Selectivity is the main parameter you are after for in developing your separation. Selectivity is the ability of the column to discriminate two analytes in your mixture.
By the definition it is a ratio of the capacity factors of your analytes, or the ratio of the adjusted retention volumes
It is believed that the logarithm of the capacity factor represents the energy of analyte excessive interaction with the stationary phase. Excessive means that in HPLC we deal with the competitive process. Eluent molecules always occupy all adsorption sites, and analyte to get retained on the surface has to spend some energy to withdraw the eluent molecule from the surface. This could be written in the form:
We can now express the selectivity in terms of energy
The resulting expression does not have any terms related to the eluent adsorption energy, which means that the selectivity does not depend on the eluent type and composition. This is in the ideal case, but in reality selectivity indeed show very very low dependence on the eluent composition and type.
If you change the eluent composition peaks will retain longer, but the ratio of their adjusted retention times will stay approximately the same.
This is ideal consideration. If the change of the eluent composition affect types of analyte-surface interactions, or analyte ionization or solvation, you may see dramatic change of the selectivity.