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Journal of Interdisciplinary Mathematics Volume 12, 2009 - Issue 2: Interdisciplinary Research in Mathematical Sciences for Undergraduates
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Original Articles

Evolutionary dynamics on small-order graphs

M. Broom Department of Mathematics, University of Sussex, Brighton BN1 9RF, U.K. E-mail: [email protected]
,
J. Rychtář Department of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC, 27402, U.S.A. E-mail: [email protected]
&
B. Stadler Department of Computer Science, Department of Computer Science, Greensboro, NC, 27402, U.S.A. E-mail: [email protected]
Pages 129-140 | Received 01 Feb 2008, Published online: 28 May 2013

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Asmaa Jaafar Oudah & Ali Abd Aubad. (2021) Analysing the structure of A4-graphs for Mathieu groups. Journal of Discrete Mathematical Sciences and Cryptography 24:7, pages 1907-1913.
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M. Broom, J. Rychtář & B.T. Stadler. (2011) Evolutionary Dynamics on Graphs - the Effect of Graph Structure and Initial Placement on Mutant Spread. Journal of Statistical Theory and Practice 5:3, pages 369-381.
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Articles from other publishers (39)

Nikhil Sharma & Arne Traulsen. (2022) Suppressors of fixation can increase average fitness beyond amplifiers of selection. Proceedings of the National Academy of Sciences 119:37.
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Travis Monk & André van Schaik. (2022) Martingales and the fixation time of evolutionary graphs with arbitrary dimensionality. Royal Society Open Science 9:5.
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Hendrik Richter. (2021) Spectral analysis of transient amplifiers for death–birth updating constructed from regular graphs. Journal of Mathematical Biology 82:7.
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Benjamin Allen, Christine Sample, Patricia Steinhagen, Julia Shapiro, Matthew King, Timothy Hedspeth & Megan Goncalves. (2021) Fixation probabilities in graph-structured populations under weak selection. PLOS Computational Biology 17:2, pages e1008695.
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Josep Díaz & Dieter Mitsche. (2021) A survey of the modified Moran process and evolutionary graph theory. Computer Science Review 39, pages 100347.
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Magdi S. Mahmoud, Mojeed O. Oyedeji & Yuanqing Xia. 2021. Advanced Distributed Consensus for Multiagent Systems. Advanced Distributed Consensus for Multiagent Systems 229 265 .
Travis Monk & André van Schaik. (2020) Wald’s martingale and the conditional distributions of absorption time in the Moran process. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476:2241, pages 20200135.
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Francisco Herrerías-Azcué, Vicente Pérez-Muñuzuri & Tobias Galla. (2019) Motion, fixation probability and the choice of an evolutionary process. PLOS Computational Biology 15:8, pages e1007238.
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Laura Hindersin, Bin Wu, Arne Traulsen & Julian García. (2019) Computation and Simulation of Evolutionary Game Dynamics in Finite Populations. Scientific Reports 9:1.
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Kamran Kaveh, Alex McAvoy & Martin A. Nowak. (2019) Environmental fitness heterogeneity in the Moran process. Royal Society Open Science 6:1, pages 181661.
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George B. Mertzios & Paul G. Spirakis. (2018) Strong bounds for evolution in networks. Journal of Computer and System Sciences 97, pages 60-82.
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Travis Monk. (2018) Martingales and the fixation probability of high-dimensional evolutionary graphs. Journal of Theoretical Biology 451, pages 10-18.
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Jeong-Ok Choi & Unjong Yu. (2018) Fixation probability on clique-based graphs. Physica A: Statistical Mechanics and its Applications 492, pages 2129-2135.
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Andreas Pavlogiannis, Josef Tkadlec, Krishnendu Chatterjee & Martin A. Nowak. (2017) Amplification on Undirected Population Structures: Comets Beat Stars. Scientific Reports 7:1.
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Fernando Alcalde Cuesta, Pablo González Sequeiros, Álvaro Lozano Rojo & Rubén Vigara Benito. 2017. Bioinformatics and Biomedical Engineering. Bioinformatics and Biomedical Engineering 209 220 .
GeorgeB. Mertzios. 2016. Encyclopedia of Algorithms. Encyclopedia of Algorithms 109 113 .
