Genki Ichinose

Robustness of cooperation on scale-free networks under continuous topological change.

In this paper, we numerically investigate the robustness of cooperation clusters in prisoners dilemma played on scale-free networks, where the network topologies change by continuous removal and addition of nodes. Each removal and addition can be either random or intentional. We therefore have four different strategies in changing network topology: random removal and random addition (RR), random removal and preferential addition (RP), targeted removal and random addition (TR), and targeted removal and preferential addition (TP). We find that cooperation clusters are most fragile against TR, while they are most robust against RP, even for large values of the temptation coefficient for defection. The effect of the degree mixing pattern of the network is not the primary factor for the robustness of cooperation under continuous change in network topology, which is quite different from the cases observed in static networks. Cooperation clusters become more robust as the number of links of hubs occupied by cooperators increase. Our results might infer the fact that a huge variety of individuals is needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.

Coevolution of role preference and fairness in the ultimatum game

Traditional economics assumes that humans are rational. However, it is known that humans behave fairly in the ultimatum game (UG). There are various explanations for this apparent paradox, such as the “inequity aversion.” However, the role preference (proposer or responder) of humans in the UG is obscure. I conducted a UG scenario experiment where subjects were asked their role preference in addition to their decision in the game. The results showed that the subjects prefer to be proposers rather than responders. In particular, it was found that rational subjects had a high preference for the proposer role. On the basis of these results, I conducted evolutionary simulations of the UG, where each individual has role preference intensity. A role is allocated to the individual proportional to the preference intensity. The results showed coevolution of role preference and fairness. The preference for the proposer role evolved when rational strategy evolved, whereas this preference weakened as rationality decreased. This indicates that fairness has a strong link with role preference; in other words, human fairness is always threatened by the “power and position” of some particular individuals. Hence, its equal distribution among individuals may be effective in maintaining a high level of fairness.

Collective Chasing Behavior between Cooperators and Defectors in the Spatial Prisoner’s Dilemma

Cooperation is one of the essential factors for all biological organisms in major evolutionary transitions. Recent studies have investigated the effect of migration for the evolution of cooperation. However, little is known about whether and how an individuals’ cooperativeness coevolves with mobility. One possibility is that mobility enhances cooperation by enabling cooperators to escape from defectors and form clusters; the other possibility is that mobility inhibits cooperation by helping the defectors to catch and exploit the groups of cooperators. In this study we investigate the coevolutionary dynamics by using the prisoner’s dilemma game model on a lattice structure. The computer simulations demonstrate that natural selection maintains cooperation in the form of evolutionary chasing between the cooperators and defectors. First, cooperative groups grow and collectively move in the same direction. Then, mutant defectors emerge and invade the cooperative groups, after which the defectors exploit the cooperators. Then other cooperative groups emerge due to mutation and the cycle is repeated. Here, it is worth noting that, as a result of natural selection, the mobility evolves towards directional migration, but not to random or completely fixed migration. Furthermore, with directional migration, the rate of global population extinction is lower when compared with other cases without the evolution of mobility (i.e., when mobility is preset to random or fixed). These findings illustrate the coevolutionary dynamics of cooperation and mobility through the directional chasing between cooperators and defectors.

Emergence of cooperative linkages by random intensity of selection on a network

By assuming the random intensity of selection, the emergence of cooperation on a network is studied. We constructed an evolutionary model in which an individual plays the prisoners dilemma game, and updates both its strategy and neighbor connections in response to its relative success in the game. The constant (strong or weak) and random intensities of selection are compared. The random intensities of selection are introduced to realize complex environmental effects on the fitness of each individual. Breaking the links on the network is realized according to fixed global parameters. We found that cooperative clusters emerged when cooperators unilaterally broke the link with defectors. The emergent networks under these conditions had a high clustering coefficient and shared some properties with a scale-free network. In addition, after a cooperator with high fitness emerged circumstantially under the random intensity of selection, we observed that the cooperative linkages emerged and spread rapidly through the network. This situation frequently occurred because of the stochastic effect on the fitness of cooperators. Thus, the origin of such phenomena is qualitatively different from the Lotka-Volterra system in which deterministic processes control the system. Cooperative linkages spread more when defectors maintained many links with cooperators.

Positive and negative effects of social impact on evolutionary vaccination game in networks

Preventing infectious disease like flu from spreading to large communities is one of the most important issues for humans. One effective strategy is voluntary vaccination, however, there is always the temptation for people refusing to be vaccinated because once herd immunity is achieved, infection risk is greatly reduced. In this paper, we study the effect of social impact on the vaccination behavior resulting in preventing infectious disease in networks. The evolutionary simulation results show that the social impact has both positive and negative effects on the vaccination behavior. Especially, in heterogeneous networks, if the vaccination cost is low the behavior is more promoted than the case without social impact. In contrast, if the cost is high, the behavior is reduced compared to the case without social impact. Moreover, the vaccination behavior is effective in heterogeneous networks more than in homogeneous networks. This implies that the social impact puts people at risk in homogeneous networks. We also evaluate the results from the social cost related to the vaccination policy.

