On the probability of genotypes in population genetics
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
A partition $X$ describes that there exists $\alpha_i$ kinds of alleles occurring $i$ loci for each $i$. All genes have multiple alleles, i.e., they exist in more than two allelic forms, although any one diploid organism can carry no more than two alleles. The number of possible genotypes in a multiple allel series depends on the number of alleles. We will deal with an $n$ locus model in which mutation and gene conversion are taken into consideration. In this paper, we firstly find the probability $p_n (x)$ of genotype $$ p_{n+1} (x)= p_n (x) \sum_{k=1}^r q_{kx} p_n (k) $$ with the rates of mutation and gene conversion. Also we find the probability of genotype without the rates of mutation and gene conversion and we apply this probability to two examples.
Abstract
A partition $X$ describes that there exists $\alpha_i$ kinds of alleles occurring $i$ loci for each $i$. All genes have multiple alleles, i.e., they exist in more than two allelic forms, although any one diploid organism can carry no more than two alleles. The number of possible genotypes in a multiple allel series depends on the number of alleles. We will deal with an $n$ locus model in which mutation and gene conversion are taken into consideration. In this paper, we firstly find the probability $p_n (x)$ of genotype $$ p_{n+1} (x)= p_n (x) \sum_{k=1}^r q_{kx} p_n (k) $$ with the rates of mutation and gene conversion. Also we find the probability of genotype without the rates of mutation and gene conversion and we apply this probability to two examples.
참고문헌 (5)
- Francisco J.Ayala, "Population and Evolutionary Genetics; A Primer", pp.1982, The Ben-jamin
- 최원, "The application of stochastic analysis to population genetics model", Journal of Applied Mathematics and Informatics, 23(1-2), pp.455~460 (2007), 한국전산응용수학회
- M.Kimura, "The number of alleles that can be maintained in a nite population", Genetics, 49 (1964)
- T. Ohta, "On the evolution of multigene families", Theor. Por. Biol, 23, pp.216~240 (1983)
- A.Shimizu, "Stationary distribution of a diffusion process taking values in proba-bility distributions on the partitions", Proceeding of a Workshop held in Nagoya (1985)