Semi-major axis and masses of a synthetic population of planets orbiting a 0.2 M_⊙ star, colour-coded by initial disc metallicity. The three panels correspond to the three different gas accretion rates: Eq. 1 with β = 1 (top), Eq. A.2 (centre), and Eq. 1 with β = 2 (bottom). The dashed and solid purple lines represent the pebble isolation mass at the initial and final simulation time, respectively. The insets show the occurrence rate of super-Earths (black lines) and giant planets (brown lines) as a function of the initial disc metallicity.