Stochastic evolution of bad memes.

Dawkins introduced a groundbreaking concept suggesting that humans, similar to other animals, operate as gene-propagating machines. Following in his footsteps, Blackmore posits that humans might distinguish themselves from other animals by also serving as specialized meme-replicating machines. Here we introduce a mathematical model that examines the impact of social conformity on the propagation of bad memes (memes with low intrinsic appeal). We state the meme equations, which give us the number of different kinds of memes living in the population and its total amount. We show that, unlike a virus, bad memes have a very low probability of initially spreading. However, as memes are produced in large numbers, some will eventually experience a stochastic rise and persist for extended periods, aided by social conformism within groups. We develop analytical approximations to calculate the mean time taken for memes to become extinct and the mean time spent in each population state. These approximations enable us to apply the meme equations to conduct a qualitative analysis.

When stochasticity leads to cooperation.

The evolution of cooperation has gained more attention after Smith introduced game theory in the study of evolutionary biology. Subsequent works have extensively explained this phenomenon, consistently showing the importance of spatial structure for the evolution of cooperation. Here we analyze the effect of stochasticity on the evolution of cooperation in group-structured populations. We find a simple formula for the fixation probability of cooperators and show that cooperation can be favored by selection if a condition similar to Hamilton's rule is satisfied, which is also valid for strong selection and high migration. In fact, cooperation can be favored even in the absence of population viscosity and in the limit of an infinite number of finite-size groups. We discuss the importance of stochastic fluctuations in helping cooperation. We argue that this may be a general principle because fluctuations favoring the cooperators are often much more impactful than those favoring the defectors.

Hidden role of mutations in the evolutionary process.

Mutations not only alter allele frequencies in a genetic pool but may also determine the fate of an evolutionary process. Here we study which allele fixes in a one-step, one-way model including the wild type and two adaptive mutations. We study the effect of the four basic evolutionary mechanisms-genetic drift, natural selection, mutation, and gene flow-on mutant fixation and its kinetics. Determining which allele is more likely to fix is not simply a question of comparing fitnesses and mutation rates. For instance, if the allele of interest is less fit than the other, then not only must it have a greater mutation rate, but also its mutation rate must exceed a specific threshold for it to prevail. We find exact expressions for such conditions. Our conclusions are based on the mathematical description of two extreme but important regimes, as well as on simulations.

Moderate immigration may promote a peak of cooperation among natives.

In a world of hardening borders, nations may deprive themselves of enjoying the benefits of cooperative immigrants. Here we analyze the effect of efficient cooperative immigrants on a population playing public goods games. We considered a population structured on a square lattice with individuals playing public goods games with their neighbors. The demographics are determined by stochastic birth, death, and migration. The strategies spread through imitation dynamics. Our model shows that cooperation among natives can emerge due to social contagion of good role-model agents that can provide better quality public goods. Only a small fraction of efficient cooperators, among immigrants, is enough to trigger cooperation across the native population. We see that native cooperation achieves its peak at moderate values of immigration rate. Such efficient immigrant cooperators act as nucleation centers for the growth of cooperative clusters, which eventually dominate defection.

Positive interactions may decrease cooperation in social dilemma experiments.

A social dilemma appears in the public goods problem, where the individual has to decide whether to contribute to a common resource. The total contributions to the common pool are increased by a synergy factor and evenly split among the members. The ideal outcome occurs if everyone contributes the maximum amount. However, regardless of what the others do, each individual is better off by contributing nothing. Yet, cooperation is largely observed in human society. Many mechanisms have been shown to promote cooperation in humans, alleviating, or even resolving, the social dilemma. One class of mechanisms that is under-explored is the spillover of experiences obtained from different environments. There is some evidence that positive experiences promote cooperative behaviour. Here, we address the question of how experiencing positive cooperative interactions - obtained in an environment where cooperation yields high returns - affects the level of cooperation in social dilemma interactions. In a laboratory experiment, participants played repeated public goods games (PGGs) with rounds alternating between positive interactions and social dilemma interactions. We show that, instead of promoting pro-social behaviour, the presence of positive interactions lowered the level of cooperation in the social dilemma interactions. Our analysis suggests that the high return obtained in the positive interactions sets a reference point that accentuates participants' perceptions that contributing in social dilemma interactions is a bad investment.

Role-separating ordering in social dilemmas controlled by topological frustration.

''Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.

Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas.

