We have developed a method for simulating the evolution of an ensemble of one-atom-high islands from deposition and nucleation to coarsening. Using this method we have studied three regimes of coarsening; coarsening due to island coalescence, coarsening driven by evaporation, and the case in which both mechanisms act simultaneously. The parameters have been chosen to mimic coarsening of Ag on Ag(001); they are not meant to reproduce the experimental results for Ag quantitatively, but to provide simulations relevant to metal-on-metal homoepitaxy. We find that the scaling laws proposed by the mean-field theory for the time dependence of the number of islands and the island size distribution function work well in the limiting case when coarsening is dominated by island diffusion and coalescence. In the opposite limit, when coarsening is dominated by evaporation, the scaling predicted for the island size works well, but the island size distribution predicted by the mean-field theory is narrower than the one found in simulations. In the case when island migration and evaporation are both important, the evolution of the number of islands shows a crossover; at early times it scales as if coarsening takes place by island coalescence, and at later times it scales as if coarsening is dominated by evaporation. Regardless of the coarsening mechanism, most islands disappear by coalescence.