  (abriged) In this paper we establish a Lowest Luminosity Limit (LLL) for the
use of synthesis codes. The limit is defined by the following statement: The
total luminosity of the cluster modeled must be larger than the individual
contribution of any of the stars included in the assumed isochrones. This limit
is independent of the assumptions on the IMF and almost independent on the star
formation history. We have obtained the LLL for a wide range of ages (5 Myr to
20 Gyr) and metallicities (Z=0 to Z=0.019) from Girardi et al. (2002)
isochrones. Using the LLL and the results of evolutionary synthesis models we
have also obtained the minimal cluster mass, Mmin, for which the results of
synthesis models may suffer from a severe bias in the computation of colors. We
show that the results of synthesis models for clusters with mass equal to Mmin
have a relative dispersion about or larger than 32% (i.e. a dispersion of 0.35
mag) in the corresponding photometric bands. This effect is more important for
near infrared bands (except in the case where Asymptotic Giant Branch stars
dominate the luminosity in optical bands). In particular, Mmin takes values
between 10^4 and 10^5 Mo for the K band. From the observational point of view,
we show that in surveys that reach luminosities near the LLL, the color
distributions will be skewed toward the color with lower effective sources
(toward the red in general), and that the skewness is a signature of the
distribution of initial cluster masses in the survey. We also apply the LLL to
Globular Clusters showing that sampling effects are relevant in these clusters
and that they can explain (at least partially) the bias of the observed colors
with respect to the predictions of synthesis models.
