In this paper we establish a necessary condition for the application of stellar population synthesis models to observed star clusters .
Such a condition is expressed by the requirement that the total luminosity of the cluster modeled be larger than the contribution of the most luminous star included in the assumed isochrones , which is referred to as the Lowest Luminosity Limit ( LLL ) .
This limit is independent of the assumptions on the IMF and almost independent of the star formation history .
We have obtained the Lowest Luminosity Limit for a wide range of ages ( 5 Myr to 20 Gyr ) and metallicities ( Z =0 to Z =0.019 ) from the ( ) isochrones .
Using the results of evolutionary synthesis models , we have also obtained the minimal cluster mass associated with the LLL , { \cal M } ^ { min } , which is the mass value below which the observed colors are severely biased with respect to the predictions of synthesis models .
We explore the relationship between { \cal M } ^ { min } and the statistical properties of clusters , showing that the magnitudes of clusters with mass equal to { \cal M } ^ { min } have a relative dispersion of 32 % at least ( i.e. , 0.35 mag ) in all the photometric bands considered ; analogously , the magnitudes of clusters with mass larger than 10 \times { \cal M } ^ { min } have a relative dispersion of 10 % at least .
The dispersion is comparatively larger in the near infrared bands : in particular , { \cal M } ^ { min } takes values between 10 ^ { 4 } and 10 ^ { 5 } 
M _ { \odot } for the K band , implying that severe sampling effects may affect the infrared emission of many observed stellar clusters .
As an example of an application to observations , we show that in surveys that reach the Lowest Luminosity Limit the color distributions will be skewed toward the color with the smallest number of effective sources , which is usually the red , and that the skewness is a signature of the cluster mass distribution in the survey .
We also apply our results to a sample of Globular Clusters , showing that they seem to be affected by sampling effects , a circumstance that could explain , at least partially , the bias of the observed colors with respect to the predictions of synthesis models .
Finally , we extensively discuss the advantages and the drawbacks of our method : it is , on the one hand , a very simple criterion for the detection of severe sampling problems that bypasses the need for sophisticated statistical tools ; on the other hand , it is not very sensitive , and it does not identify all the objects in which sampling effects are important and a statistical analysis is required .
As such , it defines a condition necessary but not sufficient for the application of synthesis models to observed clusters .