(A) Blowup of the phase diagram of Figure 2 showing the region with reduced EGF and excess Notch. The arrow (P3) represents gradual increases in ectopic Notch activity in the background of an EGF hypomorph, lin-3(e1417) or CB1417 in (Barkoulas et al., 2013) (fit to ~0.28 × WT). The boundary between the 33333 and 33133 domains makes a slight angle with the vertical, thus induction of P6.p to the 1° fate is partially rescued by Notch. (B) Fate proportions vs. Notch dosage in the model. The red bump in the left column reflects the partial rescue of P6.p induction by mild ectopic Notch activity. Under higher Notch doses, P6.p is converted to the 2° fate, as observed in a comparable experiment with EGF RNAi (Barkoulas et al., 2013). Correspondence with the data in (Barkoulas et al., 2013) is shown with the pie charts. An extra condition, C2, near maximum induction, was added to illustrate the model in the next panel. (C) Model trajectories for the EGF hypomorph, and the cross with a silent Notch gain-of-function line (N = WT + 0.1, the line C2 in B). In contrast to prior fate plane depictions, we show with arrows the flow experienced by P6.p during the competence window, including autocrine Notch signaling. Thus, the red trajectory follows the arrows. All cells begin at the same location at the beginning of competence (intersection of colored lines). The P6.p cells move toward the saddle or decision point (white cross) that separates the 1° and 2° fates, and then spread out along the line exiting that point. In C2, a small ectopic Notch signal pushes the P6.p points away from the decision point and more flow into the red 1° fate domain. (D) Enhancement of 2° induction by mild EGF activity (Zand et al., 2011). In this Notch sensitized background (N = WT + 0.16, D1), there is no AC or EGF signaling, and cells flow into the saddle point (white cross) separating the 3° and 2° fates and then diverge into two streams, using the same representation as in C. In D2 we add ectopic EGF activity [lin-15(ts)] (EGF = 0.16, +red arrow) which moves cells away from the line that flows into the saddle point. Thus, more cells are deflected toward the 2° fate by the flow around the saddle point. EGF never points toward the 2° fate, yet by acting early in the competence period can effect a large change in outcomes precisely because the background in D1 is poised near the saddle point and the flow around the cross rotates by 90°.