23,808 research outputs found
Universality of weak selection
Weak selection, which means a phenotype is slightly advantageous over
another, is an important limiting case in evolutionary biology. Recently it has
been introduced into evolutionary game theory. In evolutionary game dynamics,
the probability to be imitated or to reproduce depends on the performance in a
game. The influence of the game on the stochastic dynamics in finite
populations is governed by the intensity of selection. In many models of both
unstructured and structured populations, a key assumption allowing analytical
calculations is weak selection, which means that all individuals perform
approximately equally well. In the weak selection limit many different
microscopic evolutionary models have the same or similar properties. How
universal is weak selection for those microscopic evolutionary processes? We
answer this question by investigating the fixation probability and the average
fixation time not only up to linear, but also up to higher orders in selection
intensity. We find universal higher order expansions, which allow a rescaling
of the selection intensity. With this, we can identify specific models which
violate (linear) weak selection results, such as the one--third rule of
coordination games in finite but large populations.Comment: 12 pages, 3 figures, accepted for publication in Physical Review
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
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
Fast flowing populations are not well mixed
In evolutionary dynamics, well-mixed populations are almost always associated
with all-to-all interactions; mathematical models are based on complete graphs.
In most cases, these models do not predict fixation probabilities in groups of
individuals mixed by flows. We propose an analytical description in the
fast-flow limit. This approach is valid for processes with global and local
selection, and accurately predicts the suppression of selection as competition
becomes more local. It provides a modelling tool for biological or social
systems with individuals in motion.Comment: 19 pages, 8 figure
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