  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 outburst with a period of ~4.6 yr. We present
optical photometric observations of LS I +61 303 spanning ~1.5 yr and
contemporaneous Halpha equivalent width (EW Halpha) 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 EW Halpha 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 EW Halpha 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 EW Halpha, 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 EW Halpha 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.
