• Korean Journal of Mathematics
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• v.27 no.1
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• pp.1-8
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• 2019

We will deal with an n locus model in which mutation and gene conversion are taken into consideration. Also random partitions of the number n determined by chromosomes with n loci should be investigated. The diffusion process describes the time evolution of distributions of the random partitions. In this paper, we find the probability of distribution of the diffusion process with special diffusion operator $L_1$ and we show that the average probability of genes at different loci on one chromosome can be described by the rate of gene frequency of mutation and gene conversion.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.397-404
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• 2005

In this note, we characterize the limiting diffusion of a diploid model by defining the discrete generator for the resealed Markov chain. We conclude that this limiting diffusion model is with uncountable state space and mutation selection and special 'mutation or gene conversion rate'.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.1-7
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• 2020

A partition X describes that there exists α_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 $$p_{n+1}(x)=p_n(x){\sum\limits_{k=1}^{r}}q_{kx}p_n(k)$$ 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.

• Korean Journal of Poultry Science
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• v.8 no.1
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• pp.1-5
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• 1981

In trying to predict the effect of genetics on the broiler in the year 2000, this is a relatively short period of time as far as broiler genetics in concerned. Modern broiler genetics started around 1945 and tremendous gains when made in past 35 years. Futher improvements on broiler will depend on the evolution and revolution: 1. Evolution: (1) Growth rate has been made 4-5% per year. (2) Feed conversion has improved approximately 1% per year. (3) Abdominal fat is becoming a major complaint in broiler. (4) Because of the changing life-style, broiler meat sales in the future will be more and more in cut-up form. (5) Breeding for stress resistance and selection for docile temperament can be important in order to funker improve fled efficiency. (6) In female parent stock, reproduction characteristics are in many can negatively correlated with the desired broiler traits. (7) Egg production and hatchability in moot commercial parent nod m at a fairly high level. (8) In male parent stock, the heavier and mon super-meat-type male lines are desired to Product better broilers. 2. Revolution: Trying to forecast revolutionary change in broiler genetics is highly speculative, as sudden change are aften unpredictable. (1) Species hybridization, such as a turkey-chicken cross (2) Biochemical tools, such as blood typing. (3) Mutation breeding by radiation or chemical mutagentia. (4) Broiler breeding would be to change the phenotypic appearance by single gene, such as naked, wingless. (5) Changes in production techniques. such as growing in cage or growing in filtered air positive pressure houses.