1,633 research outputs found
Spatial heterogeneity promotes coexistence of rock-paper-scissor metacommunities
The rock-paper-scissor game -- which is characterized by three strategies
R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and
R excludes S -- serves as a simple prototype for studying more complex
non-transitive systems. For well-mixed systems where interactions result in
fitness reductions of the losers exceeding fitness gains of the winners,
classical theory predicts that two strategies go extinct. The effects of
spatial heterogeneity and dispersal rates on this outcome are analyzed using a
general framework for evolutionary games in patchy landscapes. The analysis
reveals that coexistence is determined by the rates at which dominant
strategies invade a landscape occupied by the subordinate strategy (e.g. rock
invades a landscape occupied by scissors) and the rates at which subordinate
strategies get excluded in a landscape occupied by the dominant strategy (e.g.
scissor gets excluded in a landscape occupied by rock). These invasion and
exclusion rates correspond to eigenvalues of the linearized dynamics near
single strategy equilibria. Coexistence occurs when the product of the invasion
rates exceeds the product of the exclusion rates. Provided there is sufficient
spatial variation in payoffs, the analysis identifies a critical dispersal rate
required for regional persistence. For dispersal rates below , the
product of the invasion rates exceed the product of the exclusion rates and the
rock-paper-scissor metacommunities persist regionally despite being extinction
prone locally. For dispersal rates above , the product of the exclusion
rates exceed the product of the invasion rates and the strategies are
extinction prone. These results highlight the delicate interplay between
spatial heterogeneity and dispersal in mediating long-term outcomes for
evolutionary games.Comment: 31pages, 5 figure
Scale-free memory model for multiagent reinforcement learning. Mean field approximation and rock-paper-scissors dynamics
A continuous time model for multiagent systems governed by reinforcement
learning with scale-free memory is developed. The agents are assumed to act
independently of one another in optimizing their choice of possible actions via
trial-and-error search. To gain awareness about the action value the agents
accumulate in their memory the rewards obtained from taking a specific action
at each moment of time. The contribution of the rewards in the past to the
agent current perception of action value is described by an integral operator
with a power-law kernel. Finally a fractional differential equation governing
the system dynamics is obtained. The agents are considered to interact with one
another implicitly via the reward of one agent depending on the choice of the
other agents. The pairwise interaction model is adopted to describe this
effect. As a specific example of systems with non-transitive interactions, a
two agent and three agent systems of the rock-paper-scissors type are analyzed
in detail, including the stability analysis and numerical simulation.
Scale-free memory is demonstrated to cause complex dynamics of the systems at
hand. In particular, it is shown that there can be simultaneously two modes of
the system instability undergoing subcritical and supercritical bifurcation,
with the latter one exhibiting anomalous oscillations with the amplitude and
period growing with time. Besides, the instability onset via this supercritical
mode may be regarded as "altruism self-organization". For the three agent
system the instability dynamics is found to be rather irregular and can be
composed of alternate fragments of oscillations different in their properties.Comment: 17 pages, 7 figur
Quantum Structure in Competing Lizard Communities
Almost two decades of research on applications of the mathematical formalism
of quantum theory as a modeling tool in domains different from the micro-world
has given rise to many successful applications in situations related to human
behavior and thought, more specifically in cognitive processes of
decision-making and the ways concepts are combined into sentences. In this
article, we extend this approach to animal behavior, showing that an analysis
of an interactive situation involving a mating competition between certain
lizard morphs allows to identify a quantum theoretic structure. More in
particular, we show that when this lizard competition is analyzed structurally
in the light of a compound entity consisting of subentities, the contextuality
provided by the presence of an underlying rock-paper-scissors cyclic dynamics
leads to a violation of Bell's inequality, which means it is of a non-classical
type. We work out an explicit quantum-mechanical representation in Hilbert
space for the lizard situation and show that it faithfully models a set of
experimental data collected on three throat-colored morphs of a specific lizard
species. Furthermore, we investigate the Hilbert space modeling, and show that
the states describing the lizard competitions contain entanglement for each one
of the considered confrontations of lizards with different competing
strategies, which renders it no longer possible to interpret these states of
the competing lizards as compositions of states of the individual lizards.Comment: 28 page
Presence of a loner strain maintains cooperation and diversity in well-mixed bacterial communities
Cooperation and diversity abound in nature despite cooperators risking exploitation from defectors and superior competitors displacing weaker ones. Understanding the persistence of cooperation and diversity is therefore a major problem for evolutionary ecology, especially in the context of well-mixed populations, where the potential for exploitation and displacement is greatest. Here we demonstrate that a âloner effectâ, described by economic game theorists, can maintain cooperation and diversity in real-world biological settings. We use mathematical models of public-good-producing bacteria to show that the presence of a loner strain, which produces an independent but relatively inefficient good, can lead to rock-paper-scissor dynamics, whereby cooperators outcompete loners, defectors outcompete cooperators, and loners outcompete defectors. These model predictions are supported by our observations of evolutionary dynamics in well-mixed experimental communities of the bacterium Pseudomonas aeruginosa. We find that the coexistence of cooperators and defectors, which respectively produce and exploit the iron-scavenging siderophore pyoverdine, is stabilized by the presence of loners with an independent iron-uptake mechanism. Our results establish the loner effect as a simple and general driver of cooperation and diversity in environments that 40 would otherwise favour defection and the erosion of diversity.Publisher PDFPeer reviewe
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
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