The physics of polarization spectroscopy (PS) is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The numerical solution of the time-dependent density matrix equations enables us to investigate the effects of strong saturation on PS signal levels and line shapes. Bath levels not directly coupled by the laser radiation are included in the numerical modeling to investigate the effects of collisional rates and different types of collisions on signal levels and Line shapes. The effects of Doppler broadening are included by solving the density matrix equations for numerous velocity groups. At low laser power we find that the homogeneously broadened PS line shape is Lorentzian-cubed, as compared to the Lorentzian predicted in several previous low-power analytical solutions. In the low laser power regime, the line-center PS signal is proportional to (collision rate)(-6), obviously greatly complicating the application of unsaturated PS for quantitative concentration measurements in flames and plasmas. As the transition begins to saturate at higher laser intensities, the dependences of the signal strength on the laser intensity and on the collision rate decrease drastically, although the line-center PS signal is still approximately proportional to (collision rate)(-2). The dependence of the PS signal intensity on the ratio of the population-transfer collision rate to the dephasing collision rate Is minimized for saturating pump beam intensities. For resonances that are both Doppler- and collision-broadened the low-power PS line shape is Lorentzian with a linewidth equal to the collisional width for the case where the Doppler width is much greater than the collisional width. At low pump laser intensities, the PS signal is very dependent on the ratio of Doppler broadening to collisional broadening when the Doppler width is greater than the collisional width. However, at high intensity, the Line-center PS signal intensity becomes nearly independent of collision rate when the collisional linewidth is less than the Doppler linewidth. Quantitative application of polarization spectroscopy for concentration measurements in flames and plasmas will almost certainly require resolution of the PS line shape and/or accurate measurement of the saturation curve.