Philippine Journal of Science
152 (5): 1527-1538, October 2023
ISSN 0031 – 7683
Date Received: 14 Jul 2022

Inheritance Pattern of Huntington’s Disease,
a Multiplayer Game

Yvette Fajardo-Lim* and Genrev Josiah Villamin

Department of Mathematics and Statistics, De La Salle University,
Manila 1004 Philippines

*Corresponding author: yvette.lim@dlsu.edu.ph

[Download]
Fajardo-Lim Y, Villamin GJ. 2023. Inheritance Pattern of Huntington’s
Disease, a Multiplayer Game. Philipp J Sci 152(5): 1527–1538.
https://doi.org/10.56899/152.05.01

 

ABSTRACT

Evolutionary game theory (EGT) is one of several major developments of game theory. EGT covers ecology and population genetics, among other fields in biology. Most studies in EGT were on a two-player game but non-linearities in biology often occur that need to be considered. Huntington’s disease (HD), named after the person who wrote the first detailed description of the disease in 1872, is a neurodegenerative disease that is inherited. This is a case in population genetics, which follows the inheritance pattern called the dominant lethal. In this study, we presented this disease as a multiplayer game among the alleles of the HD gene. We utilized Gokhale and Traulsen’s model, wherein a payoff matrix for a four-player game was reduced into a payoff matrix for a two-player game. Depending on the fitness values of each genotype, we have determined that populations consisting of both Huntington and normal alleles may converge to either a purely Huntington, a purely normal, or a mixed composition where both types of genes coexist. If the normal genotype produces more surviving offspring than the other genotypes, then even if a small frequency of normal alleles is injected into a purely Huntington population, the population will be replaced by the normal genotype over time. Such a result was obtained using replicator dynamics and analysis of the stability of equilibrium points. Similar analyses on other genotypes were provided in relation to the inheritance pattern of HD.