  The distribution of chemical abundances and their variation in time are
important tools to understand the chemical evolution of galaxies: in
particular, the study of chemical evolution models can improve our
understanding of the basic assumptions made for modelling our Galaxy and other
spirals. To test a standard chemical evolution model for spiral disks in the
Local Universe and study the influence of a threshold gas density and different
efficiencies in the star formation rate (SFR) law on radial gradients
(abundance, gas and SFR). We adopt a one-infall chemical evolution model where
the Galactic disk forms inside-out by means of infall of gas, and we test
different thresholds and efficiencies in the SFR. The model is scaled to the
disk properties of three Local Group galaxies (the Milky Way, M31 and M33) by
varying its dependence on the star formation efficiency and the time scale for
the infalling gas into the disk. Using this simple model we are able to
reproduce most of the observed constraints available in the literature for the
studied galaxies. The radial oxygen abundance gradients and their time
evolution are studied in detail. The present day abundance gradients are more
sensitive to the threshold than to other parameters, while their temporal
evolutions are more dependent on the chosen SFR efficiency. The most massive
disks seem to have evolved faster (i.e. with more efficient star formation)
than the less massive ones, thus suggesting a downsizing in star formation for
spirals. The threshold and the efficiency of star formation play a very
important role in the chemical evolution of spiral disks and an efficiency
varying with radius can be used to regulate the star formation. The oxygen
abundance gradient can steepen or flatten in time depending on the choice of
this parameter
