  Network structure has a large impact on constant-selection evolutionary
dynamics, with which multiple types of different fitnesses (i.e., strengths)
compete on the network. Here we study constant-selection dynamics on two-layer
networks in which the fitness of a node in one layer affects that in the other
layer, under birth-death processes and uniform initialization, which are
commonly assumed. We show mathematically and numerically that two-layer
networks are suppressors of selection, which suppresses the effects of the
different fitness values between the different types on final outcomes of the
evolutionary dynamics (called fixation probability), relative to the
constituent one-layer networks. In fact, many two-layer networks are
suppressors of selection relative to the most basic baseline, the Moran
process. This result is in stark contrast with the results for conventional
one-layer networks for which most networks are amplifiers of selection.
