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Research on one random assortment model of chromosome. (Chinese. English summary) Zbl 1474.92071

Summary: The divisive and genetic process of one kind of unicellular organisms is studied in this paper. According to their genetic way, a random assortment model of chromosomes based on hyper-geometric distribution is constructed. By using the properties of Markov chains, the average time and probability of the non-absorbed state being absorbed by the two absorption states are obtained. It is concluded that there are infinite stationary distributions. The biological significance of this conclusion is that no matter how many labeled chromosomes there are in the parent generation, the genetic tendency of cell division transmission is to be purified. Finally, the numerical analysis verifies the correctness of the conclusion.

MSC:

92D10 Genetics and epigenetics
60J28 Applications of continuous-time Markov processes on discrete state spaces
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