مطالعه ي شبه پايداري در ديناميك تكاملي بر روي شبكه ي بي مقياس با استفاده از فرآيند موران

چكيده انگليسي :

IUT Degree Master of Science Title Study of Metastability in Evolutionary Dynamics on a Scale Free Network Using Moran Process Author Mojdeh Talebi Baram Supervisor F Fazileh Assis Prof Department Physics Date September Language Persian Abstract One of the key factors that guarantee the survival and development of living organisms is existance of cooperation among them Accepting this issue we can understand how such complex biological structures are created Single cells gathering to help each other to survive can create organisms that are more complete and more resistant One of the first theories of evolution proposed by Darwin According to this theory individuals who are more compatible with environment have more chance to survive This phenomenon is called natural selection It s important to understand how coopration emerges between creatures because it opposes natural selection Even among the individuals of a same species there are difference weakness and superior traits so why powerful individual should help others to survive them In fact describing process of emergence of cooperative behavior is a challenging problem In a biologist in the field of evolution Robert Trivers mentioned a simple model that described interaction between two independent individuals which could explain such a cooperation behavior In this situation although cooperation was beneficial eventually individuals tend to defect This interaction is a well known game in the framework of game theory that called prisoner s dilemma It was first introduced by two Mathematician Merrill Flood and Melvin Dresher Rationality is a fundamental assumption in game theory but if we use game theory to describe evolution rationality is ignored and evolution is studied by focusing on frequency of species in population therefore we study evolution in framework of evolutionary game theory EGT In this theory individuals interact with each other Interactions are described by game theory and gain payoff In EGT payoffs of each individual refer to fitness In an infinite well mixed population where all individuals have equal chance to interact with everyone else the evolutionary dynamics is conveniently described by the replicator equation Finite populations require stochastic formulation One way that influences fixation probability and so emerges coopration in population is studying evolution on a complex networks such as scale free network Evolutionary graph theory describes how structured population affects evolution This theory supposes that individuals set to nodes of graph and edges connect nodes In EGT where the fitness and selection are frequency dependent and vary with the population composition we analyze the dynamics of snowdrift games characterized by a metastable coexistence state on a scale free network Using Moran process in the weak selection limit we demonstrate how the scale free structure affects the system s metastable state and leads to anomalous fixation Simulation results show that structured populations make strategies gather together and hence other strategies fail to invade them So we can see how coopration survives and promotes Keywords Game Theory Evolutionary Dynamics Scale Free Network Moran Process Snowdrift Game Evolutionary Graph Theory PDF created with pdfFactory trial version www pdffactory com

طالبي برام، مژده

مطالعه ي شبه پايداري در ديناميك تكاملي بر روي شبكه ي بي مقياس با استفاده از فرآيند موران

بازي جاده برفي , نظريه تكاملي گراف