The gamma-ray binary LS I +61 303 is composed of a Be star and a compact companion orbiting in an eccentric orbit. Variable flux modulated with the orbital period of ~26.5 d has been detected from radio to very high-energy gamma rays. In addition, the system presents a superorbital variability of the phase and amplitude of the radio outbursts with a period of ~4.6 yr. We present optical photometric observations of LS I +61 303 spanning ~1.5 yr and contemporaneous Hα equivalent width (EWHα) data. The optical photometry shows, for the first time, that the known orbital modulation suffers a positive orbital phase shift and an increase in flux for data obtained 1-yr apart. This behavior is similar to that already known at radio wavelengths, indicating that the optical flux follows the superorbital variability as well. The orbital modulation of the EWHα presents the already known superorbital flux variability but shows, also for the first time, a positive orbital phase shift. In addition, the optical photometry exhibits a lag of ~0.1-0.2 in orbital phase with respect to the EWHα measurements at similar superorbital phases, and presents a lag of ~0.1 and ~0.3 orbital phases with respect noncontemperaneous radio and X-ray outbursts, respectively. The phase shifts detected in the orbital modulation of thermal indicators, such as the optical flux and the EWHα, are in line with the observed behavior for nonthermal indicators, such as X-ray or radio emission. This shows that there is a strong coupling between the thermal and nonthermal emission processes in the gamma-ray binary LS I +61 303. The orbital phase lag between the optical flux and the EWHα is naturally explained considering different emitting regions in the circumstellar disk, whereas the secular evolution might be caused by the presence of a moving one-armed spiral density wave in the disk. Tables 1 and 2 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/575/L6