Fig 3. Phase diagram of the linear model equation which plots the largest eigenvalue of the adjacency matrix μ_max versus the ratio s/γ for the 9 empirical mutualistic networks explained in Table 1.

All the networks lie in the unstable region μ_max > s/γ, and hence they do not satisfy the condition of the linear model μ_max < s/γ, which is necessary to have a feasible (i.e. 〈x*〉 > 0) and stable solution. Hence the linear model of Eq (3) predicts that these 9 existing ecosystems should indeed collapse (i.e. 〈x*〉 = 0 for all of them) in contradiction to the fact that they are real feasible ecosystems present in nature.