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In addressing the origins of Darwinian evolution, recent experimental work has been focussed on the discovery of simple physical effects which would provide a relevant selective advantage to protocells competing with each other for a limited supply of lipid. In particular, data coming from Szostak's lab suggest that the transition from simple prebiotically plausible lipid membranes to more complex and heterogeneous ones, closer to real biomembranes, may have been driven by changes in the fluidity of the membrane and its affinity for the available amphiphilic compound, which in turn would involve changes in vesicle growth dynamics. Earlier work from the same group reported osmotically-driven competition effects, whereby swelled vesicles grow at the expense of isotonic ones. In this paper, we try to expand on these experimental studies by providing a simple mathematical model of a population of competing vesicles, studied at the level of lipid kinetics. In silico simulations of the model are able to reproduce qualitatively and often quantitatively the experimentally reported competition effects in both scenarios. We also develop a method for numerically solving the equilibrium of a population of competing model vesicles, which is quite general and applicable to different vesicle kinetics schemes., Comment: 15 pages, 6 figures, 1 table