On the effect of discrete numbers of stars in chemical evolution models

We examine the impact of discrete numbers of stars in stellar populations on the results of Chemical Evolution Models. We explore the resulting dispersion in the true yields and their possible relation with the dispersion in observational data based on a Simple Closed-Box model. In this framework we find that the dispersion is larger for the less evolved or low abundance regions. Thus, the age-metallicity relation may be a tracer of the Star Formation History of our Galaxy. This theoretical dispersion is especially high for the relative abundance log(N/O) in regions where the total number of stars created is still low. This may explain part of the scatter in the N/O ratio observed in star forming galaxies. We have also found a first order theoretical estimation for the goodness of a linear fit of the helium abundance vs. 12 + log (O/H) with values of the regression coefficient between 0.9 and 0.7 (independent of sampling effects). We conclude that it is necessary to include these sampling effects in a more realistic Chemical Evolution Model in order that such a model reproduces, at the same time, the mean value and the dispersion of observed abundances.