  LS I +61 303 is a puzzling Be/X-ray binary with variable gamma-ray emission
at up TeV energies. The nature of the compact object and the origin of the
high-energy emission are unclear. One family of models invokes particle
acceleration in shocks from the collision between the B-star wind and a
relativistic pulsar wind, while another centers on a relativistic jet powered
by accretion. Recent high-resolution radio observations showing a putative
"cometary tail" pointing away from the Be star near periastron have been cited
as support for the pulsar-wind model. We wish here to carry out a quantitative
assessment of these competing models for this extraordinary source. We apply a
3D SPH code for dynamical simulations of both the pulsar-wind-interaction and
accretion-jet models. The former yields a description of the shape of the
wind-wind interaction surface. The latter provides an estimation of the
accretion rate. The results allow critical evaluation of how the two distinct
models confront the data in various wavebands under a range of conditions. When
one accounts for the 3D dynamical wind interaction under realistic constraints
for the relative strength of the B-star and pulsar winds, the resulting form of
the interaction front does not match the putative "cometary tail" claimed from
radio observations. On the other hand, dynamical simulations of the
accretion-jet model indicate that the orbital phase variation of accretion
power includes a secondary broad peak well away from periastron, thus providing
a plausible way to explain the observed TeV gamma ray emission toward apastron.
We conclude that the colliding-wind model is not clearly established for LS I
+61 303, while the accretion-jet model can reproduce many key characteristics
of the observed TeV gamma-ray emission.
