We use the chemical evolution predictions of cosmological hydrodynamic simulations with our latest theoretical stellar population synthesis, photoionization, and shock models to predict the strong line evolution of ensembles of galaxies from z = 3 to the present day. In this paper, we focus on the brightest optical emission-line ratios, [N II]/Hα and [O III]/Hβ. We use the optical diagnostic Baldwin-Phillips-Terlevich (BPT) diagram as a tool for investigating the spectral properties of ensembles of active galaxies. We use four redshift windows chosen to exploit new near-infrared multi-object spectrographs. We predict how the BPT diagram will appear in these four redshift windows given different sets of assumptions. We show that the position of star-forming galaxies on the BPT diagram traces the interstellar medium conditions and radiation field in galaxies at a given redshift. Galaxies containing active galactic nucleus (AGN) form a mixing sequence with purely star-forming galaxies. This mixing sequence may change dramatically with cosmic time, due to the metallicity sensitivity of the optical emission-lines. Furthermore, the position of the mixing sequence may probe metallicity gradients in galaxies as a function of redshift, depending on the size of the AGN narrow-line region. We apply our latest slow shock models for gas shocked by galactic-scale winds. We show that at high redshift, galactic wind shocks are clearly separated from AGN in line ratio space. Instead, shocks from galactic winds mimic high metallicity starburst galaxies. We discuss our models in the context of future large near-infrared spectroscopic surveys.