  We re-evaluate the roles of different dust sources in dust production as a
function of metallicity in late-type dwarf galaxies, with the goal of
understanding the relation between dust content and metallicity. The dust
content of late-type dwarf galaxies with episodic star formation is studied
with a multicomponent model of dust evolution, which includes dust input from
AGB stars, type II SNe and dust mass growth by accretion of gas species in the
ISM. Dust growth in the ISM becomes an important dust source in dwarf galaxies,
on the timescale of 0.1 - few Gyrs. It increases the dust-to-gas ratio (DGR)
during post-burst evolution, unlike type II SNe, which eject grains into the
ISM only during starbursts. Before the dust growth in the ISM overtakes the
dust production, AGB stars can be major sources of dust in metal-poor dwarf
galaxies. Our models reproduce the relation between the DGR and oxygen
abundance, derived from observations of a large sample of dwarf galaxies. The
steep decrease in the DGR at low O values is explained by the relatively low
efficiency of dust condensation in stars. The scatter observed at higher O
values is determined mainly by different critical metallicities for the
transition from stardust- to ISM-growth dominated dust production, depending on
the star formation history. In galaxies with episodic star formation,
additional dispersion in the DGR is introduced by grain destruction during
starbursts, followed by an increase of the dust mass due to dust growth in the
ISM during post-burst evolution. We find that the carbon-to-silicate ratio
changes dramatically, when the ISM growth becomes the dominant dust source,
therefore this ratio can be used as an indicator of the transition. The
observed DGR-O relation in dwarf galaxies favours low condensation efficiencies
in type II SNe, together with an increase in the total dust mass by means of
dust growth in the ISM.
