Mathematical analysis of Markov-process models of biological evolution

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K05283
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Meiji University
• Principal Investigator: Wakano Joe Yuichiro 明治大学, 総合数理学部, 専任教授 (10376551)
• Project Period (FY): 2016-04-01 – 2020-03-31
• 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

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.

Free Research Field

数理生物学

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。