  Aims: Recent theoretical predictions for the winds of Wolf-Rayet stars
indicate that their mass-loss rates scale with the initial stellar metallicity
in the local Universe.We aim to investigate how this predicted dependence
affects the models of Wolf-Rayet stars and their progeny in different chemical
environments. Methods: We compute models of stellar structure and evolution for
Wolf-Rayet stars for different initial metallicities, and investigate how the
scaling of the Wolf-Rayet mass-loss rates affects the final masses, the
lifetimes of the WN and WC subtypes, and how the ratio of the two populations
vary with metallicity. Results: We find significant effects of metallicity
dependent mass-loss rates for Wolf-Rayet stars. For models that include the
scaling of the mass-loss rate with initial metallicity, all WR stars become
neutron stars rather than black holes at twice the solar metallicity; at lower
$Z$, black holes have larger masses. We also show that our models that include
the mass-loss metallicity scaling closely reproduce the observed decrease of
the relative population of WC over WN stars at low metallicities.
