Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China.
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138.
Proc Natl Acad Sci U S A. 2019 Dec 17;116(51):25398-25404. doi: 10.1073/pnas.1908936116. Epub 2019 Nov 26.
The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals' behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds [Formula: see text], where k is the average number of neighbors of an individual and [Formula: see text] captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.
环境对种群的进化动态有很强的影响。受内在和外在因素的驱动，环境本质上是不断变化的。为了捕捉瞬息万变的环境，我们考虑了一个具有博弈转换的进化动力学模型，其中个体的行为以及他们在一个时间步中所玩的博弈会影响下一个时间步中要玩的博弈。在这个模型中，我们研究了结构种群中的合作进化，并发现了一个简单的规则：如果利他行为提供的好处 b 与相应的成本 c 的比值超过[公式：见文本]，弱选择有利于合作而不是背叛，其中 k 是个体邻居的平均数量，[公式：见文本]捕捉了博弈转换的影响。即使在每个个体博弈中都不能有利于合作，如果允许在相互合作后转换到一个相对有价值的博弈，在背叛后转换到一个价值较低的博弈，那么合作可能会有一个有利的结果。特别是，不同博弈中微小的变化可以显著促进合作。我们的研究结果表明，简单的博弈转换可以作为支持高度连接的种群中亲社会行为的一种机制。
