Fixation Probabilities on Complete Star and Bipartite Digraphs

Chunming Zhang, Yingjiang Wu, Wanping Liu and Xiaofan Yang

Discrete Dynamics in Nature and Society, 2012, vol. 2012, 1-21

Abstract:

This paper exactly formulates the th-order fixation probabilities on complete star digraphs (CSDs), which extend the results from Broom and Rychtář (2008). By applying these probability formulae, some asymptotic properties on CBDs are analyzed, and certain CSDs are determined to be amplifiers of selection for arbitrary relative fitness larger than 1, while all the CSDs are proved to be amplifiers of selection for fixed relative fitness slightly larger than 1. A numerical method for fixed population structure (by solving a linear system) is developed to calculate the fixation probabilities on complete bipartite digraphs (CBDs), and some conjectures are finally given through simulations.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:940465

DOI: 10.1155/2012/940465

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