UTILIZING DISCRETE HIDDEN MARKOV MODELS TO ANALYZE TETRAPLOID PLANT BREEDING

In plant heredity, the phenotype is the result of observation that can be directly observed, while the genotype is the underlying hidden factor that underlies the expression of the phenotype. The genotype is an important aspect that needs to be understood to explain the pattern of trait inheritance and predict trait inheritance in subsequent generations. The discrete hidden Markov model is a model generated by pair of an unobserved Markov chain and an observation process. This model can be applied to tetraploid plant crosses by modeling genotypes as hidden state and phenotypes as the obeservation process. The probability of dominant phenotype in monohybrid, dihybrid and trihybrid crosses occurring over ten generations during that period is as follows 61,305%, 37,583%, and 23,041%. Furthermore, as more traits are crossed, the probability of dominant phenotype appearing within ten generations decreases. When the dominant phenotype occurs over ten generations, the same genotype can be obtained in monohybrid, dihybrid, and trihybrid crosses, which is heterozygous in the first and second generations, while from the third to the tenth generation it is homozygous dominant.