# Universality of fixation probabilities in randomly structured populations

@article{Adlam2014UniversalityOF, title={Universality of fixation probabilities in randomly structured populations}, author={Ben Adlam and Martin A. Nowak}, journal={Scientific Reports}, year={2014}, volume={4} }

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…

## 42 Citations

Counterintuitive properties of fixation probability and fixation time in population structures with spatially periodic resource distribution

- Biology
- 2022

This work identifies levels of heterogeneity for which a previously deleterious mutant, in a uniform environment, becomes beneficial and discusses ‘fitness shift’ model where the fitness function of one type is identical to the other up to a constant spatial shift.

Counterintuitive properties of the fixation time in network-structured populations

- Computer ScienceJournal of The Royal Society Interface
- 2014

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

- MathematicsNature
- 2017

It is found that cooperation flourishes most in societies that are based on strong pairwise ties, and a solution for weak selection that applies to any graph or network is provided.

Most Undirected Random Graphs Are Amplifiers of Selection for Birth-Death Dynamics, but Suppressors of Selection for Death-Birth Dynamics

- MathematicsPLoS Comput. Biol.
- 2015

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

- Biology
- 2020

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

- MathematicsScientific Reports
- 2017

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

- Computer SciencebioRxiv
- 2021

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.

Martingales and the fixation probability of high-dimensional evolutionary graphs.

- MathematicsJournal of theoretical biology
- 2018

Effects of motion in structured populations

- BiologyJournal of The Royal Society Interface
- 2017

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

- Economics
- 2017

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.

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