TY - JOUR

T1 - Mathematical Modelling of Metapopulation Dynamics

T2 - Revisiting its Meaning

AU - Seno, H.

N1 - Funding Information:
The author greatly appreciates the valuable discussions of Kazunori Sato, Shizuoka University, and Yasuhisa Saito, Shimane University, about this research subject. Besides the author is much grateful to the referees and the associate editor for their valuable comments to complete the manuscript.
Publisher Copyright:
© 2016 EDP Sciences.

PY - 2016

Y1 - 2016

N2 - In this paper, we revisit the metapopulation dynamics model of typical Levins type, and reconsider its mathematical modeling. For the metapopulation dynamics with three states for the patch of a habitat composed of a number patches available for the reproduction, 'vacant', 'small' (i.e., threatened to the extinction) and 'large' (i.e., far from the extinction risk) in terms of population size in the patch, we reconstruct the mathematical model in a general form, making use of the difference in time scale between the state transition and the dispersal of individuals within the patchy habitat. The typical Levins type of metapopulation dynamics model appears only for a specific case with some additional assumptions for mathematical simplification. Especially we discuss the rationality of mass-action terms for the patch state transition in the Levins model, and find that such mass-action term could be rational for the modeling of metapopulation dynamics only in some ideal condition.

AB - In this paper, we revisit the metapopulation dynamics model of typical Levins type, and reconsider its mathematical modeling. For the metapopulation dynamics with three states for the patch of a habitat composed of a number patches available for the reproduction, 'vacant', 'small' (i.e., threatened to the extinction) and 'large' (i.e., far from the extinction risk) in terms of population size in the patch, we reconstruct the mathematical model in a general form, making use of the difference in time scale between the state transition and the dispersal of individuals within the patchy habitat. The typical Levins type of metapopulation dynamics model appears only for a specific case with some additional assumptions for mathematical simplification. Especially we discuss the rationality of mass-action terms for the patch state transition in the Levins model, and find that such mass-action term could be rational for the modeling of metapopulation dynamics only in some ideal condition.

KW - Mathematical modeling

KW - Metapopulation dynamics

KW - Quasi-stationary state approximation

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U2 - 10.1051/mmnp/201611404

DO - 10.1051/mmnp/201611404

M3 - Review article

AN - SCOPUS:84979271483

VL - 11

SP - 34

EP - 46

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

SN - 0973-5348

IS - 4

ER -