  Pure luminosity evolution models for galaxies provide an unacceptable fit to
the redshifts and colors of faint galaxies. In this paper we demonstrate, using
HST morphological number counts derived both from the $I_{814}$-band of WFPC2
in the Medium Deep Survey (MDS) and the Hubble Deep Field (HDF) and from the
$H_{1.6}$-band of NICMOS, and ground-based spectroscopic data of the Hawaii
Deep Field and the Canada-France Redshift Survey, that number evolution is
necessary for galaxies, regardless of whether the cosmic geometry is flat,
open, or $\Lambda$-dominated. Furthermore, we show that the number evolution is
small at redshifts of z<1, but large at z>1, and that this conclusion is valid
for all the three cosmological models under consideration. If the universe is
open or $\Lambda$-dominated, the models, which are subject to the constraint of
the conservation of the comoving mass density of galaxies, naturally predict a
population of star-forming galaxies with the redshift distribution peaking at
$z=2\sim3$, which seems to be consistent with the recent findings from
Lyman-break photometric selection techniques. If the cosmological model is
flat, however, the conservation of the comoving mass density is invalid. Hence,
in order to account for the steep slope of B-band number counts at faint
magnitudes in the flat universe, such a star-forming galaxy population has to
be introduced ad hoc into the modelling alongside the merger assumption.
