Korean J. Math.  Vol 28, No 1 (2020)  pp.1-7
DOI: https://doi.org/10.11568/kjm.2020.28.1.1

On the probability of genotypes in population genetics

Won Choi

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.


Keywords


genotype, mutation and gene conversion rate. allele.

Subject classification

92D10, 60H30, 60G44

Sponsor(s)

This research was supported by Incheon National University Research Grant, 2019-2020.

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References


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ISSN: 1976-8605 (Print), 2288-1433 (Online)

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