Date of this Version
Gandhi, Ronit. "Utilizing Markov Chains to Estimate Allele Progression through Generations." Undergraduate Honors Thesis. University of Nebraska - Lincoln. 2023.
All populations display patterns in allele frequencies over time. Some alleles cease to exist, while some grow to become the norm. These frequencies can shift or stay constant based on the conditions the population lives in. If in Hardy-Weinberg equilibrium, the allele frequencies stay constant. Most populations, however, have bias from environmental factors, sexual preferences, other organisms, etc. We propose a stochastic Markov chain model to study allele progression across generations. In such a model, the allele frequencies in the next generation depend only on the frequencies in the current one.
We use this model to track a recessive allele through successive generations of a lineage. Eventually, the allele will be “cancelled out” by the genotype of an organism becoming homozygous dominant. We estimate the number of generations it will take for this allele to be "cancelled out" by computing a hitting time in the Markov chain. This will allow us to efficiently communicate the trends of allele frequencies and estimate the speed of growth or decay of alleles.