Date of Publication

2022

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

Yvette F. Lim

Defense Panel Chair

Ederlina G. Nocon

Defense Panel Member

Derick Erl P. Sumalapao
Angelyn R. Lao

Abstract/Summary

Since evolutionary game theory (EGT) was initiated in the 1970s, there have only been limited applications which took into account non-linearities of natural systems. Non-linearities need to be considered since biological interactions can be highly non-linear. The inclusion of multiple players in evolutionary games is an example of introducing non-linearities. In this paper, we study Huntington’s disease and yellow mice, two cases in population genetics which follow the lethal inheritance patterns called dominant lethal and recessive lethal, respectively. By utilizing Gokhale and Traulsen’s technique, which is able to simplify multiplayer games into two-player games, we show that the case of Huntington’s disease is a direct application of Gokhale and Traulsen’s model for Mendelian inheritance, while the case of yellow mice is a special case as a result of the “discarded” recessive genotype. In each of these cases, we construct the $2 \times 4$ payoff matrix of a four-player two-strategy game and compute its entries. The average payoff of each strategy is solved to determine the equilibrium points of these games using replicator dynamics. Analyses regarding their stability are also provided in relation to the inheritance pattern of the cases mentioned. As different cases in population genetics are expected to not always have the same results, this study on the inheritance pattern of Huntington’s disease and yellow mice hopes to provide additional knowledge that may be useful for further research on EGT, population genetics, and biology.

Abstract Format

html

Language

English

Format

Electronic

Physical Description

viii, 97 leaves

Keywords

Game theory

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Embargo Period

8-11-2022

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