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Jennifer Dunne, in a recent paper (Dunne et al., 2009), defines the structural robustness of a food web as a minimum level of secondary extinction that occurs in response to a particular perturbation (species removal). This is roughly what I’ve termed “resistance”, but I think that structural robustness will be a very useful and more precise definition. The paper is part of a recent issue of the Philosophical Transactions of the Royal Society on food webs. Several papers in that volume point to the relationship between diversity and “robustness” (often used less specifically than defined by Dunne), but the nature of this relationship, if any, remains problematic.

Given our (the CEG group) growing collection of ancient and modern data sets, plus the array of CEG programs that we now have, I’ve decided to examine this question a bit more closely using a number of different communities. The main questions are:

1. Is there a straightforward relationship between species richness and food web robustness?
2. Does the relationship differ between marine and terrestrial communities?
3. Does it differ on the basis of geological age?
4. Does it differ between fossil and modern communities, given differences in data completeness?

Both topological or structural perturbations, as well as CEG dynamic perturbations are being performed on each data set. Answers to the above questions most likely differ dependent on whether species interactions are purely topological, or are dynamic! Perturbations are bottom-up disruptions of primary productivity, removal of top predators (top-down cascades), removal of most connected, and removal of least connected species.

The figure shows results from the Early Permian Waurika locality of Oklahoma. These data were compiled by Ken Angielczyk. The treatment is a bottom-up disruption of primary productivity at three different levels of species diversity: 1x, 2x and 3x observed (higher) taxon diversity. Treatments are also repeated for three different models for trophic link distributions, exponential $p(r)=Me^{-r}$, mixed power law-exponential $p(r) = e^{-r/ \varepsilon}$ where $\varepsilon = e^{(\gamma-1)\ln(M)/\gamma}$, and power law $p(r)=M^{\gamma -1}r^{-\gamma}$. Two conclusions: First, the effect of increasing total species diversity is to reduce the variance of the results, and perhaps reduce the overall mean (i.e. increase robustness), but the significance of this change has to be tested. Second, there is a striking difference among the trophic link distributions. The transition from Level I to Level II secondary extinction is discontinuous for the exponential and mixed distributions, but continuous for the power law (though the interval of transition is represented by acceleration of secondary extinction). What causes this?