Evolution of the disc-stability criterion (Toomre parameter Q) and clump properties. In the upper panel is shown the evolution of the Toomre parameter with z (Eq. (68), grey line). On this timeline, vertical arrows indicate a merger event (with short and long arrows for minor and major mergers, respectively). For 11 <z< 1.5, the Toomre parameter is larger than the critical value Q>Q_crit = 1, and therefore the disc is stable, but for 1.5 <z< 0.25 (highlighted by the two vertical black lines), the disc becomes unstable. During the unstable transition, bounded by two merger events, many clumps are formed and migrate. The lower panel shows a zoom of this unstable period. The blue and green lines show the number of clumps (left y-axis) and the average individual mass of these clumps (right y-axis), respectively. After a merger event, disc instabilities lead to the formation of a large number of clumps (42) with small individual masses (). Then, during a series of merger events, clumps are destroyed and formed again, but with higher individual masses. Between two merger events, the number of clumps increases while the individual mass remains stable. A decrease in one or two clumps is linked to the migration process. It is interesting to note that the migration process creates a temporary stable disc (Q>Q_crit = 1). In the second part of the unstable period, only one clump is formed but with a much higher mass. Finally, this single clump is disrupted and the disc becomes stable again.