Inheritance Pattern of Huntington’s Disease, a Multiplayer Game

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.