Mathematics, Department of

 

Date of this Version

5-2015

Citation

Published as: B. Deng, B. Hinds, E.N. Moriyama and X. Zheng, ``Bioinformatic Game Theory and Its Application to Biological Affinity Networks,'' Applied Mathematics, Vol. 4, pp. 92-108, 2013.

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professors Bo Deng and Etsuko Moriyama. Lincoln, Nebraska: May, 2015

Copyright (c) 2015 Brittney Nicole Keel

Abstract

The exact evolutionary history of any set of biological sequences is unknown, and all phylogenetic reconstructions are approximations. The problem becomes harder when one must consider a mix of vertical and lateral phylogenetic signals. In this dissertation we propose a game-theoretic approach to clustering biological sequences and analyzing their evolutionary histories. In this context we use the term evolution as a broad descriptor for the entire set of mechanisms driving the inherited characteristics of a population. The key assumption in our development is that evolution tries to accommodate the competing forces of selection, of which the conservation force seeks to pass on successful structures and functions from one generation to the next, while the diversity force seeks to maintain variations that provide sources of novel structures and functions. One branch of the mathematical theory of games is brought to bear. It translates this evolutionary game hypothesis into a mathematical model in two-player zero-sum games, with the zero-sum assumption conforming to one of the fundamental constraints in nature in mass and energy conservation. We demonstrate why and how a mechanistic and localized adaptation to seek out greater information for conservation and diversity may always lead to a global Nash equilibrium in phylogenetic similarity.

Advisers: Bo Deng and Etsuko Moriyama