111,990 research outputs found
Roles of mutation rate and co-existence of multiple strategy updating rules in evolutionary prisoner's dilemma games
The emergence and maintenance of cooperation has attracted intensive
scholarly interest and has been analysed within the framework of evolutionary
game theory. The role of innovation, which introduces novel strategies into the
population, is a relatively understudied aspect of evolutionary game theory.
Here, we investigate the effects of two sources of innovation---mutation and
heterogeneous updating rules. These mechanisms allow agents to adopt strategies
that do not rely on the imitation of other individuals. The model
introduces---in addition to canonical imitation-based strategy
updating---aspiration-based updating, whereby agents switch their strategy by
referring solely to the performance of their own strategy; mutation also
introduces novel strategies into the population. Our simulation results show
that the introduction of aspiration-based rules into a population of imitators
leads to the deterioration of cooperation. In addition, mutation, in
combination with heterogeneous updating rules, also diminishes cooperators.
This phenomenon is prominent when a large proportion of the population consists
of imitators rather than adopters of aspiration-based updating. Nevertheless, a
high mutation rate, in combination with a low aspiration level, has positive
nonlinear effects, and a heterogeneous population achieves a higher level of
cooperation than the weighted average of homogeneous populations. Our results
demonstrate the profound role of innovation in the evolution of cooperation.Comment: 7 pages, 8 figures, Figs 3(b) and 8 were added following the
reviewers' comment
Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation
Real social interactions occur on networks in which each individual is
connected to some, but not all, of others. In social dilemma games with a fixed
population size, heterogeneity in the number of contacts per player is known to
promote evolution of cooperation. Under a common assumption of positively
biased payoff structure, well-connected players earn much by playing
frequently, and cooperation once adopted by well-connected players is
unbeatable and spreads to others. However, maintaining a social contact can be
costly, which would prevent local payoffs from being positively biased. In
replicator-type evolutionary dynamics, it is shown that even a relatively small
participation cost extinguishes the merit of heterogeneous networks in terms of
cooperation. In this situation, more connected players earn less so that they
are no longer spreaders of cooperation. Instead, those with fewer contacts win
and guide the evolution. The participation cost, or the baseline payoff, is
irrelevant in homogeneous populations but is essential for evolutionary games
on heterogeneous networks.Comment: 4 figures + 3 supplementary figure
From Local to Global Dilemmas in Social Networks
Social networks affect in such a fundamental way the dynamics of the population they support that the global, population-wide behavior that one observes often bears no relation to the individual processes it stems from. Up to now, linking the global networked dynamics to such individual mechanisms has remained elusive. Here we study the evolution of cooperation in networked populations and let individuals interact via a 2-person Prisoner's Dilemma – a characteristic defection dominant social dilemma of cooperation. We show how homogeneous networks transform a Prisoner's Dilemma into a population-wide evolutionary dynamics that promotes the coexistence between cooperators and defectors, while heterogeneous networks promote their coordination. To this end, we define a dynamic variable that allows us to track the self-organization of cooperators when co-evolving with defectors in networked populations. Using the same variable, we show how the global dynamics — and effective dilemma — co-evolves with the motifs of cooperators in the population, the overall emergence of cooperation depending sensitively on this co-evolution
Evolutionary dynamics on any population structure
Evolution occurs in populations of reproducing individuals. The structure of
a biological population affects which traits evolve. Understanding evolutionary
game dynamics in structured populations is difficult. Precise results have been
absent for a long time, but have recently emerged for special structures where
all individuals have the same number of neighbors. But the problem of
determining which trait is favored by selection in the natural case where the
number of neighbors can vary, has remained open. For arbitrary selection
intensity, the problem is in a computational complexity class which suggests
there is no efficient algorithm. Whether there exists a simple solution for
weak selection was unanswered. Here we provide, surprisingly, a general formula
for weak selection that applies to any graph or social network. Our method uses
coalescent theory and relies on calculating the meeting times of random walks.
