Algebra of group-based models of evolution
Bollen, GP Guus · TU/e Research Portal · 2011
Evolution can be described by a statistical model based on an abelian group. We describe such a model, and provide facts about the polynomial equations that hold for the model. Once found, these equations could aid in statistical tests that can be used to achieve a better understanding of evolution. In order to find these polynomial equations, we first transform our variables and parameters in such a way that the transformed variables are monomials in the transformed parameters times a coefficient. Then, we provide criteria for these equations. Finally, we investigate the models based on the groups Z/2Z and Z/3Z more thoroughly, in order to facilitate finding the polynomial equations.