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Simulation of evolutionisms for the double-membrane prokaryotes based on Parrondo's model

Wang Lu, Ye Shun-qiang, Wang Meng, Ye Ye, Xie Neng-gang

Lake proposed a hypothesis that symbiosis between a clostridium and actinobacterium produced the double-membrane prokaryotes and endosymbiosis. On the basis of LakeÂ’s hypothesis, this paper explains the rationality from quantitative analysis by using game theory so as to show symbiosis is a successful direction of evolution. The paper devises a multiagent ParrondoÂ’s model, which consists of game A and game B. Game A reflects the interaction relationship among individuals. Considering the symbiosis and endosymbiosis of actinobacteria and clostridia, we match them into the double-membrane prokaryotes by pairs. Complementary cooperationmechanismis adopted if the same type of individuals encounter, whereas competitive mechanism is adopted if the different types of individuals encounter. Game B reflects the environmental effect on individuals and is devised to be a negative-sum game, reflecting the harsh natural environment. It has two branches depend on the divisibility of a moduleM. One branch represents the unfavorable factors of environment, which has little probability to win; the other indicates the favorable conditions of environmentwith a large probability ofwinning. Besides, we set up a feedback mechanism to express the photosynthesis of the doublemembrane prokaryotes. Through feedback of thismechanism, the structure of gameB is improved. The improvement ismainly reflected in two aspects: quantitative and qualitative changes. Quantitative change means the winning probability of the favorable branch increases, while qualitative change indicates the module M becomes large. The simulation results show the endosymbiosis and the photosynthesis can make the doublemembrane prokaryotes obtain a greater fitness and a higher survival percentage.