  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.
