  We describe a semi-analytic model to predict the triaxial shapes of dark
matter halos utilizing the sequences of random merging events captured in
merger trees to follow the evolution of each halo's energy tensor. When coupled
with a simple model for relaxation toward a spherical shape, we find that this
model predicts distributions of halo axis length ratios which approximately
agree with those measured from cosmological N-body simulations once constrained
to match the median axis ratio at a single halo mass. We demonstrate the
predictive and explanatory power of this model by considering conditioned
distributions of axis length ratios, and the mass-dependence of halo shapes,
finding these to be in good agreement with N-body results. This model provides
both insight into the physics driving the evolution of halo triaxial shapes,
and rapid quantitative predictions for the statistics of triaxiality connected
directly to the formation history of the halo.
