  Observations of evolution in the dust-to-metal ratio allow us to constrain
the dominant dust processing mechanisms. In this work, we present a study of
the dust-to-metal and dust-to-gas ratios in a sub-sample of ~500 DustPedia
galaxies. Using literature and MUSE emission line fluxes, we derived gas-phase
metallicities (oxygen abundances) for over 10000 individual regions and
determine characteristic metallicities for each galaxy. We study how the
relative dust, gas, and metal contents of galaxies evolve by using metallicity
and gas fraction as proxies for evolutionary state. The global oxygen abundance
and nitrogen-to-oxygen ratio are found to increase monotonically as galaxies
evolve. Additionally, unevolved galaxies (gas fraction > 60%, metallicity 12 +
log(O/H) < 8.2) have dust-to-metal ratios that are about a factor of 2.1 lower
(a factor of six lower for galaxies with gas fraction > 80%) than the typical
dust-to-metal ratio (Md/MZ ~ 0.214) for more evolved sources. However, for high
gas fractions, the scatter is larger due to larger observational uncertainties
as well as a potential dependence of the dust grain growth timescale and
supernova dust yield on local conditions and star formation histories. We find
chemical evolution models with a strong contribution from dust grain growth
describe these observations reasonably well. The dust-to-metal ratio is also
found to be lower for low stellar masses and high specific star formation rates
(with the exception of some sources undergoing a starburst). Finally, the
metallicity gradient correlates weakly with the HI-to-stellar mass ratio, the
effective radius and the dust-to-stellar mass ratio, but not with stellar mass.
