Probability of topological secondary extinction. Prey guild diversity is 150, and consumer in-degree ranges from 1 to 10.

I suspect that the dichotomous topological extinction results have to do with the presence of two distinct types of species-level networks in the simulations. I’ll explore the reasons for that later, but right now, I want to know if this explanation is feasible. The networks would differ in having very different types of species composing the guilds, different in their in-degrees and hence resistance to topological secondary extinction. A clue is given by how the probability of extinction varies with in-degree. The first figure illustrates this, although it is not the probability surface for our particular 3-guild community (calculations performed with GNUPlot, which is unfortunately limited in its ability to calculate factorials in the necessary range). We see that the probability of extinction declines nonlinearly as in-degree increases.

If we focus on the primary consumer guild only, the suggestion of distinct classes of networks becomes a bit more obvious. Plotted here (second figure) are the simulation results for this guild only. The expected levels of secondary extinction are overlaid again, as previously. There is apparently one set of networks that conform reasonably well to the expected results, but another set with very high extinction at even low levels of perturbation. I hypothesize that these latter networks comprise consumer species of very low in-degree. The likelihood of getting such networks must be fairly high; this can be determined, I think, by examining the multinomial probabilities of such networks. It is quite possible that at low guild diversities and metanetwork complexity, the multinomial likelihood surface is relatively flat. We’ll see.

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