One of the final pieces needed to explain the critical/threshold point in a bottom-up CEG perturbation is an understanding of which species become extinct, and what the species dynamics look like during the cascade. Therefore, what I’ve done is to modify the basic simulation to capture the demographic properties (technically, the carrying capacities) of each species; results in HUGE output files. Shown here in this figure are the species dynamics for the guild of shallow infaunal carnivores (e.g. naticid snails) at three different perturbation levels. Note that the levels correspond to a low secondary extinction response, and the two critical points identified earlier. The top row of figures plot the dynamics of surviving species, and lower show those of the species which become extinct. The community dynamics were recorded for 250 steps beyond the initial perturbation. The first thing to note is that species become extinct very quickly. Beginning K for each species is standardized at 1, and the species that become extinct have, on average, lower in-degrees, i.e. lower numbers of prey, than do surviving species (statistical tests to follow later). That result matches expectations of the CEG combinatoric model.

The other thing to note is that at the low and mid-perturbation levels ($\omega =$ 0.2 and 0.55), species’ K respond immediately to a perturbation of the producer guilds, oscillate for several steps, but eventually settle down to a new stable K. This is a transition to new stable states for the species populations. At the perturbation level which coincides with the major critical point of secondary extinction, however, there is no indication that the species ever settle to a new state. Instead, there seems to be bifurcation and subsequent alternation between two alternative stable states; the species are lit up by the disturbance (each species is given a different colour in the corresponding plot for easy distinction). The series is quasi-periodic though, in that the system never returns to quite the same point on alternating steps. It is possible that the series eventually converge to a single, or two, stable points, but the current data cannot address that. Therefore, I’ll next repeat this simulation, but extend the data capture to 1,000 steps ($\approx$2Gb file). Hopefully that will give some indication of whether the series are converging, diverging, are stable, or perhaps chaotic. Also, the results for the other guilds need to be examined.