Program topo_CEG needed a bit of re-writing. The adjacency matrices generated from real communities are very large, due to high species richnesses. The matrices are so large that they cannot be initialized as simple arrays in C++, at least not on the stack. Had to use the Boost MultiArray function.
I ran 10 simulations of the Dicynodon Assemblage Zone (DAZ) community. Topological secondary extinction increases slowly, and then somewhat exponentially, as a result of increasing bottom-up perturbation. This is very encouraging in that the results are similar to the analytical results that can be obtained by using the combinatoric version of the model presented in Roopnarine (2006); results of application of this model to the DAZ were presented in Roopnarine et al. (2007). The main difference is that the simulations capture the effect of the stochasticity of the perturbation vector. Now, if we compare these results to those obtained with the full CEG simulation model applied to the DAZ, there are two obvious differences:
- First, the full model yields higher levels of secondary extinction.
- Second, the full model yields the “typical” CEG result, which means that there is, at some level of perturbation, a rapid increase (threshold) in the level of secondary extinction.
Therefore, topological extinction cannot account for the CEG results.
What else is there? The obvious missing feature are the top-down cascades that are initiated as a result of compensation for lost links/resources. And there is also link strength variance. These two features apparently generate a lot of the nonlinearity of the model. Exactly how much can be measured by basically subtracting the topological results from the full model results. This will require combining the full simulation program and topo-CEG. Going to need a bit of parallelization here!