  The population structure often impacts evolutionary dynamics. In
constant-selection evolutionary dynamics between two types, amplifiers of
selection are networks that promote the fitter mutant to take over the entire
population, and suppressors of selection do the opposite. It has been shown
that most undirected and unweighted networks are amplifiers of selection under
a common updating rule and initial condition. Here, we extensively investigate
how edge weights influence selection on undirected networks. We show that
random edge weights make small networks less amplifying than the corresponding
unweighted networks in a majority of cases and also make them suppressors of
selection (i.e., less amplifying than the complete graph, or equivalently, the
Moran process) in many cases. Qualitatively, the same result holds true for
larger empirical networks. These results suggest that amplifiers of selection
are not as common for weighted networks as for unweighted counterparts.
