Confidence limits of evolutionary synthesis models - III. On time-integrated quantities

Evolutionary synthesis models are a fundamental tool to interpret the prope rties of observed stellar systems. In order to achieve a meaningful compari son between models and real data, it is necessary to calibrate the models t hemselves, i.e. to evaluate the dispersion due to the discreteness of star formation as well as the possible model errors. In this paper we show that linear interpolations in the log M log t(k) plane, that are customary in th e evaluation of isochrones in evolutionary synthesis codes, produce unphysi cal results. We also show that some of the methods used in the calculation of time-integrated quantities (kinetic energy, and total ejected masses of different elements) may produce unrealistic results. We propose alternative solutions to solve both problems. Moreover, we have quantified the expecte d dispersion of these quantities due to stochastic effects in stellar popul ations. As a particular result, we show that the dispersion in the N-14/C-1 2 ratio increases with time.