Shaolin Tan & Jinhu Lü. (2014) Characterizing the effect of population heterogeneity on evolutionary dynamics on complex networks. Scientific Reports 4:1.
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F. Alcalde Cuesta, P. González Sequeiros & Á. Lozano Rojo. (2015) Fast and asymptotic computation of the fixation probability for Moran processes on graphs. Biosystems 129, pages 25-35.
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Paulo Shakarian, Abhivav Bhatnagar, Ashkan Aleali, Elham Shaabani & Ruocheng GuoPaulo Shakarian, Abhinav Bhatnagar, Ashkan Aleali, Elham Shaabani & Ruocheng Guo. 2015. Diffusion in Social Networks. Diffusion in Social Networks 75 91 .
Burton Voorhees. 2015. ISCS 2014: Interdisciplinary Symposium on Complex Systems. ISCS 2014: Interdisciplinary Symposium on Complex Systems 67 76 .
Chaitanya S. Gokhale & Arne Traulsen. (2014) Evolutionary Multiplayer Games. Dynamic Games and Applications 4:4, pages 468-488.
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Wes Maciejewski & Gregory J. Puleo. (2014) Environmental evolutionary graph theory. Journal of Theoretical Biology 360, pages 117-128.
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Ben Adlam & Martin A. Nowak. (2014) Universality of fixation probabilities in randomly structured populations. Scientific Reports 4:1.
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Laura Hindersin & Arne Traulsen. (2014) Counterintuitive properties of the fixation time in network-structured populations. Journal of The Royal Society Interface 11:99, pages 20140606.
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Josep Díaz, Leslie Ann Goldberg, George B. Mertzios, David Richerby, Maria Serna & Paul G. Spirakis. (2012) Approximating Fixation Probabilities in the Generalized Moran Process. Algorithmica 69:1, pages 78-91.
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Shaolin Tan, Jinhu Lu, Guanrong Chen & David J. Hill. (2014) When Structure Meets Function in Evolutionary Dynamics on Complex Networks. IEEE Circuits and Systems Magazine 14:4, pages 36-50.
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George B. Mertzios. 2008. Encyclopedia of Algorithms. Encyclopedia of Algorithms 1 6 .
Marcus Frean, Paul B. Rainey & Arne Traulsen. (2013) The effect of population structure on the rate of evolution. Proceedings of the Royal Society B: Biological Sciences 280:1762, pages 20130211.
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Burton Voorhees & Alex Murray. (2013) Fixation probabilities for simple digraphs. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469:2154, pages 20120676.
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Shaolin Tan, Jinhu Lu, Xinghuo Yu & David Hill. (2013) Characterizing the effect of network structure on evolutionary dynamics via a novel measure of structural heterogeneity. Characterizing the effect of network structure on evolutionary dynamics via a novel measure of structural heterogeneity.
George B. Mertzios, Sotiris Nikoletseas, Christoforos Raptopoulos & Paul G. Spirakis. (2013) Natural models for evolution on networks. Theoretical Computer Science 477, pages 76-95.
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George B. Mertzios & Paul G. Spirakis. 2013. Automata, Languages, and Programming. Automata, Languages, and Programming 669 680 .
Mark Broom & Bernhard Voelkl. (2012) TWO MEASURES OF EFFECTIVE POPULATION SIZE FOR GRAPHS. Evolution 66:5, pages 1613-1623.
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Paulo Shakarian, Patrick Roos & Anthony Johnson. (2012) A review of evolutionary graph theory with applications to game theory. Biosystems 107:2, pages 66-80.
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Chunming Zhang, Yingjiang Wu, Wanping Liu & Xiaofan Yang. (2012) Fixation Probabilities on Complete Star and Bipartite Digraphs. Discrete Dynamics in Nature and Society 2012, pages 1-21.
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C. Hadjichrysanthou, M. Broom & J. Rychtář. (2011) Evolutionary Games on Star Graphs Under Various Updating Rules. Dynamic Games and Applications 1:3, pages 386-407.
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George B. Mertzios, Sotiris Nikoletseas, Christoforos Raptopoulos & Paul G. Spirakis. 2011. Internet and Network Economics. Internet and Network Economics 290 301 .
M. Broom, C. Hadjichrysanthou & J. Rychtář. (2009) Evolutionary games on graphs and the speed of the evolutionary process. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466:2117, pages 1327-1346.
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Bernhard Voelkl. (2010) The ‘Hawk-Dove’ Game and the Speed of the Evolutionary Process in Small Heterogeneous Populations. Games 1:2, pages 103-116.
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