Mathematics of coalescent gene trees
Keywords:
Gene Tree, Coalescence, Lineages, Balanced Gene Tree, Ranked Gene TreesAbstract
Using the coalescent process continuously until all the lineages have become one, we get different possible gene trees. In this paper I had computed the probabilities of such different gene trees that occur depending on the way lineages can form. In particular I had shown the probability of any 3 sample gene tree is 1/3 and for four samples resembling caterpillar gene trees the probability is 1/18 and probability for any balanced gene tree with 4 samples is 1/9. I have also proved a theorem providing the number of ranked gene trees. This estimate will help us to determine the probability of any gene tree.
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R. Sivaraman, On Metric and Ultrametric Trees, European Journal of Molecular and Clinical Medicine, Volume 7, Issue 8, 2611 – 2615, 2020.
John Wakeley, Coalescent Theory: An Introduction, Roberts and Company, Greenwood Village, Colorado, 2009.
Michael S. Waterman, Introduction to Computational Biology: Maps, Sequences and Genomes, Chapman and Hall, London, 1995.
Elizabeth S. Allman and John A. Rhodes, Mathematical Models in Biology: An Introduction, Cambridge University Press, Cambridge, 2004.
L. Knowles and L. Kubatko, Estimating Species Trees: Practical and Theoretical Aspects, Wiley-Blackwell, College Station, Texas, 2010.
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