Category Archives: Visualization

Hive plots for visualizing complex networks

Martin Krzywinski from British Columbia Genome Sciences Centre proposes a new type of network layout to reduce ‘hairball’ mess of standard network visualizations Hive Plots – Linear Layout for Network Visualization, in which nodes are located on on radially distributed linear axes based on network structural properties and edges are drawn as curved links.  I hope there is an R package in the works.

Eric Berlow responds on networks & system analysis

In his TED talk Eric Berlow presented a causal loop diagram (CLD) of the US army’s Afghanistan Counter-Insurgency (COIN) strategy and then used its network structures and features to simplify it.

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.

Nile Delta at Night

Nile River Delta at Night from NASA’s EOS image of the day.  They write:

The Nile River and its delta look like a brilliant, long-stemmed flower in this astronaut photograph of the southeastern Mediterranean Sea, as seen from the International Space Station. The Cairo metropolitan area forms a particularly bright base of the flower. The smaller cities and towns within the Nile Delta tend to be hard to see amidst the dense agricultural vegetation during the day. However, these settled areas and the connecting roads between them become clearly visible at night. Likewise, urbanized regions and infrastructure along the Nile River becomes apparent.

Mapping Australian arid land research

Ryan McAllister and others use the network mapping methods of Martin Rosvall and Carl T Bergstrom (see previous post) to analyze the research impact of Australian arid lands literature in the paper –  McAllister et al. 2009.  Research impact within the international arid literature: An Australian perspective based on network theory.  Journal of Arid Environments 73(9) 862-871 (doi:10.1016/j.jaridenv.2009.03.014).

The figure below show the different research subfields McAllister et al. identified within arid lands research and the citation links among them.

Figure 4. Linkages between 21 partitions of the Australian arid literature (based on GN-Mod – see Table 7). Location of authoritative-hub articles (from Table 3): “Animal ecology” contains (Buckley et al., 1987) and (Morton and James, 1988), and Stafford Smith and Morton (1990); “Plant ecology” contains (Ludwig and Tongway, 1995), (Mabbutt and Fanning, 1987), (Montaña, 1992) and (Tongway and Ludwig, 1990), and Tongway et al. (1989); and “Geospatial” contains Pech et al. (1986).

Mapping Science

A nice 2008 PNAS paper Maps of random walks on complex networks reveal community structure (PNAS 105, 1118) [pdf] by Martin Rosvall and Carl T Bergstrom creates  beautiful and informative visualizations of citation networks in science (from 2004 ISI data) using a neat method for visualizing and analyzing complex networks.  Martin Rosvall has a created a website that enables the creation of similar maps of network data.

Figure 3. In Rosvall and Bergstrom 2008. A map of science based on citation patterns. Analysis of 6,128 journals connected by 6,434,916 citations were clustered into 88 modules and 3,024 directed and weighted links.

Figure 4. A map of the social sciences. The journals listed in the 2004 social science edition of Journal Citation Reports (32) are a subset of those illustrated in Fig. 3, totaling 1,431 journals and 217,287 citations.

Visualizing Planetary Boundaries

Seems like Christmas comes early this year! just announced the results  of the Visualizing Marathon 2010. One of the challenges was to visualize planetary boundaries, i.e. the concept of multiple and non-linear earth system processes presented by Johan Rockström and colleagues last year.

The winner: MICA Team #3 and the project One Day Cause + Effect: A look at energy emissions and water usage over the course of one day (by Christina Beard, Christopher Clark, Chris McCampbell, Supisa Wattanasansanee). Congratulations! The other visualizations are also well worth a look – and a few clicks as many of them are interactive.

2010 Honorable Mention: SVA Team #1: Pushing the Boundaries: A Visualization of Our Footprint on Earth. Submitted by: Clint Beharry, David Bellona, Colleen Miller, Erin Moore, Tina Ye

2010 Honorable Mention: MICA Team #1: What Kind of World Do You Want?: A visualization of planetary boundaries. Submitted by: Melissa Barat, Bryan Connor, Ann Liu, Isabel Uria

What Kind of World Do You Want?

Syr Darya river meanders

Beautiful pictures from NASA EOS showing paleo and historic river meanders in the floodplain of the Syr Darya River in Kazakstan.

The floodplain is shown here as a tangle of twisting meanders and loops (image center). The darkest areas are brushy vegetation along the present course (filled with blue-green water); wisps of vegetation are also visible along flanking swampy depressions, or sloughs. An older floodplain appears as more diffuse dark vegetation (image upper left), where relict bends are overlain by a rectangular pattern of cotton fields. The straight channel of a new diversion canal—one of 16 from this point downstream—can be seen along the east bank of the river. The older floodplain is fed from the Chardara Reservoir, immediately upstream (not shown).

Spread and mutation of panarchy

The Database of the Self in Hyperconnectivity is a graphic created by Venessa Miemis a Media Studies student, who created the figure for a course project, to communicate different ways people interact with online information (there is also an interactive version).

She used Holling’s adaptive cycle, which she calls a panarchy (but because she misses the x-scale aspect its really an adaptive cyle) to identify contexts in which individuals act, but acknowledges this in a comment discussion.  Its interesting to see resilience thinking ideas pop up in other contexts.

I’m curious to the path by which panarchy moved into media studies (a quick google showed research in tagging classification systems using it) , and I wonder if any of the research on roles of people in environmental management done by Resilience Alliance researchers (e.g. in Panarchy book or Frances Westley, Per Olsson, and Carl Folke‘s work) was carried over with the concept.  However, there are no references and no explanation of how the figure was created, but she does link to an Ecology and Society paper.