  Observations indicate dust populations vary between galaxies and within them,
suggesting a complex life cycle and evolutionary history. Here we investigate
the evolution of galactic dust populations across cosmic time using a suite of
cosmological zoom-in simulations from the Feedback in Realistic Environments
(FIRE) project, spanning $M_{\rm
vir}=10^{9-12}M_{\odot};\,M_{*}=10^{6-11}\,M_{\odot}$. Our simulations
incorporate a dust evolution model that accounts for the dominant sources of
dust production, growth, and destruction and follows the evolution of specific
dust species. All galactic dust populations in our suite exhibit similar
evolutionary histories, with gas-dust accretion being the dominant producer of
dust mass for all but the most metal-poor galaxies. Similar to previous works,
we find the onset of efficient gas-dust accretion occurs above a `critical'
metallicity threshold ($Z_{\rm crit}$). Due to this threshold, our simulations
reproduce observed trends between galactic D/Z and metallicity and element
depletion trends in the ISM. However, we find $Z_{\rm crit}$ varies between
dust species due to differences in key element abundances, dust physical
properties, and life cycle processes resulting in $Z_{\rm
crit}\sim0.05Z_{\odot},\,0.2Z_{\odot},\,0.5Z_{\odot}$ for metallic iron,
silicates, and carbonaceous dust, respectively. These variations could explain
the lack of small carbonaceous grains observed in the Magellanic Clouds. We
also find a delay between the onset of gas-dust accretion and when a dust
population reaches equilibrium, which we call the equilibrium timescale
($\tau_{\rm eq}$). The relation between $\tau_{\rm eq}$ and the metal
enrichment timescale of a galaxy, determined by its recent evolutionary
history, can contribute to the scatter in the observed relation between
galactic D/Z and metallicity.
