioka H., Unami K., and Fujihara M.
  • Journal Title: Journal of Rainwater Catchment Systems Volume: 未定
  • NAID: 130007687907
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Stochastic control of fishery resources using dynamical models for local behaviour and global population (邦題：局所的行動と大域的個体群の動態モデルを用いた水産資源の確率制御) (2016)
  • Author(s): Yoshioka H., Yaegashi Y., Unami K., and Fujihara M.
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 未定
  • Acknowledgement Compliant
• [Journal Article] Numerical comparison of shallow water models in multiply connected open channel networks (2015)
  • Author(s): Yoshioka H., Unami K., and Fujihara M.
  • Journal Title: Journal of Advanced Simulation in Science and Engineering Volume: 2 Issue: 2 Pages: 271-291
  • DOI: 10.15748/jasse.2.271
  • NAID: 130005108388
  • ISSN: 2188-5303
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A Petrov-Galerkin Finite Element Scheme for 1-D Time-independent Hamilton-Jacobi-Bellman Equations (2015)
  • Author(s): Yoshioka H., Unami K., and Fujihara M.
  • Journal Title: Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)) Volume: 71 Issue: 2 Pages: I_149-I_160
  • DOI: 10.2208/jscejam.71.I_149
  • NAID: 130005128869
  • ISSN: 2185-4661
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] 捕食者の最適駆除戦略に関する特異確率制御問題の厳密解と数値解析 (2017)
  • Author(s): 八重樫 優太, 吉岡 秀和, 宇波 耕一, 藤原 正幸
  • Organizer: 日本応用数理学会環瀬戸内応用数理研究部会第20回シンポジウム
  • Place of Presentation: 呉市海事歴史科学館
• [Presentation] 魚類の河川遡上に関連した，ある最適化問題の数学解析と数値計算 (2017)
  • Author(s): 吉岡 秀和, 白井 朋之, 田上 大助
  • Organizer: 日本応用数理学会環瀬戸内応用数理研究部会第20回シンポジウム
  • Place of Presentation: 呉市海事歴史科学館
• [Presentation] 河床付着藻類の繁茂抑制策を見出すための確率制御問題 (2017)
  • Author(s): 吉岡 秀和, 八重樫 優太
  • Organizer: 島根大学生物資源科学部研究シーズによる地域活性化と人材育成、地域企業とのコラボ
  • Place of Presentation: 島根県民会館
• [Presentation] カワウ捕食圧下における放流アユ個体群の最適管理戦略 (2016)
  • Author(s): 八重樫 優太, 吉岡 秀和, 宇波 耕一, 藤原 正幸
  • Organizer: 第73回農業農村工学会京都支部講演会
  • Place of Presentation: 大阪リバーサイドホテル
  • Year and Date: 2016-11-16
• [Presentation] Optimal installation of overhead lines preventing piscivorous birds in stochastic river environment (2016)
  • Author(s): Yaegashi H., Yoshioka H., Unami K., Fujihara M.
  • Organizer: 第24回日本雨水資源化システム学会大会研究発表会
  • Place of Presentation: 京都大学
  • Year and Date: 2016-10-29
• [Presentation] Optimal installation of overhead lines with decaying protection effect for fish from predators (2016)
  • Author(s): Yoshioka H., Yaegashi H., Unami K., Fujihara M.
  • Organizer: 第24回日本雨水資源化システム学会大会研究発表会
  • Place of Presentation: 京都大学
  • Year and Date: 2016-10-29
• [Presentation] A stochastic control model for optimal management strategy of released Plecoglossus altivelis in river environment based on a pure death process (2016)
  • Author(s): Yaegashi Y., Yoshioka H., Unami K., and Fujihara M.
  • Organizer: AsiaSim/SCS Autumn Sim 2016
  • Place of Presentation: Beijing, China
  • Year and Date: 2016-10-08
  • Int'l Joint Research
• [Presentation] 放流された内水面水産資源の最適管理戦略に関する数学解析 (2016)
  • Author(s): 吉岡 秀和, 八重樫 優太
  • Organizer: 平成28年度応用数理学会年会
  • Place of Presentation: 福岡県北九州市北九州国際会議場
  • Year and Date: 2016-09-12
• [Presentation] アユを魚食性鳥類から守るための最も経済的なテグス張り戦略 (2016)
  • Author(s): 八重樫 優太, 吉岡 秀和, 宇波 耕一, 藤原 正幸
  • Organizer: 平成28年度応用数理学会年会
  • Place of Presentation: 福岡県北九州市北九州国際会議場
  • Year and Date: 2016-09-12
• [Presentation] 養殖水産資源に対する最適漁獲開始時刻の支配方程式 (2016)
  • Author(s): 吉岡 秀和, 八重樫 優太, 次橋 健太郎
  • Organizer: 平成28年度応用数理学会年会
  • Place of Presentation: 福岡県北九州市北九州国際会議場
  • Year and Date: 2016-09-12
• [Presentation] Mathematical modeling and numerical analysis of a nonlinear degenerate elliptic equation for upstream fish migration in rivers (2016)
  • Author(s): Yoshioka H., Tagami D., Shirai T., and Yaegashi Y.
