Having not decided on what to post for Darwin Day 2017 in advance (and thus being late to the party with my annual post), I will be taking a rather circular approach to this post. I recently read a blog post on a TEDMED talk by Artem Kazneechev  on how theorists offer opportunities for collaboration across multiple research domains and existing research communities. The most extreme case is that of Paul Erdos, for whom the term "Erdos number" was coined . The Erdos number defines a degree of association on a collaboration graph between a given author and Erdos as defined through co-authorship . The role of theorists in such collaboration graphs is intriguing, and involves their role as hubs (highly-connected nodes) in a scale-free network topology . In terms of the scientific community, such hubs often serve as connectors between disciplinary groups and sub-communities.
As Kazneechev  points out, sometimes one need not be as prolific as Paul Erdos to serve as a connector. Henri Poincare was a bit less prolific, and certainly did not live out of a suitcase, but serves as a scientific connector nonetheless. In fact, all theorists are at an advantage in this regard. This makes me wonder what a collaboration graph centered on Charles Darwin would look like. While I do not have the neccessary data, I would imagine it would quite different from Erdos' graph. This is because Darwin (as far as I know) did not publish collaborative papers. However, a citation network  in which documents rather than scientists serve as the nodes might better capture Darwin's role as an influencer, and thus partially recapitulate the topology of an Erdos-based collaboration graph.
Lately, I have been doing some unfocused research on polymathy . One of the things that has fascinated me is the distinction between "domain-specific" knowledge and "general" knowledge, particularly as it relates to specialization. One criticism of modern science is that it suffers from hyper-specialization. The trend towards hyper-specialization has been constant over historical time, and now contrasts sharply with the scientists of the 16th and 17th century. This trend has been countered in a number of ways, particularly through interdisciplinary initiatives. Yet all too often, interdisciplinarity is reduced to groups of specialists gathered in the same room talking past one another.
A "T" shape skillset in terms of employment skills and educating talent. COURTESY: T-Summit 2014.
I am interested in taking a landscape model approach to modeling polymathy as a function of expertise and semantic specialization. In getting there, we have to understand the relationships (various dimensions) of specialization and generalized knowledge. According to the education and tech literature, the traditional polymath can be modeled as a "T". In fact, the T-shaped skillset is back in vogue in some fields (e.g. design, project management). It is somewhat difficult to make the leap from abstract skills to specific facts and other knowledge that facilitates (or constrains) scientific collaboration.
To help this along, I have worked out an ontological and semantic model of scientific expertise. In the figure above, I show the bivariate model as a shape representing the relative "depth and "breadth" of a particular style of scientific practice. While there are "Is" (specialists) and "Ts" (generalists with a single specialty), there are also "combs" (generalists with multiple specialties) and "dashes" (pure generalists). "Combs" are most analogous to the traditional polymath, but it is interesting to ask where Charles Darwin (and other theorists) would fit into this type of scheme.
While Darwin has shaped the thinking of many scholars in multiple fields (both traditional and upstart) over the past 150 years, he was also influenced by a variety of thinkers. Even more than a scientific specialist, the essence of theorists can be captured by multiple-input, multiple-output (MIMO) graphs of major ideas. This can extend even beyond the lifetime of the scientist. The following graphical example of influencers and the influenced (inputs and outputs) is from Semantic Scholar, and shows Charles Darwin's position in a semi-directed citation network within the Computer Science community.
Charles Darwin's academic influence as MIMO graph. See profile for details on how graph is computed.
 Kazneechev, A. (2012). Theorists as Connectors: from Poincare to mathematical medicine. Theory, Evolution, and Games Group blog, November 4.
 Newman, M.E.J. (2004). Who Is the Best Connected Scientist? A Study of Scientific Coauthorship Networks. Lecture Notes in Physics, 650, 337–370.
 Alicea, B. (2011). Academic Connectivity and the Future of Scientific Ideas. Synthetic Daisies blog, September 9.
 Newman, M.E.J. (2001). The structure of scientific collaboration networks. PNAS, 98(2), 404-409.
 More information about citation networks and their usefulness to the practice of science can be found in: Editorial (2010). On citing well. Nature Chemical Biology, 6, 79.
 A few popular readings on polymathy: Arbesman, S. (2013). Let's Bring the Polymath -- and the Dabblers -- Back. Wired, December 13 AND Mazie, S. How to be a Polymath. Big Think blog.