Red ellipses represent the two threshold points.
The story so far: We have a food web of a shallow coastal marine community from the Late Miocene of the Dominican republic. The metanetwork comprises 29 guilds, 139 guild-level links, and 130 species. A perturbation of the system, where all three primary producer guilds plus detritus were systematically and incrementally removed from derived species-level networks, results in the typical CEG result: that is, a relatively flat and low level of secondary extinction (
) over a broad range of perturbation magnitude (
), succeeded by a rapid transition to a state of high secondary extinction. In fact, for this community, there are two transitions. The first occurs at 
, and represents a very minor but secular increase in . The second transition occurs at 
and represents a catastrophic increase in . Topological-only perturbation of the system makes it very clear that these transitions correspond exactly to two stages of the perturbation: First, the complete extinction or removal of benthic autotrophs and complete disruption of the particulate detritus supply. The second and greater transition occurs at the complete extinction of the benthic macroalgae and macrophytes. Accompanying the second transition is the complete extinction of the benthic herbivore guilds which specialize on the macroalgae and macrophytes (and derived detritus), comprising families such as the Phasianellidae, Cerithiidae, Vitrinellidae, Haminoeidae and Retusidae. This is accompanied by extinction of species in other more generalist guilds that include macroalgae in their diet.
Extinction of those heterotrophic taxa is not itself the cause of the major tipping point though. Simulations where the perturbation is specifically removal of these herbivores result in very low levels of secondary extinction, with no tipping point or threshold. The obvious question then is, why does extinction of the macroalgae drive the system to a new state? The qualitative answer is that the complete loss of this resource, and the bottom-up propagation to the herbivores, in turn cause intense top-down cascades of compensatory responses from higher level consumers. These cascades propagate throughout the network, even to the remaining source of production, the phytoplankton. The result is a tremendous loss of species. A very curious thing, however, is that phytoplankton productivity in the network is almost 3 times greater than macroalgal productivity, reflecting the much greater diversity of planktivores. So why does the collapse coincide with loss of the macroalgae?
Perturbation of macroalgae (top) and phytoplankton (bottom), and resulting loss of autotrophic productivity because of top-down effects (left), and secondary extinction of heterotrophic species (right).
I performed two separate perturbations to answer this question. First, I perturbed the system by removing macroalgae only, and second by removing phytoplankton only. The top row of the second figure shows the results of the first experiment. Secondary loss of autotrophic resources (left column) as a result of top-down effects is effectively zero. Secondary extinction of heterotrophs (right column) is significant but not dramatic. There is a mild increase in the region of 
, which represents the loss of the specialized herbivore guilds. Removing phytoplankton had a more dramatic impact, reflecting the greater overall dependence of the community on phyloplankton resources. There is a clear threshold, occurring at approximately 
. At this point, resource loss to the community is great enough to trigger the catastrophic top-down cascades and feedback within the network. Therefore, it seems that in the previous experiment, where all resource guilds were perturbed, the complete loss of macroalgae triggers the top-down cascades and compensatory feedback that in turn deplete phytoplankton resources to the point where the system transitions to a higher state of secondary extinction. This conclusion is supported by the fact that when all producer guilds are perturbed, the contribution or perturbation of phytoplankton at the tipping point is 38%, whereas when only phytoplankton are perturbedm the tipping point occurs at 50%.
Some closing observations:
- Topological analyses of network vulnerabilities are likely to underestimate the severity of link losses when those links have variable interaction strengths, and the nodes have varying properties. In the case of a biological community, species could and are likely to alter interaction strengths to compensate for lost resources (i.e. links). Topological vulnerability analyses should be well suited for networks with static properties, perhaps such as power grids and the internet (though I’m no expert here!), but are ill-suited for dynamic networks, such as those describing transportation, metabolic/physiologic and ecologic systems.
- An hierarchically structured, directed network such as an ecological community should be resistant to a broad array of random perturbations. This is a function of both the underlying link distributions (as already understood in the case of static networks or graphs), as well as the compensatory abilities of consumer species, and the variance of dietary breadth. The network is, however, vulnerable to the loss of highly linked nodes. Here I am referring specifically to basal, autotrophic nodes, and not necessarily keystone consumer species. Not all autotrophic nodes are equal, however, as shown in the above results. Nevertheless, because of the complexity of the species interactions and the hierarchical divisions of ecological functions, there should be strong nonlinearities in the network responses. This is borne out by the differences between the topological-only and fully dynamic simulation results. The nonlinearities are expressed as two or more alternative states of secondary extinction, separated by rather sharply defined thresholds of perturbation. I can think of no way in which to analytically predict the threshold points, but heuristically I would argue that they should exist in every ecological community.
- Perturbation of top-level consumers are observed in nature to often result in top-down cascading effects, compatible with such notions as keystone predators. I will show in later results that the CEG model captures all this. The results will also show, however, that while top-down effects can be locally catastrophic, i.e. for individual species or groups of closely linked species, they are never globally catastrophic in the manner in which bottom-up perturbations are. This conclusion has implications for understanding the role of ecological collapse in large scale extinctions observed in the fossil record. It also has implications for the ongoing biodiversity crisis, where species far removed from the “tops” of food webs are increasingly threatened by climate change and habitat destruction.
- An close examination of many of the results presented in this blog will show apparent “bifurcation” of the results, e.g. beyond the threshold point in the lower right graph above. These observations suggest that there is more than one type of species-level network that can be derived from the same metanetwork. So, while the higher-level organization of the community is the same, networks are being generated that vary enough in their interspecific link topologies to yield very different responses to the same level of perturbation. I believe that this is a statistical property of the underlying trophic link distributions and the resulting multinomial probabilities from which the species-level networks are drawn stochastically. In the case of the above results, where one set of networks is significantly more resistant than the other (i.e. they have a much higher tipping point), this mathematical feature of the model is not likely to be of great relevance ecologically. That is because the lower threshold is already so high, in this case, 50% shutdown of primary productivity. Those are catastrophic environmental conditions and would occur with very low frequency in nature on a large scale. There are cases, however, such as the Early Triassic Lystrosaurus zone community, where there seem to be multiple alternative states at very low perturbation levels. Those communities would very likely have experienced frequent low-level perturbations, and then one has to consider whether: (1) this feature of the model is a mathematical artifact, in which case one wonders about the constraints necessary to prohibit it in nature, or (2) the feature is real, and then one wonders how species within a community cope with such a situation.
Large reductions in the abundance of exploited land predators have led to significant range contractions for those species…(read more 
