Resonance offsets of the consecutive pairs for the resonant chain of Kepler-80 (planets d, e, b, and c). Cyan diamonds show the observed values (as in Fig. 3), while gray symbols show the simulation outcomes where no tides are considered (circles), or with tides (following Eq. (5)) applied to the inner planet (triangles), first two planets (crosses), first three planets (stars), and all the planets (squares, see the long-term evolution in Fig. 4). Integrations were made for 5 × 10⁶ yr with Q′ = 0.05 and the parameters of Table 1.