Stochastic analysis on models of population genetics

• 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
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,230,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
• 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 / マルコフ過程 / 出生死滅過程 / 自然淘汰 / 遺伝的浮動 / 互助的突然変異 / 一般化拡散過程 / 極限分布 / 確率的自然淘汰

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] Compensatory evolution in diploid populations (2008)
  • Author(s): M. Ichinose
  • Journal Title: Theoretical Population Biology 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] Conditional distributions which do not satisfy the Chapman-Kolmogorov equation (2007)
  • Author(s): Iizuka, M.
  • Journal Title: Journal of the Mathematical Society of Japan 59 Pages: 971-983
  • NAID: 10019989225
  • 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
  • NAID: 120005366085
  • Peer Reviewed
• [Journal Article] Asymptotic conditional distributions related to one-dimensional generalized diffusion processes (2006)
  • Author(s): Iizuka, M., Maeno, M., Tomisaki, M.
  • Journal Title: Tsukuba Journal of Mathematics 30 Pages: 273-327
  • NAID: 120005366085
• [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] Models of compensatory molecular evolution (2008)
  • Author(s): Iizuka, M., Ichinose, M., Kado, T., Takefu, M.
  • Organizer: 第20回国際遺伝学会議(The XXth International Congress of Genetics at Berlin)
  • Place of Presentation: ベルリン国際会議センタ
  • 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