The evolution and long-term sustenance of cooperation has consistently piqued scholarly interest across the disciplines of evolutionary biology and social sciences. Previous theoretical and experimental studies on collective risk social dilemma games have revealed that the risk of collective failure will affect the evolution of cooperation. In the real world, individuals usually adjust their decisions based on environmental factors such as risk intensity and cooperation level. However, it is still not well understood how such conditional behaviours affect the evolution of cooperation in repeated group interactions scenario from a theoretical perspective. Here, we construct an evolutionary game model with repeated interactions, in which defectors decide whether to cooperate in subsequent rounds of the game based on whether the risk exceeds their tolerance threshold and whether the number of cooperators exceeds the collective goal in the early rounds of the game. We find that the introduction of conditional cooperation strategy can effectively promote the emergence of cooperation, especially when the risk is low. In addition, the risk threshold significantly affects the evolutionary outcomes, with a high risk promoting the emergence of cooperation. Importantly, when the risk of failure to reach collective goals exceeds a certain threshold, the timely transition from a defective strategy to a cooperative strategy by conditional cooperators is beneficial for maintaining high-level cooperation.

The fact that people often have preference rankings for their partners is a distinctive aspect of human behavior. Little is known, however, about how this talent as a powerful force shapes human behavioral traits, including those which should not have been favored by selection, such as cooperation in social dilemma situations. Here we propose a dynamic model in which network-structured individuals can switch their interaction partners within neighborhoods based on their preferences. For the partner switching, we propose two interruption regimes: dictatorial regime and negotiating regime. In the dictatorial regime, focal individuals are able to suspend interactions out of preferences unilaterally. In the negotiating regime, either focal individuals or the associated partners agree to suspend, then these interactions can be successfully suspended. We investigate the evolution of cooperation under both preference-driven partner switching regimes in the context of both the weakened variant of the donation game and the standard one. Specifically, we theoretically approximate the critical conditions for cooperation to be favored by weak selection in the weakened donation game where cooperators bear a unit cost to provide a benefit for each active neighbor and simulate the evolutionary dynamics of cooperation in the standard donation game to test the robustness of the analytical results. Under dictatorial regime, selection of cooperation becomes harder when individuals have preferences for either cooperator or defector partners, implying that the expulsion of defectors by cooperators is overwhelmed by the chasing of defectors towards cooperators. Under negotiating regime, both preferences for cooperator and defector partners can significantly favor the evolution of cooperation, yet underlying mechanisms differ greatly. For preferences over cooperator partners, cooperator-cooperator interaction relationships are reinforced and the associated mutual reciprocity can resist and assimilate defectors. For preferences over defector partners, defector-defector interaction relationships are anchored, weakening defectors\' exploitation over cooperators. Cooperators are thus offered much time space to interact among cospecies and spread. Our work may help better understand the critical role of preference-based adaptive partner switching in promoting the evolution of cooperation.

Bacteria typically reside in heterogeneous environments with various chemogradients where motile cells can gain an advantage over nonmotile cells. Since motility is energetically costly, cells must optimize their swimming speed and behaviour to maximize their fitness. Here, we investigate how cheating strategies might evolve where slow or nonmotile microbes exploit faster ones by sticking together and hitching a ride. Starting with physical and biological first principles, we computationally study the effects of sticking on the evolution of motility in a controlled chemostat environment. We find that stickiness allows for slow cheaters to dominate when chemoattractants are dispersed at intermediate distances. In this case, slow microbes exploit faster ones until they consume the population, leading to a tragedy of commons. For long races, slow microbes do gain an initial advantage from sticking, but eventually fall behind. Here, fast microbes are more likely to stick to other fast microbes and co-operate to increase their own population. We therefore conclude that whether the nature of the hitchhiking interaction is parasitic or mutualistic, depends on the chemoattractant distribution.

In this paper, a mechanism called proximity inheritance is introduced in the birth-death process of a networked population involving the Prisoner\'s Dilemma game. Different from the traditional birth-death process, in the proposed model, players are distributed in a spatial space and offspring is distributed in the neighbourhood of its parents. That is, offspring inherits not only the strategy but also the proximity of its parents. In this coevolutionary game model, a cooperative neighbourhood gives more neighbouring cooperative offspring and a defective neighbourhood gives more neighbouring defective offspring, leading to positive feedback among cooperative interactions. It is shown that with the help of proximity inheritance, natural selection will favour cooperation over defection under various conditions, even in the presence of mutation. Furthermore, the coevolutionary dynamics could lead to self-organized substantial network clustering, which promotes an assortment of cooperative interactions. This study provides a new insight into the evolutionary mechanism of cooperation in the absence of social attributions such as reputation and punishment.

