Applications of evolutionary game theory in select population dynamics

• Main Author: Villamin, Genrev Josiah A.
• Format: text
• Language: English
• Published: Animo Repository 2022
• Subjects: Game theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etdm_math/7; https://animorepository.dlsu.edu.ph/cgi/viewcontent.cgi?article=1006&context=etdm_math
• Institution: De La Salle University

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.