2E-05 On an approximate formula for the distribution of 2-locus 2-allele model

• Published in: Genes & Genetic Systems Vol. 86; no. 6; p. 429
• Main Author: MIURA Chiaki
• Format: Journal Article
• Language: Japanese
• Published: The Genetics Society of Japan 2011
• ISSN: 1341-7568

Many theoretical values of population genetics statistics has been obtained by using the diffusion method and calculating the distribution of the gene frequency analytically. Even after the advent of the gene genealogy, the research of the diffusion method doesn't lose the importance because some statistics can be obtained rather to use the diffusion method according to the model. In the field of the probability theory, On the other hand, the theory that guarantees the asymptotic expansion along the Brownian motion for the diffusion process with a strong solution has been progressed. It enabled the asymptotic expansion of the density function of a concrete higher dimensional diffusion process. This time, an asymptotic approximation of the density function of 2-allele 2-lous model was obtained as a 3-dimentional normal distribution by invoking this theory. It was shown by comparing with simulations that this approximate formula gives a good approximation when mutation rates are high.