Stochastic analysis on models of population genetics

2008 Fiscal Year Final Research Report

• Project/Area Number: 18540137
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyushu Dental College
• Principal Investigator: IIZUKA Masaru Kyushu Dental College, 歯学部, 准教授 (20202830)
• Project Period (FY): 2006 – 2008
• Keywords: 確率過程 / 拡散過程 / 集団遺伝学 / 分子進化 / 確率モデル / 拡散モデル

Research Abstract

生物集団の進化機構の解明を目的とする集団遺伝学では、多くの数理モデルが様々な確率過程を用いて記述される。本研究では、確率過程論的方法、コンピュータ・シミュレーション、有限要素法を用いた偏微分方程式の数値解析を併用して集団遺伝学における幾つかの確率モデル(拡散モデルやマルコフ連鎖モデルなど)に関する諸性質(突然変異体が進化する条件、個体数の確率的変動の効果、モデルを記述する確率過程の極限分布の性質など)の研究を行った。

Research Products

• [Journal Article] Compensatory evolution in diploid populations (2008)
  • Author(s): Motoshi Ichinose, Masaru Iizuka, Tomoyuki Kado and Masasuke Takefu
  • Journal Title: Theoretical Population Biology vol.74 Pages: 199-207
  • Peer Reviewed
• [Journal Article] Tomisaki, Conditional distributions which do not satisfy the Chapman-Kolmogorov equation (2007)
  • Author(s): Masaru Iizuka, Miyuki Maeno. and Matsuyo Tomisaki
  • Journal Title: Journal of the Mathematical Society of Japan vol.59 Pages: 971-983
  • Peer Reviewed
• [Journal Article] Asymptotic conditional distributions related to one-dimensional generalized diffusion processes (2006)
  • Author(s): Masaru Iizuka, Miyuki Maeno. and Matsuyo Tomisaki
  • Journal Title: Tsukuba Journal of Mathematics vol.30 Pages: 273-327
  • Peer Reviewed
• [Presentation] Models of Compensatory Molecular Evolution (2008)
  • Author(s): Masaru Iizuka, Motoshi Ichinose, Tomoyuki Kado and Masasuke Takefu
  • Organizer: The XXth International Congress of Genetics
  • Place of Presentation: International Congress Centrum(Berlin)
  • Year and Date: 2008-07-14
• [Presentation] Compensatory Fitness Interaction in Molecular Evolution (2006)
  • Author(s): Masaru Iizuka, Motoshi, Ichinose, Tomoyuki Kado and Masasuke Takefu
  • Organizer: Japanese-Korean Joint Meeting for Mathematical Biology
  • Place of Presentation: Kyushu University(Fukuoka)
  • Year and Date: 2006-09-16