It has been suggested that a continuous low star formation rate has been the dominant regime in IZw 18 and in dwarf galaxies for the lifetime of these objects (Legrand et al. 1999). Here, we discuss and model various star-forming histories for IZw 18. Particularly, we show that if the metallicity observed in IZw 18 results from starburst events only, the observed colors constrain the fraction of the metals ejected from the galaxy to be less than 50-70 %. We demonstrate that the continuous star formation scenario reproduces the observed parameters of IZw 18. A continuous star formation rate (SFR) of about 10E-4 Msol/yr during 14 Gyr reproduces precisely the observed abundances. This SFR is comparable with the lowest SFR observed in low surface brightness galaxies (van Zee et al. 1997). Generalized to all galaxies, the low continuous SFR scenario accounts for various facts: the presence of star formation in quiescent dwarfs and LSBG, the metallicity increase with time in the most underabundant DLA systems, and the metal content extrapolations to the outskirts of spiral galaxies. Also the apparent absence of galaxies with a metallicity lower than IZw 18, the apparent absence of HI clouds without optical counterparts, and the homogeneity of abundances in dwarfs galaxies are natural outcomes of the scenario. This implies that, even if starbursts are strong and important events in the life of galaxies, their more subdued but continuous star formation regime cannot be ignored when accounting for their chemical evolution.
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