There have been five mass extinctions on Earth over the last 450 million years. The last mass extinction occurred 65 million years ago and there is strong evidence the extinction was initiated by an asteroid ten kilometres in diameter colliding with Earth. It is an open question whether the previous four mass extinctions were initiated by a collision.
One general approach to answering this question is to perform N-body simulations of the planets and a large number of asteroids, and use the results to estimate the likelihood Earth was hit by a sufficiently large asteroid at or near the time of mass extinction.
I will present a summary of results for preliminary N-body simulations I have performed on the Pan cluster at the University of Auckland.