Cooperation is key to the survival of all biological systems. The spatial structure of a system constrains who interacts with whom (interaction partner) and who acquires new traits from whom (role model). Understanding when and to what degree a spatial structure affects the evolution of cooperation is an important and challenging topic. Here, we provide an analytical formula to predict when natural selection favours cooperation where the effects of a spatial structure are described by a single parameter. We find that a spatial structure promotes cooperation (spatial reciprocity) when interaction partners overlap role models. When they do not, spatial structure inhibits cooperation even without cooperation dilemmas. Furthermore, a spatial structure in which individuals interact with their role models more often shows stronger reciprocity. Thus, imitating individuals with frequent interactions facilitates cooperation. Our findings are applicable to both pairwise and group interactions and show that strong social ties might hinder, while asymmetric spatial structures for interaction and trait dispersal could promote cooperation.

In this paper, we proposed a frequency dependent fitness-based process, which is an extension of both the standard Moran process and the Wright-Fisher process. Some individuals are selected into a parent\'s pool and reproduce. Then the offspring is selected to replace individuals in the entire parent generation. We explored the influence of the size of parent pool and the number of offspring on a single cooperator\'s fixation. The less offspring leads to higher fixation probability of s single cooperator. Meanwhile, the fixation probability decreases with the growth of the local level. In other words, the direction of the number of offspring\'s impact on fixation probability is in accordance with that of the local level\'s impact. The less offspring in one generation or the smaller parent\'s pool contributes to promoting cooperation with the fitness-based updating rule.

In this paper, we propose a strategy-updating rule driven by local information, which is called Local process. Unlike the standard Moran process, the Local process does not require global information about the strategic environment. By analyzing the dynamical behavior of the system, we explore how the local information influences the fixation of cooperation in two-player evolutionary games. Under weak selection, the decreasing local information leads to an increase of the fixation probability when natural selection does not favor cooperation replacing defection. In the limit of sufficiently large selection, the analytical results indicate that the fixation probability increases with the decrease of the local information, irrespective of the evolutionary games. Furthermore, for the dominance of defection games under weak selection and for coexistence games, the decreasing of local information will lead to a speedup of a single cooperator taking over the population. Overall, to some extent, the local information is conducive to promoting the cooperation.

Reputation can promote cooperation in public goods game and player\'s cooperative behavior is not pure economical rationality, but habituation would influence their behaviors as well. One\'s habituation can be formed by repeated behaviors in daily life and be affected by habitual preference. We aim to investigate the sustainable cooperation based on reputation and habit formation. To better investigate the impacts of reputation and habitual preference on the evolution and sustainability of cooperation. We introduce three types of agents into our spatial public goods game. Through numerical simulations, we find that the larger habitual preference make cooperation easier to emerge and maintain. Additionally, we find that a moderate number of agents who want to obtain more reputation (ICs) are best for the sustainability of cooperation. Finally, we observe that the variation of donations of ICs can influence greatly on the equilibrium of public goods game. When ICs reduce their donations, a proper contribution will be better to maintain the cooperative behaviors.

The long-term coexistence of cooperation and defection is a common phenomenon in nature and human society. However, none of the theoretical models based on the Prisoner\'s Dilemma (PD) game can provide a concise theoretical model to explain what leads to the stable coexistence of cooperation and defection in the long-term even though some rules for promoting cooperation have been summarized (Nowak, 2006, Science 314, 1560-1563). Here, based on the concept of direct reciprocity, we develop an elementary model to show why stable coexistence of cooperation and defection in the PD game is possible. The basic idea behind our theoretical model is that all players in a PD game prefer a cooperator as an opponent, and our results show that considering strategies allowing opting out against defection provide a general and concise way of understanding the fundamental importance of direct reciprocity in driving the evolution of cooperation.

Tag-based ethnocentric cooperation is a highly robust behavior which can evolve and prevail under a wide variety of conditions. Recent studies have demonstrated, however, that ethnocentrism can temporarily be suppressed by other competing strategies, especially in its early evolutionary stages. In a series of computational experiments, conducted with an agent-based evolutionary model of tag-mediated cooperation, we addressed the question of whether a stochastically established and once dominant non-ethnocentric strategy such as indiscriminate altruism can stably persist and permanently outweigh ethnocentrism. Our model, simulated on various complex network topologies, employs simple haploid genetics and asexual reproduction of computational agents equipped with memory and heritable phenotypic traits. We find that in combination with an implemented memory mechanism and tags, random bias acting in favor of altruists can lead to their long-lasting victory over all other types of strategists. The difference in density between altruistic and ethnocentric cooperators increases with greater rewiring of the underlying network, but decreases with growing population size. These findings suggest that randomness plays an important role in promoting non-ethnocentric cooperation and contributes to our understanding of how other than adaptive mechanisms can initiate the design of novel behavioral phenotypes, thereby shaping surprisingly new evolutionary pathways.