具有Allee效应的合作进化

Allee效应对物种的续存是潜在的干扰因素,在很大程度上将增加种群局部甚至全局灭绝的可能性。对许多物种,尤其是濒临物种更容易受其影响。将Allee效应引入囚徒困境博弈模型,通过理论分析与数值模拟相结合的方法分析讨论了Allee效应对合作进化的影响。研究结果表明:在恶劣的环境条件下,Allee效应极易使物种灭绝,不利于合作进化;在相对优越的环境条件下(死亡率较低),Allee效应促进合作进化,且Allee效应强度越强,更有利于合作进化,不过种群的空间斑块占有率也会随着Allee效应强度的增强而降低,使物种最终灭绝。

Cooperative evolution of a population with the Allee effect

It is well know that the prisoner''s dilemma game is a common phenomenon in ecology. Cooperator-defector interactions are ubiquitous in a population. One considered the ecological model was the cooperative evolution in the prisoner''s dilemma game without the Allee effect. However, the Allee effect is a crucial phenomenon that has drawn considerable attention from ecologists. It describes a positive interaction among individuals in low population sizes, and these interactions may be critical for survival and reproduction. The Allee effect can be caused by any number of factors, for example, finding mates between the individuals of a species in low population densities, reduced defense against predators, special trends of social dysfunction, etc. Meanwhile, the Allee effect is a destabilizing factor in species persistence in the evolvement, and largely increases the possibility of the species'' local extinction, even its global extinction. Many species, especially the endangered species, are more susceptible to the influlence of the Allee effect. Therefore, it is important to study cooperative evolution in a population with the Allee effect. Based on the system described by Feng Zhang & Cang Hui, we formulated a new prisoner''s dilemma game model, in which the population was subjected to the Allee effect. Theoretical analysis and numerical simulation were used to investigate how the Allee effect influences cooperative evolution. The results show that, the assortment is still a necessary condition for the evolution of cooperation in the ecological context, and cooperative evolution becomes easier under density-dependent selection. At the same time, our study also indicates that the Allee effect can easily lead to the extinction of species, and acts against cooperative evolution under unfavorable environmental conditions. However, in the relatively superior environmental conditions (causing low death rate), the rise of cooperation could be much easier due to the Allee effect. As the Allee effect becomes stronger, it promotes more favorable cooperative evolution. However, the occupancy of a population will decrease as the strength of the Allee effect increases in the spatial pattern. When the value of the Allee effect is greater than the threshold value, the population eventually tends to become extinct.