When only the female sensitivity can evolve, the ‘variable cost model’ gives qualitatively different predictions about the coevolutionary dynamics of male persistence and female resistance. Dashed lines denote the value of the female threshold used in the analyses. The ‘constant cost model’ predicts either a stable cycle of escalation and retreat, or an indefinite exaggeration of male persistence (a,c). The ‘variable cost model’, however, can shut down the exaggeration of male persistence and cause the male trait to disappear from the population (b,d). In (a,c), trajectories coloured black to light grey denote increasing cost of mating for females, given through parameter values β = 10−5, β = 2 × 10−5, β = 3 × 10−5, β = 4 × 10−5 and β = 5 × 10−5, respectively. Similarly, in panels b and d, trajectories coloured black to light grey are under increasing cost of mating, through parameter values γ = 10−6, γ = 2 × 10−6, γ = 3 × 10−6, γ = 4 × 10−6, γ = 5 × 10−6, with β = 10−5 across all analyses. Remaining parameter values are: F = M = 1000, vP = vS = 0.5, vT = 0.0, αP = αs = αT = 0.0, ε = 0.005, fb = 100.