26 research outputs found
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
Most undirected random graphs are amplifiers of selection for Birth-death dynamics, but suppressors of selection for death-Birth dynamics
We analyze evolutionary dynamics on graphs, where the nodes represent
individuals of a population. The links of a node describe which other
individuals can be displaced by the offspring of the individual on that node.
Amplifiers of selection are graphs for which the fixation probability is
increased for advantageous mutants and decreased for disadvantageous mutants. A
few examples of such amplifiers have been developed, but so far it is unclear
how many such structures exist and how to construct them. Here, we show that
almost any undirected random graph is an amplifier of selection for Birth-death
updating, where an individual is selected to reproduce with probability
proportional to its fitness and one of its neighbors is replaced by that
offspring at random. If we instead focus on death-Birth updating, in which a
random individual is removed and its neighbors compete for the empty spot, then
the same ensemble of graphs consists of almost only suppressors of selection
for which the fixation probability is decreased for advantageous mutants and
increased for disadvantageous mutants. Thus, the impact of population structure
on evolutionary dynamics is a subtle issue that will depend on seemingly minor
details of the underlying evolutionary process
Counterintuitive properties of the fixation time in network-structured populations
Evolutionary dynamics on graphs can lead to many interesting and
counterintuitive findings. We study the Moran process, a discrete time
birth-death process, that describes the invasion of a mutant type into a
population of wild-type individuals. Remarkably, the fixation probability of a
single mutant is the same on all regular networks. But non-regular networks can
increase or decrease the fixation probability. While the time until fixation
formally depends on the same transition probabilities as the fixation
probabilities, there is no obvious relation between them. For example, an
amplifier of selection, which increases the fixation probability and thus
decreases the number of mutations needed until one of them is successful, can
at the same time slow down the process of fixation. Based on small networks, we
show analytically that (i) the time to fixation can decrease when links are
removed from the network and (ii) the node providing the best starting
conditions in terms of the shortest fixation time depends on the fitness of the
mutant. Our results are obtained analytically on small networks, but numerical
simulations show that they are qualitatively valid even in much larger
populations
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
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
Evolutionary game dynamics is one of the most fruitful frameworks for
studying evolution in different disciplines, from Biology to Economics. Within
this context, the approach of choice for many researchers is the so-called
replicator equation, that describes mathematically the idea that those
individuals performing better have more offspring and thus their frequency in
the population grows. While very many interesting results have been obtained
with this equation in the three decades elapsed since it was first proposed, it
is important to realize the limits of its applicability. One particularly
relevant issue in this respect is that of non-mean-field effects, that may
arise from temporal fluctuations or from spatial correlations, both neglected
in the replicator equation. This review discusses these temporal and spatial
effects focusing on the non-trivial modifications they induce when compared to
the outcome of replicator dynamics. Alongside this question, the hypothesis of
linearity and its relation to the choice of the rule for strategy update is
also analyzed. The discussion is presented in terms of the emergence of
cooperation, as one of the current key problems in Biology and in other
disciplines.Comment: Review, 48 pages, 26 figure
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Spatial Invasion of Cooperation
The evolutionary puzzle of cooperation describes situations where cooperators provide a fitness benefit to other individuals at some cost to themselves. Under Darwinian selection, the evolution of cooperation is a conundrum, whereas non-cooperation (or defection) is not. In the absence of supporting mechanisms, cooperators perform poorly and decrease in abundance. Evolutionary game theory provides a powerful mathematical framework to address the problem of cooperation using the prisoner's dilemma. One well-studied possibility to maintain cooperation is to consider structured populations, where each individual interacts only with a limited subset of the population. This enables cooperators to form clusters such that they are more likely to interact with other cooperators instead of being exploited by defectors. Here we present a detailed analysis of how a few cooperators invade and expand in a world of defectors. If the invasion succeeds, the expansion process takes place in two stages: first, cooperators and defectors quickly establish a local equilibrium and then they uniformly expand in space. The second stage provides good estimates for the global equilibrium frequencies of cooperators and defectors. Under hospitable conditions, cooperators typically form a single, ever growing cluster interspersed with specks of defectors, whereas under more hostile conditions, cooperators form isolated, compact clusters that minimize exploitation by defectors. We provide the first quantitative assessment of the way cooperators arrange in space during invasion and find that the macroscopic properties and the emerging spatial patterns reveal information about the characteristics of the underlying microscopic interactions.MathematicsOrganismic and Evolutionary Biolog