Inheritance Pattern of Huntington’s Disease, a Multiplayer Game

Abstract

Evolutionary game theory (EGT) is one of several major developments of game theory. EGTcovers ecology and population genetics, among other fields in biology. Most studies in EGTwere 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 ofthe disease in 1872, is a neurodegenerative disease that is inherited. This is a case in populationgenetics, which follows the inheritance pattern called the dominant lethal. In this study, wepresented this disease as a multiplayer game among the alleles of the HD gene. We utilizedGokhale and Traulsen’s model, wherein a payoff matrix for a four-player game was reducedinto 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 mayconverge to either a purely Huntington, a purely normal, or a mixed composition where bothtypes of genes coexist. If the normal genotype produces more surviving offspring than the othergenotypes, then even if a small frequency of normal alleles is injected into a purely Huntingtonpopulation, the population will be replaced by the normal genotype over time. Such a result wasobtained using replicator dynamics and analysis of the stability of equilibrium points. Similaranalyses on other genotypes were provided in relation to the inheritance pattern of HD.