I am interested in combining network and systems analysis to better understand complex systems, so it was great to get Eric Berlow‘s repsonse to Tom Fiddaman’s comments on his analysis of an US Army causal loop diagram talk. My PhD student Juan Carlos Rocha, is working on analyzing ecological regime shifts using network approaches and both Eric’s and Tom’s comments provide useful ideas.
Tom Fiddaman wrote:
I think the fundamental analogy between the system CLD [causal loop diagram] and a food web or other network may only partially hold. That means that the insight, that influence typically lies within a few degrees of connectivity of the concept of interest, may not be generalizable. Generically, a dynamic model is a network of gains among state variables, and there are perhaps some reasons to think that, due to signal attenuation and so forth, that most influences are local. However, there are some important differences between the Afghan CLD and typical network diagrams.
In a food web, the nodes are all similar agents (species) which have a few generic relationships (eat or be eaten) with associated flows of information or resources. In a CLD, the nodes are a varied mix of agents, concepts, and resources. As a result, their interactions may differ wildly: the interaction between “relative popularity of insurgents” and “funding for insurgents” (from the diagram) is qualitatively different from that between “targeted strikes” and “perceived damages.” I suspect that in many models, the important behavior modes are driven by dynamics that span most of the diagram or model. That may be deliberate, because we’d like to construct models that describe a dynamic hypothesis, without a lot of extraneous material.
Probably the best way to confirm or deny my hypothesis would be to look at eigenvalue analysis of existing models. I don’t have time to dig into this, but Kampmann & Oliva’s analysis of Mass’ economic model is an interesting case study. In that model, the dominant structures responsible for oscillatory modes in the economy are a real mixed bag, with important contributions from both short and longish loops.
Eric Berlow responds:
I only wish that I had more time to discuss these important issues in the 3 min time frame (I think it took me more than 3 min to read the comment itself). You articulate extremely well the difference between a network with consistently defined nodes and links and a CLD which reads basically like a brainstormed mind map. The Afghan COIN diagram is clearly the latter.
In our 2009 PNAS paper [Berlow, E. L., J. A. Dunne, N.D. Martinez, P.B. Stark, R.J. Williams, and U. Brose. 2009. Simple prediction of interaction strengths in complex food webs. Proceedings of the National Academy of Sciences 106: 187-191.], as well as Brose et al. 2005 Ecology Letters [Brose, U., E. L. Berlow, and N. D. Martinez. 2005. Scaling up keystone effects from simple to complex ecological networks. Ecology Letters. 8: 1317-1325.], we see some interesting examples in food webs where the spheres of influence remain remarkably ‘local’ to the node of interest. We also observed that the more complex the network (more species and associated links) the easier it was to predict how the removal of one species will change the abundance of another. One mechanism by which that could occur is if perturbations dampen with distance. That dampening may be due to an accumulated inefficiency of energy transfer in long paths (as you suggest). However other results suggest it is not that straightforward. The patterns we observe also may be due to the increased likelihood that a long path will contain one weak link that truncates the effect. And the more complex the web, the more chances multiple long paths from species A to species B cancel each other out. We are currently exploring these options, among others, to see if there is a more general theory of when and how more complexity leads to simpler predictions. Identifying, or successfully predicting, when it does NOT is also extremely interesting and important.
My talk had two goals. One was to stimulate discussion about whether or when our food web results (‘localization of influence’) might apply to other networks. For example, the longer the path in this Afghanistan CLD, the more likely it will include a node that is very difficult to change. So you might expect, on average, truncation of influence with distance. I do not know, but it is worth exploring. It is also interesting (as an aside) that this simple structural analysis honed in on what many experts agree are core issues that must be addressed to achieve the stated goal. My second, and perhaps more important, goal was to communicate to a broad audience (broader than I ever imagined actually!) the more general, conceptual message that often it is only by embracing the true complexity of a problem that core simple issues emerge. I think this point generally rings true but is very under-appreciated and under-applied.
In retrospect, it was probably not very smart on my part to try and make 2 points in a 3 min talk! I apologize for any confusion. Thanks for the insightful discussion.