Evolutionary prisoner's dilemma game on hierarchical lattices

An evolutionary prisoner's dilemma (PD) game is studied with players located on a hierarchical structure of layered square lattices. The players can follow two strategies [D (defector) and C (cooperator)] and their income comes from PD games with the ``neighbors.'' The adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference. Monte Carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels (Q) and by the temptation to defect. According to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low (Q<4). For larger Q, however, the highest frequency of cooperators occurs in the middle layers. The four-level hierarchical structure provides the highest average (total) income for the whole community.Comment: appendix adde

Evolutionary Prisoner's Dilemma game on the Newman-Watts networks

Maintenance of cooperation was studied for a two-strategy evolutionary Prisoner's Dilemma game where the players are located on a one-dimensional chain and their payoff comes from games with the nearest and next-nearest neighbor interactions. The applied host geometry makes possible to study the impacts of two conflicting topological features. The evolutionary rule involves some noise affecting the strategy adoptions between the interacting players. Using Monte Carlo simulations and the extended versions of dynamical mean-field theory we determined the phase diagram as a function of noise level and a payoff parameter. The peculiar feature of the diagram is changed significantly when the connectivity structure is extended by extra links as suggested by Newman and Watts.Comment: 4 figure

Distribution and composition of the lysis cassette of Lactococcus lactis phages and functional analysis of bacteriophage ul36 holin

The bacteriophage lysis cassette, which comprises a lysin and a holin gene, was analyzed in 18 Lactococcus lactis phages. A muramidase motif was found in the lysins of c2-like phages, while an amidase motif was observed in the lysins of 936-like phages. Both amidase and muramidase types were detected among the P335 phages. The P335 lysins were separated into three groups based on amino acid sequence identity. A class I holin was recognized in 936-like and c2-like phages, whereas P335-like phages possess class II holins. The P335 holins were further divided into four groups based on sequence identity. Only the holins of 936-like phages contained putative dual-start motifs. The unusual lysis cassette of the highly virulent P335-like phage ul36 contains a unique holin (orf74B) upstream of a lysin which is present in several other P335-like phages. Using the λΔSthf system, we demonstrated that gpORF74B induces cell lysis at the same time as λΔSthf::S105, the effector of λ lysis. Transcriptional analysis of ul36 lysis cassette showed that first transcripts are detected 35 min after infection of L. lactis cells. The lysis clock of phage ul36 appears to be controlled by the late expression of the holin and lysin gene

Selection of noise level in strategy adoption for spatial social dilemmas

We studied spatial Prisoner's Dilemma and Stag Hunt games where both the strategy distribution and the players' individual noise level could evolve to reach higher individual payoff. Players are located on the sites of different two-dimensional lattices and gain their payoff from games with their neighbors by choosing unconditional cooperation or defection. The way of strategy adoption can be characterized by a single $K$ (temperature-like) parameter describing how strongly adoptions depend on the payoff-difference. If we start the system from a random strategy distribution with many different player specific $K$ parameters, the simultaneous evolution of strategies and $K$ parameters drives the system to a final stationary state where only one $K$ value remains. In the coexistence phase of cooperator and defector strategies the surviving $K$ parameter is in good agreement with the noise level that ensures the highest cooperation level if uniform $K$ is supposed for all players. In this paper we give a thorough overview about the properties of this evolutionary process.Comment: 10 two-column pages, 10 figures; accepted for publication in Physical Review

Selection of dynamical rules in spatial Prisoner's Dilemma games

We study co-evolutionary Prisoner's Dilemma games where each player can imitate both the strategy and imitation rule from a randomly chosen neighbor with a probability dependent on the payoff difference when the player's income is collected from games with the neighbors. The players, located on the sites of a two-dimensional lattice, follow unconditional cooperation or defection and use individual strategy adoption rule described by a parameter. If the system is started from a random initial state then the present co-evolutionary rule drives the system towards a state where only one evolutionary rule remains alive even in the coexistence of cooperative and defective behaviors. The final rule is related to the optimum providing the highest level of cooperation and affected by the topology of the connectivity structure.Comment: 5 two-column pages, 3 figure

Evolutionary advantages of adaptive rewarding

Our wellbeing depends as much on our personal success, as it does on the success of our society. The realization of this fact makes cooperation a very much needed trait. Experiments have shown that rewards can elevate our readiness to cooperate, but since giving a reward inevitably entails paying a cost for it, the emergence and stability of such behavior remain elusive. Here we show that allowing for the act of rewarding to self-organize in dependence on the success of cooperation creates several evolutionary advantages that instill new ways through which collaborative efforts are promoted. Ranging from indirect territorial battle to the spontaneous emergence and destruction of coexistence, phase diagrams and the underlying spatial patterns reveal fascinatingly reach social dynamics that explains why this costly behavior has evolved and persevered. Comparisons with adaptive punishment, however, uncover an Achilles heel of adaptive rewarding that is due to over-aggression, which in turn hinders optimal utilization of network reciprocity. This may explain why, despite of its success, rewarding is not as firmly weaved into our societal organization as punishment.Comment: 14 pages, 8 figures; accepted for publication in New Journal of Physic