We can now evaluate large numbers of diverse and heterogeneous population
structures for their propensity to favor cooperation. We can also study how
small changes in population structure---graph surgery---affect evolutionary
outcomes. We find that cooperation flourishes most in societies that are based
on strong pairwise ties.Comment: 68 pages, 10 figure
Temporal networks provide a unifying understanding of the evolution of cooperation
Understanding the evolution of cooperation in structured populations
represented by networks is a problem of long research interest, and a most
fundamental and widespread property of social networks related to cooperation
phenomena is that the node's degree (i.e., number of edges connected to the
node) is heterogeneously distributed. Previous results indicate that static
heterogeneous (i.e., degree-heterogeneous) networks promote cooperation in
stationarity compared to static regular (i.e., degree-homogeneous) networks if
equilibrium dynamics starting from many cooperators and defectors is employed.
However, the above conclusion reverses if we employ non-equilibrium stochastic
processes to measure the fixation probability for cooperation, i.e., the
probability that a single cooperator successfully invades a population. Here we
resolve this conundrum by analyzing the fixation of cooperation on temporal
(i.e., time-varying) networks. We theoretically prove and numerically confirm
that on both synthetic and empirical networks, contrary to the case of static
networks, temporal heterogeneous networks can promote cooperation more than
temporal regular networks in terms of the fixation probability of cooperation.
Given that the same conclusion is known for the equilibrium fraction of
cooperators on temporal networks, the present results provide a unified
understanding of the effect of temporal degree heterogeneity on promoting
cooperation across two main analytical frameworks, i.e., equilibrium and
non-equilibrium ones.Comment: 7 pages, 4 figure
Resource heterogeneity and the evolution of public-goods cooperation
Authors thank NERC, BBSRC, AXA research fund, Royal Society (AB & AG) and ERC 370 (AG) for funding.Heterogeneity in resources is a ubiquitous feature of natural landscapes affecting many aspects of biology. However, the effect of environmental heterogeneity on the evolution of cooperation has been less well studied. Here, using a mixture of theory and experiments measuring siderophore production by the bacterium Pseudomonas aeruginosa as a model for public goods based cooperation, we explore the effect of heterogeneity in resource availability. We show that cooperation in metapopulations that were spatially heterogeneous in terms of resources can be maintained at a higher level than in homogeneous metapopulations of the same average resource value. The results can be explained by a positive covariance between fitness of cooperators, population size, and local resource availability, which allowed cooperators to have a disproportionate advantage within the heterogeneous metapopulations. These results suggest that natural environmental variation may help to maintain cooperation.Publisher PDFPeer reviewe
Evolutionary game dynamics in phenotype space
Evolutionary dynamics can be studied in well-mixed or structured populations.
Population structure typically arises from the heterogeneous distribution of
individuals in physical space or on social networks. Here we introduce a new
type of space to evolutionary game dynamics: phenotype space. The population is
well-mixed in the sense that everyone is equally likely to interact with
everyone else, but the behavioral strategies depend on distance in phenotype
space. Individuals might behave differently towards those who look similar or
dissimilar. Individuals mutate to nearby phenotypes. We study the `phenotypic
space walk' of populations. We present analytic calculations that bring
together ideas from coalescence theory and evolutionary game dynamics. As a
particular example, we investigate the evolution of cooperation in phenotype
space. We obtain a precise condition for natural selection to favor cooperators
over defectors: for a one-dimensional phenotype space and large population size
the critical benefit-to-cost ratio is given by b/c=1+2/sqrt{3}. We derive the
fundamental condition for any evolutionary game and explore higher dimensional
phenotype spaces.Comment: version 2: minor changes; equivalent to final published versio
Evolutionary Game Dynamics in Populations with Heterogenous Structures
Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place. In particular, averaging payoffs garnered through game interactions rather than accumulating the payoffs can altogether remove the cooperative advantage of heterogeneous graphs while such a difference does not affect the outcome on homogeneous structures. In addition, the rate at which game interactions occur can alter the evolutionary outcome. Less interactions allow heterogeneous graphs to support more cooperation than homogeneous graphs, while higher rates of interactions make homogeneous and heterogeneous graphs virtually indistinguishable in their ability to support cooperation. Most importantly, we show that common measures of evolutionary advantage used in homogeneous populations, such as a comparison of the fixation probability of a rare mutant to that of the resident type, are no longer valid in heterogeneous populations. Heterogeneity causes a bias in where mutations occur in the population which affects the mutant\u27s fixation probability. We derive the appropriate measures for heterogeneous populations that account for this bias
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