| In the process of biological evolution,in addition to competition,cooperation is everywhere.Cooperation exists both in lower organisms and in higher organisms.However,according to Darwin’s theory of natural selection,the existence of cooperation is unreasonable,because cooperative behavior will make our cooperation objects more adaptive,and our own adaptability will be reduced.Why sacrifice our adaptability to help competitors improve their adaptability? Cooperation runs counter to self-interest,how does cooperation,selflessness,and altruism appear and sustain? This problem has aroused widespread concern among scholars from many fields.Classical interpretation theories such as " kin selection theory " and " reciprocity theory" believe that the self-inhibition behavior of both partners will enable the cooperation to be maintained.However,recent studies have found that such interpretation mechanisms are flawed because they cannot explain the speculative behavior prevalent in cooperative systems.The reason may be due to these classic interpretation mechanism does not take into account external factors affecting the system,while empirical research shows that individual behavior to a large extent influenced by the outside world.Considering the influence of external ecological pressure,based on the classical cooperative evolutionary game theory,this paper uses model analysis and numerical simulation to study the evolutionary dynamics of individual cooperative behavior in the population,and explain the biological significance of this evolution.At the same time,considering the impact of habitat destruction,two mathematical models were established to investigate the impact of habitat destruction on the evolution of cooperative behavior.Secondly,considering the influence of external predation pressure,two three-dimensional differential equation models based on the prisoner’s dilemma game and the public goods game are established to study the influence of predation pressure on the evolution of cooperative behavior.Through our research,the main conclusions of this paper are as follows:(1)In the prisoner’s dilemma game,habitat destruction have influence on the population fraction of cooperators and defectors.When the degree of habitat destruction increases gradually,the proportion of cooperators will increase first and then decrease,and when the degree of damage to the environment is moderate,the fraction of cooperators will reach a maximum.In the public goods game,there are similar conclusions.(2)The cost-benefit ratio in the prisoner’s dilemma game also has an impact on the fraction of cooperators.As the cost-benefit ratio becomes smaller and smaller,the fraction of cooperators will become higher and higher,which means that smaller cost-benefits have a positive effect on cooperative behavior.(3)The multiplication factor in the public goods game affects the cooperators.The results show that as the multiplication factor increases,the proportion of cooperators will increase monotonically.(4)Monte Carlo simulations were used on the grid to study the effects of spatial structure on cooperative evolution.The results show that when the neighbor structure is von Loyman structure(k =4),the fraction of cooperators will increase first and then decrease as the degree of habitat damage increases.When the neighbor structure is a molar structure(k =8),the fraction of cooperators increases monotonically as the degree of habitat destruction increases.In addition,we also obtained distribution patterns of strategies under different neighborhood structures.The results show that when the neighbors increase,the level of cooperation of the group does not increase,but decreases.The deeper reason is that the more individuals involved in the game,the more individuals who want to take a “free rider”,which ultimately leads to a reduction in cooperative behavior.However,as habitat damage is too great,participants realize that cooperative strategies can enable them to gain greater group interests,so more and more individuals choose to cooperate.(5)In the prisoner’s dilemma game,external predation pressure will have an impact on cooperative behavior.When the predation pressure is small,individuals in the population tend to choose a defective strategy during the game.When the predation pressure reaches a moderate level,the individual will choose the cooperative strategy.When the predation pressure is too high,the proportion of cooperators will become smaller.Similar results have emerged in the public goods game.In summary,this study shows that when ecological pressure(including habitat destruction and predation pressure)is moderate,individuals in the population tend to choose a cooperative strategy,and the common interests generated by cooperation can effectively offset this pressure.When the ecological pressure is too large,the living environment is too bad,resulting in the continuous death of individuals in the population,which will not be conducive to the evolution of cooperative behavior. |
