  We study the Cauchy problem for nonlocal reaction diffusion equations with
bistable nonlinearity in 1D spatial domain and investigate the asymptotic
behaviors of solutions with a one-parameter family of monotonically increasing
and compactly supported initial data. We show that for small values of the
parameter the corresponding solutions decay to 0, while for large values the
related solutions converge to 1 uniformly on compacts. Moreover, we prove that
the transition from extinction (converging to 0) to propagation (converging to
1) is sharp. Numerical results are provided to verify the theoretical results.
