Evolution of cooperation on dynamical graphs

There are two key characteristic of animal and human societies: (1) degree heterogeneity, meaning that not all individual have the same number of associates; and (2) the interaction topology is not static, i.e. either individuals interact with different set of individuals at different times of their life, or at least they have different associations than their parents. Earlier works have shown that population structure is one of the mechanisms promoting cooperation. However, most studies had assumed that the interaction network can be described by a regular graph (homogeneous degree distribution). Recently there are an increasing number of studies employing degree heterogeneous graphs to model interaction topology. But mostly the interaction topology was assumed to be static. Here we investigate the fixation probability of the cooperator strategy in the prisoner’s dilemma, when interaction network is a random regular graph, a random graph or a scale-free graph and the interaction network is allowed to change. We show that the fixation probability of the cooperator strategy is lower when the interaction topology is described by a dynamical graph compared to a static graph. Even a limited network dynamics significantly decreases the fixation probability of cooperation, an effect that is mitigated stronger by degree heterogeneous networks topology than by a degree homogeneous one. We have also found that from the considered graph topologies the decrease of fixation probabilities due to graph dynamics is the lowest on scale-free graphs

A tér és időbeli heterogenitás szerepe az együttműködés ökológiájában és evolúciójában = The role of environmental heterogeneity in the ecology and evolution of co-operation

Megmutattam, hogy a heterogén forráseloszlás elősegítheti az együttműködés kialakulását. A biológiailag releváns aszinkron döntési szituációban, hótorlasz játékban akkor várhatunk teljes együttműködést, ha strukturált populációban az együttműködés szinergisztikus hatása elég nagy. Dinamikus gráfokon az együttműködés megtelepedésének valószínűsége kisebb, mint statikus gráfokon. A skálafüggetlen gráf tudja a legjobban pufferelni a változás hatását. A szelektív partnerválasztás/kapcsolat megszakítás lehetősége jelentősen növelheti az együttműködés megtelepedésének valószínűségét. Valós RNS enzimek mutagenezis kísérletei alapján készített rátermettségtérkép alapján a fenotipikus hibaküszöb egy nagyságrenddel megengedőbb, mint a genotipikus hibaköszöb. Ez egy jelentős előrelépés az Eigen paradoxon megoldásában. Kimutattuk, hogy metabolikus replikátorok vannak az élőlények metabolizmusában. Az ATP előállítás univerzálisan autokatailitusnak bizonyult. Egyes szervezetekben a NAD, CoA, THF, kinonok és cukrok előállítása is autokatalitikus. A kodon középső betűje szerint csoportosulnak a katalitikusan fontosabb - kevésbé fontos aminosavak. A legfontosabb katalitikus aminosavak (hisztidin, aszparaginsav, glutaminsav) kodonjának közepén adenin van. Megmutattuk, hogy a klonális növények térbeli munkamegosztása előnyös időben állandó vagy nem túlságosan változó környezetben. | We have shown that heterogeneous resource distribution can facilitate cooperation. We expect full cooperation with the biologically relevant asynchronous decision in the Snowdrift game if the population is structured and the synergistic effect of cooperation is high. The fixation probability of cooperation on dynamical graphs is lower than on static graphs. Scale free graphs can buffer the effect of changing interactions the most. Selective partner choice and link abortion can greatly enhance the evolution of cooperation. We have constructed a fitness landscape based on mutagenesis data of real ribozymes. The estimated phenotypic error threshold is one magnitude better than the genotypic one. This is a big leap forward in solving the Eigen's Paradox. We have identified metabolic replicators in the metabolism of organism. It seems that ATP is universally produced in an autocatalytic manner. In certain organisms the production of NAD, CoA, THF, quinines and sugars can also be autocatalytic. The catalytically more important amino acids (histidine, aspartic acid, glutamic acid) share the same middle codon: adenine. The genetic code is structured (among others) by the catalytic propensities of the coded amino acids. We have shown that spatial division of labour in clonal plants is advantageous in stable or not too fluctuating environments

Different reactions to adverse neighborhoods in games of cooperation

In social dilemmas, cooperation among randomly interacting individuals is often difficult to achieve. The situation changes if interactions take place in a network where the network structure jointly evolves with the behavioral strategies of the interacting individuals. In particular, cooperation can be stabilized if individuals tend to cut interaction links when facing adverse neighborhoods. Here we consider two different types of reaction to adverse neighborhoods, and all possible mixtures between these reactions. When faced with a gloomy outlook, players can either choose to cut and rewire some of their links to other individuals, or they can migrate to another location and establish new links in the new local neighborhood. We find that in general local rewiring is more favorable for the evolution of cooperation than emigration from adverse neighborhoods. Rewiring helps to maintain the diversity in the degree distribution of players and favors the spontaneous emergence of cooperative clusters. Both properties are known to favor the evolution of cooperation on networks. Interestingly, a mixture of migration and rewiring is even more favorable for the evolution of cooperation than rewiring on its own. While most models only consider a single type of reaction to adverse neighborhoods, the coexistence of several such reactions may actually be an optimal setting for the evolution of cooperation.Comment: 12 pages, 5 figures; accepted for publication in PLoS ON

