Fixation Probabilities on Complete Star and Bipartite Digraphs | Zendy

Chunming Zhang | Zendy; Yingjiang Wu | Zendy; Wanping Liu | Zendy; Xiaofan Yang | Zendy

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Fixation Probabilities on Complete Star and Bipartite Digraphs

Author(s) -

Chunming Zhang,

Yingjiang Wu,

Wanping Liu,

Xiaofan Yang

Publication year - 2012

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2012/940465

Subject(s) - bipartite graph , fixation (population genetics) , selection (genetic algorithm) , population , mathematics , combinatorics , star (game theory) , computer science , algorithm , graph , artificial intelligence , mathematical analysis , demography , sociology

This paper exactly formulates the kth-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

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