  We determine the asymptotic spreading speed of an invasive species, which
invades the territory of a native competitor, governed by a diffusive
competition model with a free boundary in a spherically symmetric setting. This
free boundary problem was studied recently in [7] but only rough bounds of the
spreading speed was obtained there. We show in this paper that the spreading
speed has an asymptotic limit (as time goes to infnity), which is given by a
certain traveling wave type system of one space dimension, called a semi-wave.
This appears to be the first result that gives the precise asymptotic spreading
speed for a two species system with free boundaries.