Cooperation Achieved by Migration and Evolution in a Multilevel Selection Context

The idea that natural selection can be meaningfully applied at the group level may be more important than previously thought. This perspective, a modern version of group selection, is called multilevel selection. Multilevel selection theory could incorporate previous explanations for the evolution of cooperation including kin selection. There is general agreement that natural selection favors noncooperators over cooperators in the case of an unstructured population. Therefore, the evolution of cooperation by multilevel selection often requires positive assortment between cooperators and noncooperators. The question is how this positive assortment can arise. We constructed an individual-based model of multilevel selection and introduced migration and evolution. The results showed that positive assortment was generated especially when a migration strategy was adopted in which individuals respond specifically to bad environmental conditions. It was also shown that the evolution could further facilitate positive assortment by working with migration. The fact that cooperation was achieved by such migration and by evolution highlights the importance of sensitiveness to the environment and of fluctuations in group size, respectively

Heterogeneous network promotes species coexistence: metapopulation model for rock-paper-scissors game

Understanding mechanisms of biodiversity has been a central question in ecology. The coexistence of three species in rock-paper-scissors (RPS) systems are discussed by many authors; however, the relation between coexistence and network structure is rarely discussed. Here we present a metapopulation model for RPS game. The total population is assumed to consist of three subpopulations (nodes). Each individual migrates by random walk; the destination of migration is randomly determined. From reaction-migration equations, we obtain the population dynamics. It is found that the dynamic highly depends on network structures. When a network is homogeneous, the dynamics are neutrally stable: each node has a periodic solution, and the oscillations synchronize in all nodes. However, when a network is heterogeneous, the dynamics approach stable focus and all nodes reach equilibriums with different densities. Hence, the heterogeneity of the network promotes biodiversity.

Asymptotic stability of a modified Lotka-Volterra model with small immigrations

Predator-prey systems have been studied intensively for over a hundred years. These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the deterministic cyclic oscillations also exhibit divergent extinction. Thus, we have no solution for asymptotic stability in predator-prey systems, unlike most natural predator-prey interactions that sometimes exhibit stable and persistent coexistence. Here, we demonstrate that adding a small immigration into the prey or predator population can stabilize the LV system. Although LV systems have been studied intensively, there is no study on the non-linear modifications that we have tested. We also checked the effect of the inclusion of non-linear interaction term to the stability of the LV system. Our results show that small immigrations invoke stable convergence in the LV system with three types of functional responses. This means that natural predator-prey populations can be stabilized by a small number of sporadic immigrants.

Multi-species coexistence in Lotka-Volterra competitive systems with crowding effects

Classical Lotka-Volterra (LV) competition equation has shown that coexistence of competitive species is only possible when intraspecific competition is stronger than interspecific competition, i.e., the species inhibit their own growth more than the growth of the other species. Note that density effect is assumed to be linear in a classical LV equation. In contrast, in wild populations we can observed that mortality rate often increases when population density is very high, known as crowding effects. Under this perspective, the aggregation models of competitive species have been developed, adding the additional reduction in growth rates at high population densities. This study shows that the coexistence of a few species is promoted. However, an unsolved question is the coexistence of many competitive species often observed in natural communities. Here, we build an LV competition equation with a nonlinear crowding effect. Our results show that under a weak crowding effect, stable coexistence of many species becomes plausible, unlike the previous aggregation model. An analysis indicates that increased mortality rate under high density works as elevated intraspecific competition leading to the coexistence. This may be another mechanism for the coexistence of many competitive species leading high species diversity in nature.

Epidemics of random walkers in metapopulation model for complete, cycle, and star graphs

We present the metapopulation dynamic model for epidemic spreading of random walkers between subpopulations. A subpopulation is represented by a node on a graph. Each agent or individual is either susceptible (S) or infected (I). All agents move by random walk on the graph; namely, each agent randomly determines the destination of migration. The reaction-diffusion equations are presented as ordinary differential equations, not partial differential equations. To evaluate the risk of each subpopulation (node), we obtain the solutions of reaction-diffusion equations analytically and numerically for small, complete, cycle and star graphs. If a graph is homogeneous, or if every node has the same degree, then the solution never changes for any nodes. However, when a graph is heterogeneous, the infection density in equilibrium differs entirely among nodes. For example, on star graphs, the hub seems to be a supply source of disease because the infection density at the hub is much higher than that at the other nodes. On every graph, the epidemic thresholds are identical for all nodes.