A stochastic differential game approach toward animal migration

Yoshioka, Hidekazu

doi:10.1007/s12064-019-00292-4

Cited by 6 publications

(22 citation statements)

References 133 publications

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“…In our model, the population dynamics are described with stochastic differential equations (SDEs) [45]. We show that a life cycle of single species, which involves growth, reproduction, and migration of population, can be reasonably described with the stochastic optimal switching, unifying the previous models for a migration event as only a part of life history [57,58]. We demonstrate that finding the optimal migration strategy with the present model reduces to solving an HJB equation, the optimality equation, of the quasi-variational form.…”

Section: Introductionmentioning

confidence: 76%

“…Figure 1 is a conceptual diagram of the population dynamics considered in this paper. Each migration event is assumed to occur within a much shorter time-scale than that of the whole life history [57,58] and is therefore considered to be impulsive. Partial migration that only a part of population migrates [74] is not considered in this paper.…”

Section: Basic Problem Settingmentioning

confidence: 99%

“…The population dynamics is described with the total population N t ≥ 0 and the representative body weight 0 ≤ X t ≤ K following the previous research [57,58], where K > 0 is the maximum body weight. This description of the population change is biologically justified if N t >> 1, which is the hereafter assumed.…”

Section: Population Dynamicsmentioning

confidence: 99%

“…A similar objective function has been used for population dynamics of fish migration in Omori et al [89]. The objective function ( 6) is mathematically simpler than those of the previous models [57,58] in the sense that the cumulated profits gained in the population are not involved. There are at least three reasons of omitting these terms.…”

Section: Objective Functionmentioning

confidence: 99%

“…Conventional models of the SDP type sometimes have many variables in return for versatility and are not always easy to analyse in detail. On the other hand, models based on HJB and related equations are more efficient and have been effectively applied to migrating population dynamics especially those occurring in water bodies, like diel fish migration [55], diel migration driven by predator-prey interactions [56], and seasonal fish migration [57,58]. Models based on HJB equations can potentially serve as efficient mathematical tools for analysing life cycle of species to which conventional optimization models have been applied [59,60].…”

Section: Introductionmentioning

confidence: 99%

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Stochastic optimal switching model for migrating population dynamics

Yoshioka

Tanaka

Aranishi

et al. 2019

Journal of Biological Dynamics

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An optimal switching control formalism combined with the stochastic dynamic programming is, for the first time, applied to modelling life cycle of migrating population dynamics with non-overlapping generations. The migration behaviour between habitats is efficiently described as impulsive switching based on stochastic differential equations, which is a new standpoint for modelling the biological phenomenon. The population dynamics is assumed to occur so that the reproductive success is maximized under an expectation. Finding the optimal migration strategy ultimately reduces to solving an optimality equation of the quasi-variational type. We show an effective linkage between our optimality equation and the basic reproduction number. Our model is applied to numerical computation of optimal migration strategy and basic reproduction number of an amphidromous fish Plecoglossus altivelis altivelis in Japan as a target species.

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Section: Introductionmentioning

confidence: 76%

Section: Basic Problem Settingmentioning

confidence: 99%

Section: Population Dynamicsmentioning

confidence: 99%

Section: Objective Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic optimal switching model for migrating population dynamics

Yoshioka

Tanaka

Aranishi

et al. 2019

Journal of Biological Dynamics

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Effects of water currents on fish migration through a Feynman-type path integral approach under $$\sqrt{8/3}$$ Liouville-like quantum gravity surfaces

Pramanik

2021

Theory Biosci.

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A stochastic differential game theoretic model has been proposed to determine optimal behavior of a fish while migrating against water currents both in rivers and oceans. Then, a dynamic objective function is maximized subject to two stochastic dynamics, one represents its location and another its relative velocity against water currents. In relative velocity stochastic dynamics, a Cucker-Smale type stochastic differential equation is introduced under white noise. As the information regarding hydrodynamic environment is incomplete and imperfect, a Feynman type path integral under √ 8∕3 Liouville-like quantum gravity surface has been introduced to obtain a Wick-rotated Schrödinger type equation to determine an optimal strategy of a fish during its migration. The advantage of having Feynman type path integral is that, it can be used in more generalized nonlinear stochastic differential equations where constructing a Hamiltonian-Jacobi-Bellman (HJB) equation is impossible. The mathematical analytic results show exact expression of an optimal strategy of a fish under imperfect information and uncertainty.

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Optimization of a dynamic profit function using Euclidean path integral

Pramanik,

Polansky

2023

SN Bus Econ

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A stochastic differential game approach toward animal migration

Cited by 6 publications

References 133 publications

Stochastic optimal switching model for migrating population dynamics

Stochastic optimal switching model for migrating population dynamics

Effects of water currents on fish migration through a Feynman-type path integral approach under $$\sqrt{8/3}$$ Liouville-like quantum gravity surfaces

Optimization of a dynamic profit function using Euclidean path integral

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