We present for the first time a one-dimensional, four-fluid turbulence-driven solar wind model in order to investigate the preferential acceleration and heating of heavy ions by the resonant cyclotron interaction with parallel-propagating left-hand-polarized ion cyclotron waves. The model contains four species: electrons, protons, alpha particles, and one species of minor ions. A Kolmogorov type of cascade effect is introduced to transfer energy from the low-frequency Alfv¿n waves to the high-frequency ion cyclotron waves, which are assumed to be entirely dissipated by the wave-particle interaction. The quasi-linear theory of the wave-particle interaction is invoked to distribute the dissipated wave energy among the three ion species based on a given power law spectrum of the ion cyclotron waves and the cold plasma dispersion relation. It is found that in terms of the cold plasma dispersion relation, the dispersion generated by all ion species has an appreciable influence on both the behavior of the major species and the preferential acceleration and heating of the minor ions. The larger the number of species included in the dispersion relation is, the stronger preferential acceleration and heating produced by the waves for the heavy ions close to the Sun will be. A detailed comparison is carried out between two cases, one with and the other without the dispersive effect of the minor ions. Although the solutions for the two cases are somewhat different, they predict a more or less similar behavior of the minor ions, which essentially agrees with recent observations from SOHO. This indicates that the resonant cyclotron interaction may be responsible for the preferential acceleration and heating of minor ions in the fast solar wind. Furthermore, the influence of minor ions on the proton-alpha solar wind is found to be dominated by the dispersive effect of the minor ions. Even though such an influence is exaggerated by the cold plasma dispersion relation, it is still small and remains within the present observational uncertainties. Therefore minor ions may be treated approximately as test particles in the solar wind. ¿ 2000 American Geophysical Union