| Project/Area Number |
16K05283
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Meiji University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | Wright-Fisher process / 確率的な揺らぎ / 空間非一様 / 分散率の進化 / 進化ゲーム理論 / Wrightの島モデル / 自然選択 / 空間非一様性 / Wright-Fisher過程 / スケール極限 / 偏微分方程式 / 応用数学一般 / 生物数学 |
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| Outline of Final Research Achievements |
As a Markov process representing biological evolution, we proposed mathematical models with islands each having different size and fecundity. Due to the finiteness of island sizes, stochastic fluctuation appears. In the limit of a large number of islands, the fluctuation is averaged in some sense, and we can mathematically analyze the evolutionary dynamics. With heterogeneous island structure, compared to the homogeneous case, evolution favors lower dispersal probability or evolutionary branching leading to increased biodiversity.
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| Academic Significance and Societal Importance of the Research Achievements |
個体数の有限性に起因する確率的な揺らぎは、ときとして進化のダイナミクスに大きな影響を与える。従来研究では、個体ベースシミュレーションによってこれらの影響が研究されてきたが、本研究ではこのようなモデルの振る舞いを数学的に明らかとしたことにより、確率的な揺らぎが進化に与える影響について、より一般的な理解を得た。
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