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On the probability of genotypes in population genetics
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논문 기본 정보

Type
Academic journal
Author
Journal
Korean Journal of mathematics 한국수학논문집 한국수학논문집 제28권 제1호 KCI Accredited Journals
Published
2020.1
Pages
1 - 7 (7page)

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On the probability of genotypes in population genetics
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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.

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