Convergence of one-dimensional diffusion processes to a jump process related to population genetics.
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.
Iizuka
M
M
General Education Course, Chikushi Jogakuen Junior College, Fukuoka-ken, Japan.
Ogura
Y
Y
D005828:Genetics, Population; D008390:Markov Chains; D008957:Models, Genetic; D008962:Models, Theoretical; D009154:Mutation; D013269:Stochastic Processes; D013997:Time Factors