67 research outputs found
The edge of neutral evolution in social dilemmas
The functioning of animal as well as human societies fundamentally relies on
cooperation. Yet, defection is often favorable for the selfish individual, and
social dilemmas arise. Selection by individuals' fitness, usually the basic
driving force of evolution, quickly eliminates cooperators. However, evolution
is also governed by fluctuations that can be of greater importance than fitness
differences, and can render evolution effectively neutral. Here, we investigate
the effects of selection versus fluctuations in social dilemmas. By studying
the mean extinction times of cooperators and defectors, a variable sensitive to
fluctuations, we are able to identify and quantify an emerging 'edge of neutral
evolution' that delineates regimes of neutral and Darwinian evolution. Our
results reveal that cooperation is significantly maintained in the neutral
regimes. In contrast, the classical predictions of evolutionary game theory,
where defectors beat cooperators, are recovered in the Darwinian regimes. Our
studies demonstrate that fluctuations can provide a surprisingly simple way to
partly resolve social dilemmas. Our methods are generally applicable to
estimate the role of random drift in evolutionary dynamics.Comment: 17 pages, 4 figure
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Pairwise Comparison and Selection Temperature in Evolutionary Game Dynamics
Recently, the frequency-dependent Moran process has been introduced in order to describe evolutionary game dynamics in finite populations. Here, an alternative to this process is investigated that is based on pairwise comparison between two individuals. We follow a long tradition in the physics community and introduce a temperature (of selection) to account for stochastic effects. We calculate the fixation probabilities and fixation times for any symmetric 2×2 game, for any intensity of selection and any initial number of mutants. The temperature can be used to gauge continuously from neutral drift to the extreme selection intensity known as imitation dynamics. For some payoff matrices the distribution of fixation times can become so broad that the average value is no longer very meaningful.MathematicsOrganismic and Evolutionary Biolog
Aspiration Dynamics of Multi-player Games in Finite Populations
Studying strategy update rules in the framework of evolutionary game theory,
one can differentiate between imitation processes and aspiration-driven
dynamics. In the former case, individuals imitate the strategy of a more
successful peer. In the latter case, individuals adjust their strategies based
on a comparison of their payoffs from the evolutionary game to a value they
aspire, called the level of aspiration. Unlike imitation processes of pairwise
comparison, aspiration-driven updates do not require additional information
about the strategic environment and can thus be interpreted as being more
spontaneous. Recent work has mainly focused on understanding how aspiration
dynamics alter the evolutionary outcome in structured populations. However, the
baseline case for understanding strategy selection is the well-mixed population
case, which is still lacking sufficient understanding. We explore how
aspiration-driven strategy-update dynamics under imperfect rationality
influence the average abundance of a strategy in multi-player evolutionary
games with two strategies. We analytically derive a condition under which a
strategy is more abundant than the other in the weak selection limiting case.
This approach has a long standing history in evolutionary game and is mostly
applied for its mathematical approachability. Hence, we also explore strong
selection numerically, which shows that our weak selection condition is a
robust predictor of the average abundance of a strategy. The condition turns
out to differ from that of a wide class of imitation dynamics, as long as the
game is not dyadic. Therefore a strategy favored under imitation dynamics can
be disfavored under aspiration dynamics. This does not require any population
structure thus highlights the intrinsic difference between imitation and
aspiration dynamics
Stochastic evolutionary game dynamics
In this review, we summarize recent developments in stochastic evolutionary
game dynamics of finite populations.Comment: To appear in "Reviews of Nonlinear Dynamics and Complexity" Vol. II,
Wiley-VCH, 2009, edited by H.-G. Schuste
Effect of spatial structure on the evolution of cooperation
16 pages, 14 figures.-- PACS nrs.: 89.65.−s, 87.23.Ge, 87.23.Kg, 02.50.Le.-- ArXiv pre-print available at: http://arxiv.org/abs/0806.1649Spatial structure is known to have an impact on the evolution of cooperation, and so it has been intensively studied during recent years. Previous work has shown the relevance of some features, such as the synchronicity of the updating, the clustering of the network, or the influence of the update rule. This has been done, however, for concrete settings with particular games, networks, and update rules, with the consequence that some contradictions have arisen and a general understanding of these topics is missing in the broader context of the space of 2×2 games. To address this issue, we have performed a systematic and exhaustive simulation in the different degrees of freedom of the problem. In some cases, we generalize previous knowledge to the broader context of our study and explain the apparent contradictions. In other cases, however, our conclusions refute what seems to be established opinions in the field, as for example the robustness of the effect of spatial structure against changes in the update rule, or offer new insights into the subject, e.g., the relation between the intensity of selection and the asymmetry between the effects on games with mixed equilibria.This work is partially supported by Ministerio
de Educación y Ciencia (Spain) under Grants Ingenio-MATHEMATICA and MOSAICO, and by Comunidad
de Madrid (Spain) under Grants SIMUMAT-CM and
MOSSNOHO-CM.Publicad
Evolutionary Game Theory: Theoretical Concepts and Applications to Microbial Communities
Ecological systems are complex assemblies of large numbers of individuals, interacting competitively under multifaceted environmental conditions. Recent studies using microbial laboratory communities have revealed some of the self-organization principles underneath the complexity of these systems. A major role of the inherent stochasticity of its dynamics and the spatial segregation of different interacting species into distinct patterns has thereby been established. It ensures the viability of microbial colonies by allowing for species diversity, cooperative behavior and other kinds of “social” behavior.
A synthesis of evolutionary game theory, nonlinear dynamics, and the theory of stochastic processes provides the mathematical tools and a conceptual framework for a deeper understanding of these ecological systems. We give an introduction into the modern formulation of these theories and illustrate their effectiveness focussing on selected examples of microbial systems. Intrinsic fluctuations, stemming from the discreteness of individuals, are ubiquitous, and can have an important impact on the stability of ecosystems. In the absence of speciation, extinction of species is unavoidable. It may, however, take very long times. We provide a general concept for defining survival and extinction on ecological time-scales. Spatial degrees of freedom come with a certain mobility of individuals. When the latter is sufficiently high, bacterial community structures can be understood through mapping individual-based models, in a continuum approach, onto stochastic partial differential equations. These allow progress using methods of nonlinear dynamics such as bifurcation analysis and invariant manifolds. We conclude with a perspective on the current challenges in quantifying bacterial pattern formation, and how this might have an impact on fundamental research in non-equilibrium physics
The mechanics of stochastic slowdown in evolutionary games
We study the stochastic dynamics of evolutionary games, and focus on the
so-called `stochastic slowdown' effect, previously observed in (Altrock et. al,
2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a
beneficial mutation may take longer to fixate than a neutral one. More
precisely, the fixation time conditioned on the mutant taking over can show a
maximum at intermediate selection strength. We show that this phenomenon is
present in the prisoner's dilemma, and also discuss counterintuitive slowdown
and speedup in coexistence games. In order to establish the microscopic origins
of these phenomena, we calculate the average sojourn times. This allows us to
identify the transient states which contribute most to the slowdown effect, and
enables us to provide an understanding of slowdown in the takeover of a small
group of cooperators by defectors: Defection spreads quickly initially, but the
final steps to takeover can be delayed substantially. The analysis of
coexistence games reveals even more intricate behavior. In small populations,
the conditional average fixation time can show multiple extrema as a function
of the selection strength, e.g., slowdown, speedup, and slowdown again. We
classify two-player games with respect to the possibility to observe
non-monotonic behavior of the conditional average fixation time as a function
of selection strength.Comment: Accepted for publication in the Journal of Theoretical Biology.
Includes changes after peer revie
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