Figure 5 Size of the Giant Component (IMAGE) Queen Mary University of London Caption The size of the giant component R as a function of p for dierent values of ! is shown for the Ythan Estuary (panel (a)) and the Silwood Park (panel (b)) Foodwebs [46]. We observe that for ! > 0 the percolation transition is discontinuous while for ! = 0 we obtain the typical scenario of percolation characterized by a continuous phase transition. The non-convex rate function I(R) evaluated numerically over 2105 initial realization of the random damage is shown for the Ythan Estuary (panel (c)) and the Silwood Park (panel (d)) Foodwebs and dierent value of p (symbols). The convex envelop of I(R) provided by the Legendre-Fenchel transform of !F(!)=N is shown with solid lines for the same values of p (note that for improving the clarity of the gure we have omitted to plot the linear part of the convex envelop for p = 0:24; 0:28 in panel (c) and for p = 0:20; 0:24 in panel (d)). Credit Ginestra Bianconi Usage Restrictions None License Licensed content Disclaimer: AAAS and EurekAlert! are not responsible for the accuracy of news releases posted to EurekAlert! by contributing institutions or for the use of any information through the EurekAlert system.