Az élet keletkezésének és jelenkori modellorganizmusok evolúciójának számítógépes vizsgálata = Computational study of evolution in early life and extant model organisms

Pályázatunk súlyponti témája az élet keletkezésének és korai evolúciójának vizsgálata volt, szimulációs és matematikai modellezés segítségével. Megvizsgáltuk a sejtes szerveződést megelőző felszíni anyagcsere, illetve az RNS-gének megjelenése előtti prebiotikus rendszerek evolúciójának lehetőségeit és korlátait. Tovább finomítottuk a legegyszerűbb sejtes rendszerek absztrakt dinamikájának (chemoton modell) leírását, és foglalkoztunk az RNS-replikátorok másolásának nehézségeivel. Újabb ismeretekkel szolgáltunk a genetikai kód (transzláció) és a komplex anyagcsere evolúciójának lehetséges történetéről és mechanizmusairól. További projektekben foglalkoztunk a replikátorok általános elméletével, a kooperáció, a nyelvkészség és a virulencia evolúciójával, valamint az agyban zajló evolúciós/szelekciós folyamatokkal. | Our research centred on the origin and early evolution of life, with the tools of simulation and mathematical modelling. We studied the potential and limitations of surface metabolism (preceding cellular organisation) and of the evolution of prebiotic systems (preceding RNA genes). We investigated further aspects of the abstract dynamics of the simplest cellular living organisms (chemoton model), and analyzed the difficulties associated with the copying of RNA replicators. We gleaned new insight into the possible evolutionary history and mechanisms of the genetic code (translation) and of complex metabolism. In further projects, we studied the general theory of replicators, the evolution of cooperation, language and virulence, and the evolutionary/selective processes that occur in the brain

Cooperators Unite! Assortative linking promotes cooperation particularly for medium sized associations

<p>Abstract</p> <p>Background</p> <p>Evolution of cooperative behaviour is widely studied in different models where interaction is heterogeneous, although static among individuals. However, in nature individuals can often recognize each other and chose, besides to cooperate or not, to preferentially associate with or to avoid certain individuals.</p> <p>Here we consider a dynamical interaction graph, in contrast to a static one. We propose several rules of rejecting unwanted partners and seeking out new ones, and study the probability of emergence and maintenance of cooperation on these dynamic networks.</p> <p>Results</p> <p>Our simulations reveal that cooperation can evolve and be stable in the population if we introduce preferential linking, even if defectors can perform it too. The fixation of cooperation has higher probability than that of on static graphs, and this effect is more prevalent at high benefit to cost ratios. We also find an optimal number of partners, for which the fixation probability of cooperation shows a maximum.</p> <p>Conclusions</p> <p>The ability to recognize, seek out or avoid interaction partners based on the outcome of past interactions has an important effect on the emergence of cooperation. Observations about the number of partners in natural cooperating groups are in concordance with the result of our model.</p

Graph Transformations and Game Theory: A Generative Mechanism for Network Formation

Many systems can be described in terms of networks with characteristic structural properties. To better understand the formation and the dynamics of complex networks one can develop generative models. We propose here a generative model (named dynamic spatial game) that combines graph transformations and game theory. The idea is that a complex network is obtained by a sequence of node-based transformations determined by the interactions of nodes present in the network. We model the node-based transformations by using graph grammars and the interactions between the nodes by using game theory. We illustrate dynamic spatial games on a couple of examples: the role of cooperation in tissue formation and tumor development and the emergence of patterns during the formation of ecological networks

Public Goods Games in Disease Evolution and Spread

Cooperation arises in nature at every scale, from within cells to entire ecosystems. In the framework of evolutionary game theory, public goods games (PGGs) are used to analyse scenarios where individuals can cooperate or defect, and can predict when and how these behaviours emerge. However, too few examples motivate the transferal of knowledge from one application of PGGs to another. Here, we focus on PGGs arising in disease modelling of cancer evolution and the spread of infectious diseases. We use these two systems as case studies for the development of the theory and applications of PGGs, which we succinctly review and compare. We also posit that applications of evolutionary game theory to decision-making in cancer, such as interactions between a clinician and a tumour, can learn from the PGGs studied in epidemiology, where cooperative behaviours such as quarantine and vaccination compliance have been more thoroughly investigated. Furthermore, instances of cellular-level cooperation observed in cancers point to a corresponding area of potential interest for modellers of other diseases, be they viral, bacterial or otherwise. We aim to demonstrate the breadth of applicability of PGGs in disease modelling while providing a starting point for those interested in quantifying cooperation arising in healthcare.Comment: 12 pages, 2 figures, 3 table

Coevolutionary games - a mini review

Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries.Comment: 24 two-column pages, 10 figures; accepted for publication in BioSystem