The Researches Of Evolutjon Of Cooperation Based On Game Models In Spatially Structured Populations

How natural selection can lead to cooperation has been being the frontier and hotspot in the research of evolutionary biology, evolutionary game theory has been used as a standard tool in understanding the problem of cooperation. The subject of this thesis is the evolution of cooperation in spatially structured populations, which is a new research focus of this field. Two approaches will be utilized in this dissertation. One is the differential dynamical system described by replicator equations, the phase plane and numerical solution are used to analyze the equilibria and their stability. This approach can show the temporal dynamics and evolutionary stable state. In spatial game models, mathematical methods of comparing the local payoff structures, mean-field approximation, pair approximation, as well as invasion probability analysis are also used. The other is the spatially explicit simulation, where lattice model and cellular automaton are mainly concerned. By the software Matlab, explicit graphic mode of the spatial pattern about the evolutionary dynamics can be given. We firstly introduce the basic concepts of game theory, the research methods of evolutionary game theory, as well as the research progress of the evolution of cooperation. The replicate dynamics of three classic repeated strategies in well-mixed populations are studied. In addition, the basic models and research methods of spatial game are introduced in details. Secondly, mathematical models based on specific update rules under different spatial structures are constructed to widely investigate the effect of spatial structure on the evolution of cooperation. The results show:(1) For the repeated game of the three strategies,'always defect'(ALLD),'tit-for-tat'(TFT), and'always cooperate'(ALLC) in well-mixed populations, the evolutionary stable state is ALLD in most parameter settings;(2) A spatial game model of the three strategies by using the best takes over update rule is investigated in a two-dimensional square lattice, an improved analytical method which is based on comparing the local neighborhood structures is used to derive the conditions of invasion and coexistence. Furthermore, combined with computer simulations, the parameter plane for two major parameters is divided and nine representative regions are identified. In each parameter region, a distinct spatiotemporal dynamics is characterized. Such as, spatiotemporal chaos, stable percolation network, evolutionary kaleidoscope, irregular frozen state and so on;(3) The evolution of cooperation can be promoted, all individuals adopting ALLD strategy can be fully eliminated for each parameter setting while only considering the local spatial interactions in a two-dimensional square lattice. Cooperative players can survive by forming stable spatial domains to defend invasion of defectors;(4) Spatial structure is the keystone of the evolution of intra-specific diversity;(5) Lattice structure has an ambivalent effect on the evolution of cooperation. The invasion probability analysis in one dimension confirms it promotes cooperation, while'score-dependent viability'model shows it also inhibits cooperation because of the advantage of being spiteful, which is also verified by studies about the effect of patch connectivity;(6) For lattice model, mean-field approximation fails to predict the final outcome of computer simulations, pair approximation is accurate to two dimension but fails to one dimension;(7) Specific life-history assumption has an important effect on the evolutionary dynamics;(8) The PD dynamics with non-uniform interaction rates shows that cooperation is not only enhanced in spatial structure but also inhibited, which depends on the ratio of assortative interaction rate respect to disassortative one;(9) The dynamics in regular graphs with three update rules'birth-death'(BD),'death-birth'(DB), and'imitation'(IM) shows cooperation is enhanced in spatially extended system, especially for DB and IM.