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Transition point refers to the perturbation magnitude at which there is a rapid or nearly discontinuous increase in the level of secondary extinction. One can think of it as a threshold (“tipping point”) separating two alternative states in which the food web can find itself after perturbation. The DR 525 results present an opportunity to understand the dynamics of this transition. I therefore ran a number of experiments and also examined in detail the network dynamics in this perturbation region.

The first experiment was to remove the two herbivore guilds whose topological secondary extinctions coincide with the dynamic threshold. Progressive perturbation or removal of species in these two guilds fails to reproduce the threshold. Secondary extinction among the other heterotroph guilds, and autotroph nodes, remains nearly constant and low (\bar{x}=0.18 and 0.00008 respectively) across the perturbation range. Therefore, removal of these herbivore species themselves is insufficient to generate the transition. Nevertheless, their topological extinction is a marker for the transition.

The transition can be explained by noting the points at which the autotroph guilds disappear. There are four such guilds which were perturbed: benthic microautotrophs, phytoplankton, benthic macroalgae and macrophytes, and detritus (this last one is not truly autotrophic, but is treated similarly in the metanetwork). Benthic microautotrophs and detritus are the smallest of these basal nodes because of the lower diversity of benthic micrograzers and detritivores in the community. Therefore, as we apply a uniform perturbation to all four guilds, these two disappear completely at a perturbation magnitude 0f 0.51. When we examine this point on the simulation output, we note immediately that there is a subtle, yet discrete and secular increase in secondary extinction at that point and above. The second such secular change, the tipping point, occurs at a perturbation magnitude of 0.67, which is the point at which the benthic macroautotrophs become completely extinct; there is yet planktonic production available to the community. While there are numerous phytoplankton consumers (e.g. suspension feeding bivalves) in the community, and only a minority of benthic macrograzers, a vast number of heterotrophs depend indirectly on the consumers of the benthic microautotrophs, benthic macroalgae and detritus, and the final loss of the benthic macroproducers therefore pushes the community to a state of very high secondary extinction. The transition is generated by the propagation of bottom-up losses of links that although topologically minor, result in significant top-down compensatory increases of interaction strengths, and the network collapses.

This makes perfect sense from an ecological standpoint. But we must remember that no recovery or replenishment is permitted by the model. Addition of these factors would increase model complexity significantly, and also require major assumptions of exactly how to parameterize the physical environment and metapopulation structures appropriately. Nevertheless, these do remain as potential escape routes for the community if the perturbation is localized. And a final word on the transition or tipping point. I can see no way, at this stage, in which one could easily predict the location of the tipping point solely from the network structure. That is, there is no elegant mathematical solution available because of the complexities of the network interaction. The computer simulations are algorithmic, not analytic. I do predict, however, that many if not most communities should have such a tipping point of secondary cascades and extinctions embedded in their structure. The extent to which this is true depends most likely on overall community richness, functional diversity at the higher guild level, and individual guild richnesses.

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