Mathematical modelling of seasonal migration with applications to climate change

Donohue, John G.; Piiroinen, Petri T.

doi:10.1016/j.ecolmodel.2014.12.003

Cited by 7 publications

(3 citation statements)

References 38 publications

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“…Considering the other biological scaling relationships for reproduction and mortality would enable the current model to handle migrating population dynamics of different species. Application of the current the model to predator-prey population dynamics will be feasible through considering a seasonal prey availability [77]. The current model can also be applied to population dynamics facing with environmental uncertainty [57], which can be theoretically achieved through considering the zero-sum differential game formulation [102] between the population and nature.…”

Section: Discussionmentioning

confidence: 99%

“…They are set as M 10 . We assume that the population does not migrate between the habitats in the other periods, as assumed in life cycle models of migratory population dynamics [77,78]. This assumption means that the environmental cues for migration are not available or are very weak expect during M (k) 01 and M (k) 10 .…”

Section: Basic Problem Settingmentioning

confidence: 99%

“…The present model can be seen as a stochastic counterpart of the deterministic models [77,78]. Our model has an advantage that the switching points of the life history, like migration and reproduction, are decided dynamically and naturally in a state-dependent manner.…”

Section: Remark 21mentioning

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: Discussionmentioning

confidence: 99%

Section: Basic Problem Settingmentioning

confidence: 99%