Iizuka M, Ogura Y
General Education Course, Chikushi Jogakuen Junior College, Fukuoka-ken, Japan.
J Math Biol. 1991;29(7):671-87. doi: 10.1007/BF00163918.
A conjecture on the convergence of diffusion models in population genetics to a simple Markov chain model is proved. The notion of bi-generalized diffusion processes and their limit theorems are used systematically to prove the conjecture. Three limits; strong selection-weak mutation limit, moderate selection-weak mutation limit, weak selection-weak mutation limit are considered for typical diffusion models in population genetics.
