  We use the semi-analytic method developed by Fedeli et al. for computing
strong-lensing optical depths to study the statistics of gravitational arcs in
four dark-energy cosmologies. Specifically, we focus on models with early dark
energy and compare them to more conventional models. Merger trees are
constructed for the cluster population because strong cluster lensing is
amplified by factors of two to three during mergers. We find that the optical
depth for gravitational arcs in the early dark-energy models is increased by up
to a factor of about 3 compared to the other models because of the modified
dynamics of cluster formation. In particular, the probability for gravitational
arcs in high-redshift clusters is considerably increased, which may offer an
explanation for the unexpectedly high lensing efficiency of distant clusters.
