Copyright © 2012 Chunming Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.