Fig 1. The solution of the linear model of Refs. [9, 10] shows the dependence of the average density of species 〈x*〉 as a function of the ratio s/γ, as given by Eq (5).
For small values of the interaction strength γ, the system is in the feasible and stable fixed point 〈x*〉 > 0 (lower branch of the full line in the top right quadrant). Increasing γ, at fixed s, the species density 〈x*〉 increases following the full red line, and eventually diverges at the critical point γc predicted by the linear model to be γc = s/μmax. For s/γ < μmax, the nontrivial fixed point is negative, 〈x*〉 < 0, and unstable (dashed line), so that the only stable fixed point is the collapsed state 〈x*〉 = 0 (red dot). Thus, the linear model of mutualism predicts the collapse of the ecosystem as the instantaneous extinction of an infinite number of mutualists at the diverging point s/γc.