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The split-and-drift random graph, a null model for speciation

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  • Bienvenu, François
  • Débarre, Florence
  • Lambert, Amaury

Abstract

We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on {1,…,n}. The dynamics of this Markov chain is governed by two types of events: vertex duplication, where at constant rate a pair of vertices is sampled uniformly and one of these vertices loses its incident edges and is rewired to the other vertex and its neighbors; and edge removal, where each edge disappears at constant rate. Besides the number of vertices n, the model has a single parameter rn.

Suggested Citation

  • Bienvenu, François & Débarre, Florence & Lambert, Amaury, 2019. "The split-and-drift random graph, a null model for speciation," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2010-2048.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:6:p:2010-2048
    DOI: 10.1016/j.spa.2018.06.009
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    References listed on IDEAS

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    1. Ricard V. Solé & Romualdo Pastor-Satorras & Eric Smith & Thomas B. Kepler, 2002. "A Model Of Large-Scale Proteome Evolution," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 43-54.
    2. Chauvin, Brigitte & Rouault, Alain & Wakolbinger, Anton, 1991. "Growing conditioned trees," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 117-130, October.
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