Two models of host-parasite coevolution dominate the literature: Arms Race coevolution, in which host and parasite both accumulate successive adaptations and counteradaptations that spread to fixation, and Red Queen coevolution, in which host and parasite traits are locked in a tug-of-war caused by frequency-dependent selection but never reach fixation. We are using the field cricket / parasitoid fly system to detect and characterise the genomic signature of each form of coevolution, using geographic mosaic approach combined with population genomics of both cricket and fly. Infestation by flies evokes profound immunological and behavioural changes in the crickets, and genes underlying these responses respond to relaxed selection as some populations have entirely lost singing males. We are now examining how the presence of protective silent cricket hosts within populations exerts pressure on the flies, and the form of selection that that takes will enable us to test the coevolutionary models above at a genome-wide scale.