We study the evolution of dwarf (L_H < 10^{9.6} L_Ho) star forming and quiescent galaxies in the Virgo cluster by comparing their UV to radio centimetric properties to the predictions of multizone chemo-spectrophotometric models of galaxy evolution especially tuned to take into account the perturbations induced by the interaction with the cluster intergalactic medium. Our models simulate one or multiple ram pressure stripping events and galaxy starvation. Models predict that all star forming dwarf galaxies entering the cluster for the first time loose most, if not all, of their atomic gas content, quenching on short time scales (< 150 Myr) their activity of star formation. These dwarf galaxies soon become red and quiescent, gas metal-rich objects with spectrophotometric and structural properties similar to those of dwarf ellipticals. Young, low luminosity, high surface brightness star forming galaxies such as late-type spirals and BCDs are probably the progenitors of relatively massive dwarf ellipticals, while it is likely that low surface brightness magellanic irregulars evolve into very low surface brightness quiescent objects hardly detectable in ground based imaging surveys. The small number of dwarf galaxies with physical properties intermediate between those of star forming and quiescent systems is consistent with a rapid (< 1 Gyr) transitional phase between the two dwarf galaxies populations. These results, combined with statistical considerations, are consistent with the idea that most of the dwarf ellipticals dominating the faint end of the Virgo luminosity function were initially star forming systems, accreted by the cluster and stripped of their gas by one or subsequent ram pressure stripping events.
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