Universality of fixation probabilities in randomly structured populations

  title={Universality of fixation probabilities in randomly structured populations},
  author={Ben Adlam and Martin A. Nowak},
  journal={Scientific Reports},
The stage of evolution is the population of reproducing individuals. The structure of the population is known to affect the dynamics and outcome of evolutionary processes, but analytical results for generic random structures have been lacking. The most general result so far, the isothermal theorem, assumes the propensity for change in each position is exactly the same, but realistic biological structures are always subject to variation and noise. We consider a finite population under constant… 
Counterintuitive properties of fixation probability and fixation time in population structures with spatially periodic resource distribution
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Counterintuitive properties of the fixation time in network-structured populations
The Moran process is studied, a discrete time birth–death process that describes the invasion of a mutant type into a population of wild-type individuals, and analytically it is shown that the time to fixation can decrease when links are removed from the network and the node providing the best starting conditions in terms of the shortest fixation time depends on the fitness of the mutant.
Evolutionary dynamics on any population structure
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Most Undirected Random Graphs Are Amplifiers of Selection for Birth-Death Dynamics, but Suppressors of Selection for Death-Birth Dynamics
It is shown 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.
A role of graphs in evolutionary processes
This thesis aims to understand how the underlying population structure affects the overall rate of evolution, and studies population structures that increase the fixation probability of advantageous mutants (called amplifiers of selection).
Amplification on Undirected Population Structures: Comets Beat Stars
It is shown that for a range of fitness values of the mutants, the Comet and Comet-swarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively.
Fixation probabilities in network structured meta-populations
This work studies the effect of complex network structure on the fixation probability, but instead of networks of individuals, it model a network of sub-populations with a probability of migration between them and asks how the structure of such a meta-population and the rate of migration affect the fixation probabilities.
Effects of motion in structured populations
It is proved that motion suppresses natural selection for death–birth (DB) updating or for any process that combines birth–death (BD) and DB updating, and a similar rule on dynamic graphs induced by a spatial flow is considered, indicating that continuous motion also suppressesnatural selection.
The effect of spatial fitness heterogeneity on fixation probability
This work introduces a novel formalism to approach any form of spatial fitness heterogeneity and finds that the mutant is favored relative to the resident if and only if the arithmetic mean of the mutant’s possible fitness values exceeds that of the resident.


Early appraisal of the fixation probability in directed networks.
For advantageous mutations in large populations and regardless of the network's topology, it is demonstrated that using a threshold of about [N/(r-1)](1/4) mutants, where N is the number of simulation events and r is the ratio of the mutants' fitness to that of the remainder of the population, leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations.
Evolutionary dynamics on graphs
This work determines the fixation probability of mutants, and characterize those graphs for which fixation behaviour is identical to that of a homogeneous population, and shows that the outcome of evolutionary games can depend entirely on the structure of the underlying graph.
On the fixation probability of superstars
It is shown that the fixation probability (in the limit, as graphs get larger) cannot exceed 1−1/j(r), where j(r)=Θ(r4), contrary to the claimed result.
Evolutionary dynamics on small-order graphs
Abstract We study the stochastic birth-death model for structured finite populations popularized by Lieberman et al. [E. Lieberman, C. Hauert and M. A. Nowak (2005), Evolutionary dynamics on graphs,
A Markov process of gene frequency change in a geographically structured population.
It is shown that there exists a stochastic clock that transforms the originally complicated process of gene frequency change to a random walk which is independent of the geographical structure of the population.
The effect of population structure on the rate of evolution
It is shown that the effects of population structure on the rate of evolution are more complex and subtle than previously recognized and the importance of fixation time is drawn attention.
The probability of fixation of a favoured allele in a subdivided population
The fixation probability is calculated using the diffusion approximation, showing that the effects of population structure on selected alleles cannot be understood from the behaviour of neutral markers.
Approximating evolutionary dynamics on networks using a Neighbourhood Configuration model.
An analysis of the fixation probability of a mutant on special classes of non-directed graphs
  • M. Broom, J. Rychtář
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2008
There is a growing interest in the study of evolutionary dynamics on populations with some non-homogeneous structure. In this paper we follow the model of Lieberman et al. (Lieberman et al. 2005