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Bak-Sneppen backwards

Alberts, Tom and Lee, Ga Yeong and Simper, Mackenzie (2017) Bak-Sneppen backwards. Stochastics: An International Journal of Probability and Stochastic Processes, 89 (8). pp. 1127-1142. ISSN 1744-2508. doi:10.1080/17442508.2017.1282957.

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We study the backwards Markov chain for the Bak–Sneppen model of biological evolution and derive its corresponding reversibility equations. We show that, in contrast to the forwards Markov chain, the dynamics of the backwards chain explicitly involve the stationary distribution of the model, and from this we derive a functional equation that the stationary distribution must satisfy. We use this functional equation to derive differential equations for the stationary distribution of Bak–Sneppen models in which all but one or all but two of the fitnesses are replaced at each step, subject to certain conditions on the relative locations of the replaced species. This gives a unified way of deriving Schlemm’s expressions for the stationary distributions of the isotropic four-species model, the isotropic five-species model, and the anisotropic three-species model.

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Additional Information:© 2017 Taylor & Francis. Received 20 Apr 2016, Accepted 12 Jan 2017, Published online: 31 Jan 2017. Tom Alberts thanks Siva Athreya and Eric Cator for helpful discussions, and the support of the Scott Robert Johnson fellowship at the California Institute of Technology. Ga Yeong Lee thanks the Caltech Summer Undergraduate Research Fellowships (SURF) program and Margaret Leighton for their support of her research. Mackenzie Simper thanks the internal REU program at the University of Utah’s Mathematics department for support of her research.
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
University of UtahUNSPECIFIED
Subject Keywords:Bak–Sneppen model, Markov chain, stationary distribution
Issue or Number:8
Record Number:CaltechAUTHORS:20180102-093630215
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84029
Deposited By: Tony Diaz
Deposited On:02 Jan 2018 19:31
Last Modified:15 Nov 2021 20:16

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