Path to fixation of evolutionary processes in graph-structured populations

Hajihashemi, Mahdi; Samani, Keivan Aghababaei

doi:10.1140/epjb/s10051-021-00061-7

Cited by 6 publications

(9 citation statements)

References 51 publications

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“…There is wide possibility of application of Markov chain method not only RPS game. In refrences [ 50 , 51 ], we used Markov chain method for evaluating the Moran process. In many situations the issue of social dilemma represented by either Prisoner’s Dilemma, Chicken, or Stag Hunt games [ 71 , 72 ], therefore, applying this method on archetype 2 × 2 symmetric games will lead to significant results.…”

Section: Discussionmentioning

confidence: 99%

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Multi-strategy evolutionary games: A Markov chain approach

Hajihashemi

Samani

2022

PLoS ONE

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Interacting strategies in evolutionary games is studied analytically in a well-mixed population using a Markov chain method. By establishing a correspondence between an evolutionary game and Markov chain dynamics, we show that results obtained from the fundamental matrix method in Markov chain dynamics are equivalent to corresponding ones in the evolutionary game. In the conventional fundamental matrix method, quantities like fixation probability and fixation time are calculable. Using a theorem in the fundamental matrix method, conditional fixation time in the absorbing Markov chain is calculable. Also, in the ergodic Markov chain, the stationary probability distribution that describes the Markov chain’s stationary state is calculable analytically. Finally, the Rock, scissor, paper evolutionary game are evaluated as an example, and the results of the analytical method and simulations are compared. Using this analytical method saves time and computational facility compared to prevalent simulation methods.

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Section: Discussionmentioning

confidence: 99%

“…Markov chain method has been used for analyzing evolutionary games sincessfully [ 50 – 52 ] but it has never been used in an organized and intensive way. In this paper we stabilize the Markov chain method as a reliable method for evaluating evolutionary games.…”

Section: Introductionmentioning

confidence: 99%

Multi-strategy evolutionary games: A Markov chain approach

Hajihashemi

Samani

2022

PLoS ONE

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“…During the Moran process, when initially there is only one mutant present, it must eventually pass through state i in order to reach fixation. As a result, T i is modified to reflect the time required for a single mutant to reach fixation minus the time needed for i mutants to achieve fixation 13 . Therefore we have:…”

Section: Path To Fixationmentioning

confidence: 99%

The effect of community structure on fixation process in evolutionary graph theory

Mohamadichamgavi,

Zahedian

2024

Preprint

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Evolutionary graph theory investigates how population structure shapes evolutionary dynamics. In this paper, we examine how community structure impacts mutant fixation probability and time under the Moran Birth-death process with constant fitness. Specifically, we model the population as two fully connected subpopulations (communities) linked by a few links. Using an analytical Markov-chain approach supplemented by Monte Carlo simulations, we explore how the size of the starting community where the initial mutant arises influences its eventual fixation outcomes. We demonstrate that initiating the process in a smaller community boosts fixation probability and acts as an amplifier of selection compared to a larger community or a well-mixed population. A critical relative size threshold exists for the starting community, below which it functions as a selection amplifier. The unconditional fixation time displays different patterns depending on the starting community size and fitness value. For small communities, increased fitness reduces time, whereas, for larger communities, greater fitness prolongs time. Additionally, conditional fixation time grows with increased starting community size until a critical size and then decreases. This critical size is different depending on fitness value. In general, a combination of fitness level and starting community size serves to maximize the conditional fixation time.

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“…During the Moran process, when initially one mutant is present, it must eventually pass through state i to reach fixation. As a result, T i is modified to reflect the time required for a single mutant to reach fixation minus the time needed for i mutants to achieve fixation [31]. Therefore we have:…”

Section: Path To Fixationmentioning

confidence: 99%

The effect of initial placement of mutant in subdivided population on fixation time and probability

Mohamadichamgavi,

Zahedian

2024

Preprint

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Evolutionary graph theory investigates how population structure changes evolutionary dynamics. In this paper, we examine how the structure of a subdivided population impacts mutant fixation probability and time under the Moran Birth-death process with constant fitness. Specifically, we model the population as two fully connected subpopulations (cliques) linked by a few links. Using an analytical Markov-chain approach supplemented by Monte Carlo simulations, we explore how the size of the starting clique where the initial mutant arises influences its eventual fixation outcomes. We demonstrate that initiating the process in a smaller clique boosts fixation probability and acts as an amplifier of selection compared to a well-mixed population while a bigger starting clique acts as a suppressor of selection. Also, we show that both unconditional and conditional fixation time are affected by the starting clique size and fitness value. For small cliques, increased fitness reduces unconditional fixation time, whereas, for larger cliques, greater fitness prolongs it. Additionally, conditional fixation time grows with increased starting clique size until a critical size and then decreases. This critical size is different depending on fitness value. In general, a combination of fitness level and starting clique size serves to maximize the conditional fixation time.

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Path to fixation of evolutionary processes in graph-structured populations

Cited by 6 publications

References 51 publications

Multi-strategy evolutionary games: A Markov chain approach

Multi-strategy evolutionary games: A Markov chain approach

The effect of community structure on fixation process in evolutionary graph theory

The effect of initial placement of mutant in subdivided population on fixation time and probability

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