What will blue compact dwarf galaxies evolve into?
  We present and analyse the photometric properties of a nearly complete sample
of blue compact dwarf (BCD) and irregular galaxies in the Virgo cluster from
multi-band SDSS images. Our study intends to shed light on the ongoing debate
of whether a structural evolution from present-day star-forming dwarf galaxies
in a cluster environment into ordinary early-type dwarf galaxies is possible
based on the structural properties.
  For this purpose, we decompose the surface brightness profiles of the BCDs
into the luminosity contribution of the starburst component and that of their
underlying low surface brightness (LSB) host. The latter dominates the stellar
mass of the BCD. We find that the LSB-components of the Virgo BCDs are
structurally compatible with the more compact half of the Virgo early-type
dwarfs, except for a few extreme BCDs. Thus, after termination of starburst
activity, the BCDs will presumably fade into galaxies that are structurally
similar to ordinary early-type dwarfs. In contrast, the irregulars are more
diffuse than the BCDs and are structurally similar to the more diffuse half of
the Virgo early-type dwarfs. Therefore, the present-day Virgo irregulars are
not simply non-starbursting BCDs.
  If starbursts in cluster BCDs are transient phenomena with a duration of ~100
Myr or less, during which the galaxies could not travel more than ~100 kpc,
then a substantial number of non-starbursting counterparts of these systems
must populate the same spatial volume, namely the Virgo cluster outskirts. The
majority of them would have to be early-type dwarfs, based on the abundance of
different galaxy types with similar colours and structural parameters to the
LSB-components of the BCDs. However, most Virgo BCDs have redder LSB-host
colours and a less prominent starburst than typical field BCDs, preventing a
robust conclusion on possible oscillations between BCDs and early-type dwarfs.
