Biomaterial Database

A review of evolutionary graph theory with applications to game theory. 2012

Paulo Shakarian, and Patrick Roos, and Anthony Johnson

Network Science Center and Dept. of Electrical Engineering and Computer Science, United States Military Academy, West Point, NY 10996, United States. paulo@shakarian.net

Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the "fixation probability" - the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.

UI	MeSH Term	Description	Entries
D008957	Models, Genetic	Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.	Genetic Models,Genetic Model,Model, Genetic
D009154	Mutation	Any detectable and heritable change in the genetic material that causes a change in the GENOTYPE and which is transmitted to daughter cells and to succeeding generations.	Mutations
D011157	Population Dynamics	The pattern of any process, or the interrelationship of phenomena, which affects growth or change within a population.	Malthusianism,Neomalthusianism,Demographic Aging,Demographic Transition,Optimum Population,Population Decrease,Population Pressure,Population Replacement,Population Theory,Residential Mobility,Rural-Urban Migration,Stable Population,Stationary Population,Aging, Demographic,Decrease, Population,Decreases, Population,Demographic Transitions,Dynamics, Population,Migration, Rural-Urban,Migrations, Rural-Urban,Mobilities, Residential,Mobility, Residential,Optimum Populations,Population Decreases,Population Pressures,Population Replacements,Population Theories,Population, Optimum,Population, Stable,Population, Stationary,Populations, Optimum,Populations, Stable,Populations, Stationary,Pressure, Population,Pressures, Population,Replacement, Population,Replacements, Population,Residential Mobilities,Rural Urban Migration,Rural-Urban Migrations,Stable Populations,Stationary Populations,Theories, Population,Theory, Population,Transition, Demographic,Transitions, Demographic
D005075	Biological Evolution	The process of cumulative change over successive generations through which organisms acquire their distinguishing morphological and physiological characteristics.	Evolution, Biological
D005716	Game Theory	Theoretical construct used in applied mathematics to analyze certain situations in which there is an interplay between parties that may have similar, opposed, or mixed interests. In a typical game, decision-making "players," who each have their own goals, try to gain advantage over the other parties by anticipating each other's decisions; the game is finally resolved as a consequence of the players' decisions.	Game Theories,Theories, Game,Theory, Game
D013997	Time Factors	Elements of limited time intervals, contributing to particular results or situations.	Time Series,Factor, Time,Time Factor
D040961	Genetic Drift	The fluctuation of the ALLELE FREQUENCY from one generation to the next.	Evolution, Neutral,Drift, Genetic,Neutral Evolution