Application of Stochastic Control Theory to Biophysics of Fish Migration Around a Weir Equipped with Fishways

Appl Stoch Models Bus & Ind

Yaegashi

2017

Self Cite

Establishment of cost-effective management strategy of aquaculture is one of the most important issues in fishery science, which can be addressed with bio-economic mathematical modeling. This paper deals with the aforementioned issue using a stochastic process model for aquacultured non-renewable fishery resources from the viewpoint of an optimal stopping (timing) problem. The goal of operating the model is to find the optimal criteria to start harvesting the resources under stochastic environment, which turns out to be determined from the Bellman equation (BE). The BE has a separation of variables type structure and can be simplified to a reduced BE with a fewer degrees of freedom. Dependence of solutions to the original and reduced BEs on parameters and independent variables is analyzed from both analytical and numerical standpoints. Implications of the analysis results to management of aquaculture systems are presented as well. Numerical simulation focusing on aquacultured Plecoglossus altivelis in Japan validates the mathematical analysis results. Bus. Ind. 2017, 33 476-493 The quantity W * is related to Ψ that solves the reduced BE (12), and therefore, Ψ and W * have to be simultaneously solved. The curve C is therefore a free boundary. Assuming the unique existence of such C, the one-dimensional domain 0 < w < +∞ for each t < T can be separated into the two regions: the waiting region S 1 (t) = {w; Ψ (t, w) > w} and the Appl. Stochastic Models Bus. Ind. 2017, 33 476-493 Appl. Stochastic ModelsProof of Proposition 3.3 J ,t with p = ( p) i (i = 1, 2) is denoted as J ,t,i . For each ∈ t,T , the inequalitydirectly follows from (5). This leads to

Section: Applicationmentioning

confidence: 99%

Optimization model to start harvesting in stochastic aquaculture system

Appl Stoch Models Bus & Ind

Yaegashi

2017

Self Cite

“…Such a situation is more realistic than that considered in this paper. We mention that the present model can serve as the basis of analyzing fish migration in the real open channels if it is effectively incorporated in that for the recently developed mathematical models based on the dynamic programming principle (Yoshioka 2016;Yoshioka et al 2016b). This research topic is beyond the scope of this paper and will, therefore, be addressed elsewhere.…”

Section: Mathematical Modelsmentioning

confidence: 99%

A simple game-theoretic model for upstream fish migration

2017

Theory Biosci.

Self Cite

A simple game-theoretic model for upstream fish migration, which is a key element in life history of diadromous fishes, is proposed. Foundation of the model is a minimization problem on the cost of migration with the swimming speed and school size as the variables to be simultaneously optimized. Finding the optimizer ultimately reduces to solving a self-consistency equation without explicit solutions. Mathematical analytical results lead to the sufficient condition that the self-consistency equation has a unique solution, which turns out to be identified with the condition where the unique optimizer exists. Behavior of the optimizer is analyzed both mathematically and numerically to show its biophysical and ecological consequences. The analytical results demonstrate reasonable agreement between the present mathematical model and the theoretical and experimental results of upstream migration of fish schools reported in the past research.

An optimal stopping approach for onset of fish migration

Yaegashi

2018

Theory Biosci.

Comprehending life history of migratory fish, onset of migration in particular, is a key biological and ecological research topic that still has not been clarified. In this paper, we propose a simple mathematical model for the onset of fish migration in the context of a stochastic optimal stopping theory, which is a new attempt to our knowledge. Finding the criteria of the onset of migration reduces to solving a variational inequality of a degenerate elliptic type. As a first step of the new mathematical modeling, mathematical and numerical analyses with particular emphasis on whether the model is consistent with the past observation results of fish migration are examined, demonstrating reasonable agreement between the theory and observation results. The present mathematical model thus potentially serves as a simple basis for analyzing onset of fish migration.