  [ABRIDGED] Using the Gaussian+Schechter composite luminosity functions
measured from the ESO-Sculptor Survey (de Lapparent et al. 2003), we obtain
evidence for evolution in the late spectral class containing late-type Spiral
(Sc+Sd) and dwarf Irregular (dI) galaxies. This evolution is detected as an
increase of the Sc+Sd+dI galaxy density which can be modeled as either
n(z)~1+3(z-0.15) or n(z) ~ (1+z)^2 using the currently favored cosmological
parameters Omega_m=0.3 and Omega_Lambda=0.7, with an uncertainty in both
evolution rates of order of unity. For Omega_m=1.0 and Omega_Lambda=0.0, the
linear and power-law evolution rates are 4 and 2.5 resp. Both models yield a
good match to the ESS BVRc redshift distributions to 21-22 mag and to the
number-counts to 23-23.5 mag, which probe the galaxy distribution to redshifts
z~0.5 and z~1.0 resp. This analysis illustrates how Gaussian+Schechter
composite luminosity functions provide more robust constraints on the evolution
rate than pure Schechter functions. The detected density evolution indicates
that mergers could play a significant role in the evolution of late-type Spiral
and dwarf Irregular galaxies. However, the ESO-Sculptor density increase with
redshift could also be caused by a ~1 mag brightening of the Sc+Sd+dI galaxies
at z~0.5 and a ~1.5-2.0 mag brightening at z~1, which is compatible with the
expected passive brightening of Sc galaxies at these redshifts. Distinguishing
between luminosity and density evolution is a major difficulty as these produce
the same effect on the redshift and magnitude distributions. The detected
evolution rate of the ESO-Sculptor Sc+Sd+dI galaxies is nevertheless among the
range of measured values from the other existing analyses, whether they provide
evidence for density or luminosity evolution.
