Stochastic Evolutionary Dynamics Of Biodiversity

In this paper,the evolutionary game theory is used to study the biodiver-sity of individuals in the finite stochastic population.The research is based on Monte Carlo simulation,stochastic process,and the partial differential equa-tion.We adopt time as a novel measure to depict the present of biodiversity in this paper.Here,we use the simulation method to reveal what role stochas-ticity plays in the evolution of biodiversity.The research methods and conclu-sions of biodiversity under stochastic dynamics are compared with those previ-ous researches under deterministic dynamics.Our research shows that stocha-sity plays an important role in the evolution of population.In the meanwhile,through the analysis of the stochastic evolutionary process of the population,we get the analytical results of the time that the strategies are coexistent under the weak selection intensity.And the robustness of those results are illustrated in this paper.According to the research methods and problems,this paper is divided into the following chapters:The first chapter is the introduction.In this chapter,we will introduce the background of the research,including the biodiversity of the population and the model adopted in our researches:Rock-Paper-Scissors game,and other related backgrounds.And we illustrate the current research status and the previous conclusions of biodiversity.Therefore we introduce our research object:time,and we illustrate the rationality and innovation of our research in this chapter.The second chapter is the basic knowledge.In this chapter,we introduce our research model in detail.It introduces the three strategies cyclic dominant games:Rock-Paper-Scissors game,and also the updating rules of the strategy:Fermi process.And we give the analysis of the evolutionary process of the population.The third chapter illustrates the Monte Carlo simulation results.It shows how the time that the strategies coexist is influenced by the decrease of the stochasity,which is described by the increasing selection intensity.In the mean-while,according to the analysis of the evolutionary process,we add an impor-tant transient state,extinction state,into our study object.Those simulation results are shown and analysed in this chapter.The forth chapter gives the analytical results of the time that the strategies coexist under the weak selection.We use a partial differential equation to depict the coexistent time.In the meanwhile,we give a solution of the extinction time based on stochastic process.And we illustrate that all those results are robust in the general imitation function.The fifth chapter is the summary of our research and the prospect of this project.