274 research outputs found
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
Fixation probabilities in populations under demographic fluctuations
We study the fixation probability of a mutant type when introduced into a
resident population. As opposed to the usual assumption of constant pop-
ulation size, we allow for stochastically varying population sizes. This is
implemented by a stochastic competitive Lotka-Volterra model. The compe- tition
coefficients are interpreted in terms of inverse payoffs emerging from an
evolutionary game. Since our study focuses on the impact of the competition
values, we assume the same birth and death rates for both types. In this gen-
eral framework, we derive an approximate formula for the fixation probability
{\phi} of the mutant type under weak selection. The qualitative behavior of
{\phi} when compared to the neutral scenario is governed by the invasion
dynamics of an initially rare type. Higher payoffs when competing with the
resident type yield higher values of {\phi}. Additionally, we investigate the
influence of the remaining parameters and find an explicit dependence of {\phi}
on the mixed equilibrium value of the corresponding deterministic system (given
that the parameter values allow for its existence).Comment: 31 pages, 7 figure
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
Mutualism and evolutionary multiplayer games: revisiting the Red King
Coevolution of two species is typically thought to favour the evolution of
faster evolutionary rates helping a species keep ahead in the Red Queen race,
where `it takes all the running you can do to stay where you are'. In contrast,
if species are in a mutualistic relationship, it was proposed that the Red King
effect may act, where it can be beneficial to evolve slower than the
mutualistic species. The Red King hypothesis proposes that the species which
evolves slower can gain a larger share of the benefits. However, the
interactions between the two species may involve multiple individuals. To
analyse such a situation, we resort to evolutionary multiplayer games. Even in
situations where evolving slower is beneficial in a two-player setting, faster
evolution may be favoured in a multiplayer setting. The underlying features of
multiplayer games can be crucial for the distribution of benefits. They also
suggest a link between the evolution of the rate of evolution and group size
A Minimal Model for Tag-based Cooperation
Recently, Riolo et al. [R. L. Riolo et al., Nature 414, 441 (2001)] showed by
computer simulations that cooperation can arise without reciprocity when agents
donate only to partners who are sufficiently similar to themselves. One
striking outcome of their simulations was the observation that the number of
tolerant agents that support a wide range of players was not constant in time,
but showed characteristic fluctuations. The cause and robustness of these tides
of tolerance remained to be explored. Here we clarify the situation by solving
a minimal version of the model of Riolo et al. It allows us to identify a net
surplus of random changes from intolerant to tolerant agents as a necessary
mechanism that produces these oscillations of tolerance which segregate
different agents in time. This provides a new mechanism for maintaining
different agents, i.e. for creating biodiversity. In our model the transition
to the oscillating state is caused by a saddle node bifurcation. The frequency
of the oscillations increases linearly with the transition rate from tolerant
to intolerant agents.Comment: 8 pages, 9 figure
Extinction dynamics from meta-stable coexistences in an evolutionary game
Deterministic evolutionary game dynamics can lead to stable coexistences of
different types. Stochasticity, however, drives the loss of such coexistences.
This extinction is usually accompanied by population size fluctuations. We
investigate the most probable extinction trajectory under such fluctuations by
mapping a stochastic evolutionary model to a problem of classical mechanics
using the Wentzel-Kramers-Brillouin (WKB) approximation. Our results show that
more abundant types in a coexistence can be more likely to go extinct first
well agreed with previous results, and also the distance between the
coexistence and extinction point is not a good predictor of extinction.
Instead, the WKB method correctly predicts the type going extinct first
Cyclic dominance and biodiversity in well-mixed populations
Coevolutionary dynamics is investigated in chemical catalysis, biological
evolution, social and economic systems. The dynamics of these systems can be
analyzed within the unifying framework of evolutionary game theory. In this
Letter, we show that even in well-mixed finite populations, where the dynamics
is inherently stochastic, biodiversity is possible with three cyclic dominant
strategies. We show how the interplay of evolutionary dynamics, discreteness of
the population, and the nature of the interactions influences the coexistence
of strategies. We calculate a critical population size above which coexistence
is likely.Comment: Physical Review Letters, in print (2008
Evolutionary Multiplayer Games
Evolutionary game theory has become one of the most diverse and far reaching
theories in biology. Applications of this theory range from cell dynamics to
social evolution. However, many applications make it clear that inherent
non-linearities of natural systems need to be taken into account. One way of
introducing such non-linearities into evolutionary games is by the inclusion of
multiple players. An example is of social dilemmas, where group benefits could
e.g.\ increase less than linear with the number of cooperators. Such
multiplayer games can be introduced in all the fields where evolutionary game
theory is already well established. However, the inclusion of non-linearities
can help to advance the analysis of systems which are known to be complex, e.g.
in the case of non-Mendelian inheritance. We review the diachronic theory and
applications of multiplayer evolutionary games and present the current state of
the field. Our aim is a summary of the theoretical results from well-mixed
populations in infinite as well as finite populations. We also discuss examples
from three fields where the theory has been successfully applied, ecology,
social sciences and population genetics. In closing, we probe certain future
directions which can be explored using the complexity of multiplayer games
while preserving the promise of simplicity of evolutionary games.Comment: 14 pages, 2 figures, review pape
Cancer initiation with epistatic interactions between driver and passenger mutations
We investigate the dynamics of cancer initiation in a mathematical model with
one driver mutation and several passenger mutations. Our analysis is based on a
multi type branching process: We model individual cells which can either divide
or undergo apoptosis. In case of a cell division, the two daughter cells can
mutate, which potentially confers a change in fitness to the cell. In contrast
to previous models, the change in fitness induced by the driver mutation
depends on the genetic context of the cell, in our case on the number of
passenger mutations. The passenger mutations themselves have no or only a very
small impact on the cell's fitness. While our model is not designed as a
specific model for a particular cancer, the underlying idea is motivated by
clinical and experimental observations in Burkitt Lymphoma. In this tumor, the
hallmark mutation leads to deregulation of the MYC oncogene which increases the
rate of apoptosis, but also the proliferation rate of cells. This increase in
the rate of apoptosis hence needs to be overcome by mutations affecting
apoptotic pathways, naturally leading to an epistatic fitness landscape. This
model shows a very interesting dynamical behavior which is distinct from the
dynamics of cancer initiation in the absence of epistasis. Since the driver
mutation is deleterious to a cell with only a few passenger mutations, there is
a period of stasis in the number of cells until a clone of cells with enough
passenger mutations emerges. Only when the driver mutation occurs in one of
those cells, the cell population starts to grow rapidly
When the mean is not enough: Calculating fixation time distributions in birth-death processes
Studies of fixation dynamics in Markov processes predominantly focus on the
mean time to absorption. This may be inadequate if the distribution is broad
and skewed. We compute the distribution of fixation times in one-step
birth-death processes with two absorbing states. These are expressed in terms
of the spectrum of the process, and we provide different representations as
forward-only processes in eigenspace. These allow efficient sampling of
fixation time distributions. As an application we study evolutionary game
dynamics, where invading mutants can reach fixation or go extinct. We also
highlight the median fixation time as a possible analog of mixing times in
systems with small mutation rates and no absorbing states, whereas the mean
fixation time has no such interpretation.Comment: Published in PRE. 14 pages, 6 figure
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