Thresholds for strong clumping as well as planetesimal formation rates. Initial dust-to-gas surface density ratios (Σ_d/Σ_g)_init and Stokes numbers St or dust sizes a are plotted on the ordinate and the abscissa, respectively. Blue, orange, and green colors represent our models of the streaming instability in isolation, the scenario SIwhileVSI and the scenario SIafterVSI. Simulations that do not experience strong clumping are depicted as empty circles; ones in which the planetesimal formation rate during the strong-clumping phase is less than 0.1 kyr⁻¹ are represented by half-filled circles and ones in which the rate is greater than this value as filled circles. Lines separate combinations of (surface density ratio, dust size or Stokes number) for which strong clumping does or does not occur. The minimum values of these two parameters required for strong clumping are smallest in the scenario SIafterVSI, with the combinations (0.5%, St = 0.1) and (1%, a = 3 mm) being sufficient. The planetesimal formation rates, on the other hand, are by tendency highest in the scenario SIwhileVSI.