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The generation of uniform soliton pulse trains by additive pulse mode locking has been experimentally demonstrated in a birefringent fiber laser with a passive polarizer. Numerical simulations of pulse propagation around such a fiber loop are presented which reveal that this mode-locking scheme does not result in strictly uniform pulse trains. Rather, the train of output pulses exhibits periodic fluctuations in intensity and polarization. A model for the pulse dynamics is developed which shows that these fluctuations depend on the strength of the fiber birefringence and the alignment of the polarizer with the fast- and slow-polarization axes of the fiber. It is also shown that increased uniformity of pulse trains is achieved with near alignment of the polarizer with the slow axis of the birefringence.