Exact formulas for fixation probabilities on a complete oriented star

It is already known that large complete oriented stars (COSs) with intrinsic weights are amplifiers of selection. This paper addresses the evolutionary dynamics on COSs. First, we give the exact formulas for the fixation probabilities on a COS. We then apply these formulas to study some properties of COSs. The obtained results partially reveal the way in which the fixation probabilities are affected by COSs.