Coevolution between hosts and their parasites is expected to follow a range of possible dynamics, the two extreme cases being called trench warfare (or Red Queen) and arms races. Long-term stable polymorphism at the host and parasite coevolving loci is characteristic of trench warfare, and is expected to promote molecular signatures of balancing selection, while the recurrent allele fixation in arms races should generate selective sweeps. We compare these two scenarios using a finite size...