Fig. 2.
Stability responses to diversity across a range of biologically constrained whole food web models. These changes in constraint level effectively consider all of the parameter space (here represented as an example cube; see A Concrete Example C-R section in the text), a feasibility slice (lower dimensional slice of parameter space represented as a plane) and even lower dimensional slice through the parameter space (here represented as a line). The mean stability response [solid curves, Re(λMAX)] and the 95% CI stability to diversity of (A) unconstrained random matrix models; (B) inverse method matrix model under only feasibility constraint, and; (C) inverse method matrix model under feasibility constraint and energetic constraint (i.e., imperfect conversion). Panel (i) shows the same scaling of the stability responses while panel (ii) zooms in to show the more detailed response of each case. Classical, unconstrained models (A, i, and ii) and feasibility alone models (B, i, and ii) show the characteristic destabilization curves with diversity while the energetically constrained model shows a decoupled stability response with diversity and a relatively consistent proportion of stable webs. We note in this case they are relatively weakly stable or relatively weakly unstable and do not experience the extreme instability of the classical and feasible model.