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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
I Gusti Putu Purnaba
Mathematics Department, IPB University, Indonesia
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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THE APPLICATION OF DISCRETE HIDDEN MARKOV MODEL ON CROSSES OF DIPLOID PLANT Nahrul Hayati; Berlian Setiawaty; I Gusti Putu Purnaba
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 3 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss3pp1449-1462

Abstract

The hidden Markov model consists of a pair of an unobserved Markov chain {Xk} and an observation process {Yk}. In this research, the crosses of diploid plant apply the model. The Markov chain {Xk} represents genetic structure, which is genotype of the kth generation of an organism. The observation process represents the appearance or the observed trait, which is the phenotype of the generation of an organism. Since it is unlikely to observe the genetic structure directly, the Hidden Markov model can be used to model pairs of events and unobservable their causes. Forming the model requires the use of the theory of heredity from Mendel. This model can be used to explain the characteristic of true breeding on crosses of diploid plants. The more traits crossed, the smaller probability of plants having a dominant phenotype in that period. Monohybrid, dihybrid, and trihybrid crosses have a dominant phenotype probability of 99% in the seventh, eighth, and ninth generations, with the condition of previous generations having a dominant phenotype. But in seventh generation, monohybrid crosses only have the probability of an optimal genotype of 50%, dihybrid crosses have a probability of an optimal genotype of 25% in the eighth generation, and trihybrid crosses have a probability of an optimal genotype of 12.5% in the ninth generation
Co-Authors Berlian Setiawaty Nahrul Hayati