Calibration of the K_s-band absolute magnitude of the TRGB as a function of (J − K_s) colour, based on the data of Serenelli et al. (2017). The solid line indicates the fit to models in the colour range 0.75 <  (J − K_s)< 1.3 mag and ages between 4 and 14 Gyr. Sets of different metallicities are indicated by open triangles ([Fe/H] = −1.49 dex), filled squares ([Fe/H] = −1.27 dex), open circles ([Fe/H] = −0.96 and −0.66 dex), filled triangle ([Fe/H] = −0.35 dex), and open squares ([Fe/H] = −0.25, −0.01 and +0.06 dex). Models outside these criteria are indicated by the small dots.