# Evolutionary dynamics and fixation probabilities in directed networks

@article{Masuda2009EvolutionaryDA, title={Evolutionary dynamics and fixation probabilities in directed networks}, author={Naoki Masuda and Hisashi Ohtsuki}, journal={New Journal of Physics}, year={2009}, volume={11}, pages={033012} }

In this paper, we investigate the evolutionary dynamics in directed and/or weighted networks. We study the fixation probability of a mutant in finite populations in stochastic voter-type dynamics for several update rules. The fixation probability is defined as the probability of a newly introduced mutant in a wild-type population taking over the entire population. In contrast to the case of undirected and unweighted networks, the fixation probability of a mutant in directed networks is…

## 71 Citations

### An analysis of fixation probability of a mutant on a class of weighted networks under neutral selection

- Computer ScienceIECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society
- 2011

The analytical solutions of fixation probability of mutants on the weighted networks with three different updating rules, including link dynamics, Moran process, and voter model are attained.

### Early appraisal of the fixation probability in directed networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

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.

### The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population

- Mathematics, Computer SciencePLoS Comput. Biol.
- 2021

This work proposes a model that couples the population dynamics to the network structure and shows that in this case, the isothermal theorem is being violated and the fixation probability behavior in terms of the complexity parameter.

### Fast and deterministic computation of fixation probability in evolutionary graphs

- Computer Science, Mathematics
- 2011

A novel deterministic algorithm for computing fixation probabilities for strongly connected directed, weighted evolutionary graphs under the case of neutral drift is introduced, which is shown to be a lower bound for the case where the mutant is more fit than the rest of the population (previously, this was only observed from simulation).

### Martingales and fixation probabilities of evolutionary graphs

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2014

Evolutionary graph theory is the study of birth–death processes that are constrained by population structure. A principal problem in evolutionary graph theory is to obtain the probability that some…

### Directionality of contact networks suppresses selection pressure in evolutionary dynamics.

- BiologyJournal of theoretical biology
- 2009

### FAST AND DETERMINISTIC COMPUTATION OF FIXATION

- Computer Science, Mathematics
- 2012

A novel deterministic algorithm for computing fixation probabilities for strongly connected directed, weighted evolutionary graphs under the case of neutral drift, which is shown to be a lower bound for the case where the mutant is more fit than the rest of the population (previously, this was only observed from simulation).

### 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.

### Network growth for enhanced natural selection.

- BiologyPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

This work presents a randomized mechanism for network growth that is loosely inspired in some of these topologies' key properties and demonstrates that it is capable of giving rise to structured populations for which the fixation probability significantly surpasses that of an unstructured population.

### Characterizing the effect of network structure on evolutionary dynamics via a novel measure of structural heterogeneity

- Economics2013 25th Chinese Control and Decision Conference (CCDC)
- 2013

Findings provide a fundamental principle for designing selection amplifier, which benefits advantageous invaders while inhibits unadvantageous ones in birth-death process and selection amplifiers with specified size and average degree are proposed.

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