Modeling low mass stellar populations, like clusters and dwarf galaxies, with population synthesis models requires that we evaluate the role played by stochastic fluctuations in the sampling of the IMF on the spectro-photometric properties of these sparse populations. Interacting binaries may also modify the integrated spectra of these systems depending on the final product of the binary interaction and on the frequency of binary stars. In this work we compare the relative importance of stochastic fluctuations and binary evolution on low mass galaxy properties as a function of the population age and total mass. In most cases the effects of stochastic fluctuations dominate those produced by binary interactions. We explore and quantify the relative importance of these effects through cosmic times.