Temporal changes in (a) the capture rate of planetesimals and (b) the total mass of planetesimals inside the feeding zonein the reference case (see Table 1 for the setting). Red and blue lines show the contributions of planetesimals initially located on the side far from and close to the central star relative to the initial position of the 2:1 mean motion resonance (12.6 AU), respectively; the black one shows all the contributions. Top x-axis shows the semi-major axis of the migrating planet.