  • Organizer: 第21回計算工学講演会
  • Place of Presentation: 新潟県新潟市朱鷺メッセ
  • Year and Date: 2016-05-31
• [Presentation] Finite element solution of a stochastic control model for optimal population management strategy of released Plecoglossus altivelis (2016)
  • Author(s): Yaegashi Y., Yoshioka H., Takagi K., Unami K., and Fujihara M.
  • Organizer: 第21回計算工学講演会
  • Place of Presentation: 新潟県新潟市朱鷺メッセ
  • Year and Date: 2016-05-31
• [Presentation] 放流アユの最適管理戦略に関する有限要素解析 (2016)
  • Author(s): 八重樫 優太, 吉岡 秀和, 宇波 耕一, 藤原 正幸
  • Organizer: 京都大学計算科学ユニット若手研究交流会
  • Place of Presentation: 京都大学
  • Year and Date: 2016-03-09
• [Presentation] 地域を取り巻く自然・社会科学的な事象の数理・数値モデリング (2016)
  • Author(s): 吉岡秀和
  • Organizer: 平成27年度島根大学若手研究員に対する支援研究成果報告会
  • Place of Presentation: 島根大学
  • Year and Date: 2016-03-08
• [Presentation] 斐伊川水系における水・物質輸送動態 と魚類回遊の評価および予測 (2016)
  • Author(s): 吉岡 秀和, 八重樫 優太, 宇波 耕一, 藤原 正幸
  • Organizer: 平成27年度島根大学ミッション成果報告会
  • Place of Presentation: くにびきメッセ
  • Year and Date: 2016-02-26
• [Presentation] Mathematical analysis of a primitive dynamic programming problem for water reservoirs (貯水池運用の単純な動的計画問題に対する数学解析) (2016)
  • Author(s): 藤倉 大和, 吉岡 秀和, 宇波 耕一, 藤原 正幸
  • Organizer: 平成28年度農業農村工学会応用水理研究部会
  • Place of Presentation: 岐阜市文化センター
• [Presentation] On analytical viscosity solution to a 1-D Hamilton-Jacobi-Bellman equation for upstream migration of individual fishes in rivers (2015)
  • Author(s): Yoshioka H. and Shirai T.
  • Organizer: EMAC2015
  • Place of Presentation: Adelaide, Australia
  • Year and Date: 2015-12-06
  • Int'l Joint Research
• [Presentation] 内水面漁業におけるカワウ食害の一変数確率制御モデル, (2015)
  • Author(s): 八重樫 優太, 吉岡 秀和, 宇波 耕一, 藤原 正幸
  • Organizer: 第72回農業農村工学会京都支部講演会
  • Place of Presentation: ピアザ淡海
  • Year and Date: 2015-11-19
• [Presentation] Numerical simulation on optimal countermeasure for feeding damage by great cormorant to inland fisheries based on stochastic control theory (2015)
  • Author(s): Yaegashi Y., Yoshioka H., Unami K., and Fujihara M.
  • Organizer: AsiaSim2015
  • Place of Presentation: Jeju, Korea
  • Year and Date: 2015-11-04
  • Int'l Joint Research
• [Presentation] Optimal migration strategy of individual fishes to minimize the swimming cost based on a monomial function (邦題：単項式関数に基づく遊泳コストを最小化する魚類個体の最適回遊戦略) (2015)
  • Author(s): Yoshioka H., Yaegashi Y., Unami K., and Fujihara M.
  • Organizer: 第23回日本雨水資源化システム学会大会研究発表会
  • Place of Presentation: 桜華会館
  • Year and Date: 2015-10-31
• [Presentation] 魚類遡上を記述する1次元ハミルトン・ヤコビ・ベルマン方程式 (2015)
  • Author(s): 吉岡 秀和, 宇波 耕一, 藤原 正幸
  • Organizer: 日本応用数理学会2015年度年会
  • Place of Presentation: 金沢大学
  • Year and Date: 2015-09-09