Chemical consequences of low star formation rates: stochastically   sampling the IMF
  When estimating the abundances which result from a given star formation event, it is customary to treat the IMF as a series of weight factors to be applied to the stellar yields, as a function of mass, implicitly assuming one is dealing with an infinite population. However, when the stellar population is small, the standard procedure would imply the inclusion of fractional numbers of stars at certain masses. We study the effects of small number statistics on the resulting abundances by performing an statistical sampling of the IMF to form a stellar population out of discrete numbers of stars. A chemical evolution code then follows the evolution of the population, and traces the resulting abundances. The process is repeated to obtain an statistical distribution of the resulting abundances and their evolution. We explore the manner in which different elements are affected, and how different abundances converge to the infinite population limit as the total mass increases. We include a discussion of our results in the context of dwarf spheroidal galaxies and show the recently reported internal dispersions in abundance ratios for dSph galaxies might be partly explained through the stochastic effects introduced by a low star formation rate, which can account for dispersions of over 2 dex in [C/O], [N/O], [C/Fe], [N/Fe] and [O/Fe]. 
L. Carigi and X. Hernandez