In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a win-stay-lose-shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average neighbor. Here we investigate this model in the realm of evolutionary social dilemmas on the square lattice and scale-free networks. By using the master equation and Monte Carlo simulations, we find that cooperators coexist with defectors in the whole phase diagram, even at high temptations to defect. We study the microscopic mechanism that is responsible for the striking persistence of cooperative behavior and find that cooperation spreads through second-order neighbors, rather than by means of network reciprocity that dominates in imitation-based models. For the square lattice the master equation can be solved analytically in the large temperature limit of the Fermi function, while for other cases the resulting differential equations must be solved numerically. Either way, we find good qualitative agreement with the Monte Carlo simulation results. Our analysis also reveals that the evolutionary outcomes are to a large degree independent of the network topology, including the number of neighbors that are considered for payoff determination on lattices, which further corroborates the local character of the microscopic dynamics. Unlike large-scale spatial patterns that typically emerge due to network reciprocity, here local checkerboard-like patterns remain virtually unaffected by differences in the macroscopic properties of the interaction network.

Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity.

Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two different games. While in well-mixed populations the random mixture of the two games is always equivalent to the average single game, in structured populations this is not always the case. We show that the outcome is, in fact, strongly dependent on the distance of separation of the two games in the parameter space. Effectively, this distance introduces payoff heterogeneity, and the average game is returned only if the heterogeneity is small. For higher levels of heterogeneity the distance to the average game grows, which often involves the promotion of cooperation. The presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin, and they also emphasize the importance of the population structure in amplifying facilitators of cooperation.

Targeted Cooperative Actions Shape Social Networks.

Individual acts of cooperation give rise to dynamic social networks. Traditionally, models for cooperation in structured populations are based on a separation of individual strategies and of population structure. Individuals adopt a strategy-typically cooperation or defection, which determines their behaviour toward their neighbours as defined by an interaction network. Here, we report a behavioural experiment that amalgamates strategies and structure to empirically investigate the dynamics of social networks. The action of paying a cost c to provide a benefit b is represented as a directed link point from the donor to the recipient. Participants can add and/or remove links to up to two recipients in each round. First, we show that dense networks emerge, where individuals are characterized by fairness: they receive to the same extent they provide. More specifically, we investigate how participants use information about the generosity and payoff of others to update their links. It turns out that aversion to payoff inequity was the most consistent update rule: adding links to individuals that are worse off and removing links to individuals that are better off. We then investigate the effect of direct reciprocation, showing that the possibility of direct reciprocation does not increase cooperation as compared to the treatment where participants are totally unaware of who is providing benefits to them.

Cooperation and coauthorship in scientific publishing.

Research collaboration occurs more frequently today than in the past. As a consequence, cooperation and competition are crucial determinants of academic success. In multiauthored publications, not all authors contribute evenly. Hence, some authors end up with less time or resources to work on parallel projects, decreasing their number of publications. Although detailed information on the contribution of each author in multiauthored publications is generally not available, the order of authors often discloses information on differential contributions. Here we analyze the full data set of Physical Review journals to show that, along with the increasingly number of multiauthored publications, first authors incur costs and last authors are bestowed benefits in terms of number of publications. In other words, authors publishing more often as first authors have fewer publications in the short-term than authors publishing more often as last authors. Using a simplified network representation where direct links represent the costly action of first authors towards last authors, we analyze the evolution of cooperation in multiauthored publications.

Origin and structure of dynamic cooperative networks.

Societies are built on social interactions among individuals. Cooperation represents the simplest form of a social interaction: one individual provides a benefit to another one at a cost to itself. Social networks represent a dynamical abstraction of social interactions in a society. The behaviour of an individual towards others and of others towards the individual shape the individual's neighbourhood and hence the local structure of the social network. Here we propose a simple theoretical framework to model dynamic social networks by focussing on each individual's actions instead of interactions between individuals. This eliminates the traditional dichotomy between the strategy of individuals and the structure of the population and easily complements empirical studies. As a consequence, altruists, egoists and fair types are naturally determined by the local social structures, while globally egalitarian networks or stratified structures arise. Cooperative interactions drive the emergence and shape the structure of social networks.

Distinguishing the opponents promotes cooperation in well-mixed populations.

Cooperation has been widely studied when an individual strategy is adopted against all coplayers. In this context, some extra mechanisms, such as punishment, reward, memory, and network reciprocity must be introduced in order to keep cooperators alive. Here, we adopt a different point of view. We study the adoption of different strategies against different opponents instead of adoption of the same strategy against all of them. In the context of the prisoner dilemma, we consider an evolutionary process in which strategies that provide more benefits are imitated and the players replace the strategy used in one of the interactions furnishing the worst payoff. Individuals are set in a well-mixed population, so that network reciprocity effect is excluded and both synchronous and asynchronous updates are analyzed. As a consequence of the replacement rule, we show that mutual cooperation is never destroyed and the initial fraction of mutual cooperation is a lower bound for the level of cooperation. We show by simulation and mean-field analysis that (i) cooperation dominates for synchronous update and (ii) only the initial mutual cooperation is maintained for asynchronous update. As a side effect of the replacement rule, an "implicit punishment" mechanism comes up in a way that exploitations are always neutralized providing evolutionary stability for cooperation.