A Peripheral Darwin Day post, but Centrality in his Collaboration Graph

Happy Darwin Day-ish! COURTESY: Kapil Bhagat

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 [1] 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 [2]. The Erdos number defines a degree of association on a collaboration graph between a given author and Erdos as defined through co-authorship [3]. 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 [4]. In terms of the scientific community, such hubs often serve as connectors between disciplinary groups and sub-communities.

Darwin at the center (a hub with a high degree of centrality) of a hypothetical collaboration graph. Image is actually of an evolutionary amplifier, a computational structure from Evolutionary Graph Theory. Image of Darwin is from Dinochick's blog.

As Kazneechev [1] 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 [5] 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 [6]. 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. 

Components of the "I" shape in terms of academic influence and expertise. More information on this work to come.

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.

NOTES:
[1] Kazneechev, A. (2012). Theorists as Connectors: from Poincare to mathematical medicine. Theory, Evolution, and Games Group blog, November 4.

[2] Newman, M.E.J. (2004). Who Is the Best Connected Scientist? A Study of Scientific Coauthorship Networks. Lecture Notes in Physics, 650, 337–370.

[3] Alicea, B. (2011). Academic Connectivity and the Future of Scientific Ideas. Synthetic Daisies blog, September 9.

[4] Newman, M.E.J. (2001). The structure of scientific collaboration networks. PNAS, 98(2), 404-409.

[5] 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.

[6] 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.

Review of "Arrival of the Fittest"

"Arrival of the Fittest" is the latest book by Andreas Wagner, a professor at the University of Zurich in Switzerland. The book [1] tackles a subtly complicated topic: the evolution and evolvability of innovations using a biochemical and computational perspective. For the most part, Wagner succeeds at presenting an elegant case for how the ability to naturally evolve innovations lies at the heart of the evolutionary process. To get there, however, Wagner must introduce us to a number of semi-obscure concepts (at least to the layman). The book can be summarized in four parts: survival of the most novel (I), the concept of innovability (II), the safe and the risky (III), and multiple origins, multiple solutions (IV). I will give a technical review of the book by highlighting these four interrelated themes.

I. Survival of the most novel.
To understand the propagation of innovative solutions throughout the tree of life, it is important to understand the difference between the force of evolution versus the role of selection. Wagner proposes that, rather than creating innovations, the role of natural selection is to preserve them. Innovations themselves are the result mutation, recombination and historical contingencies. The first two mechanisms are capable of randomly generating either very simple innovations or the components of more complex innovations. But to achieve the "tinkering" that seems to be prevalent in complex genetic pathways and phenotypes, we need to have standard meta-components that can lock in previous changes. This allows for the limited exploration of a fitness space without incurring the cost of losing previous advances.

Results of evolutionary tinkering which leads to variability in snake venom. COURTESY: Venomdoc.com

Wagner teases historical contingencies this into two classes: building blocks and standards. In the case of building blocks, the working components that result from previous innovation are modularized into larger units. This allows for increasing complexity to be had from a stochastic process (evolution) as well as accelerating the process of finding and retaining novelties (innovation). The coordination of building blocks often leads to standards, which are much more flexible than hyper-specialized systems but are much more able to deal with hyper-complexity.

Building blocks assembled into a complex structure.

Wagner illustrates this by comparing metabolic engines (a high-tolerance biological engine) with the internal combustion engine (a high-precision mechanical innovation). While metabolic engines can use an interchangeable set of fuels and reactants, internal combustion engines require specific specifications to operate. While one might argue that this implies mechanical engines will be "optimized" and metabolic engines will be made "good enough", this is indeed the point. Rather than survival of the fittest, we observe a survival of the fit enough, with selection acting strongest on functional novelties that augment fitness.

A high-tolerance but highly-specific engine (internal combustion) type.

II. Concept of innovability.
In the case of complex metabolic networks, the basic function has not changed throughout evolutionary history. What has changed is the number of reactions, which scales with evolutionary complexity. This scaling requires very general standards. But to make these standards interoperable across divergent evolution, a diversity of building blocks regulatory mechanisms are also required. This leads us to a set of principles which can explain general trends in innovation rather than on a case-by-case basis. Another such principle involves the number of parts and identity of a specific innovation. The number of interacting parts and their configuration provides a means to compare specific innovations in a hypothetical manner. Wagner proposes that this be done using a high-dimensional structure such as a hypercube [2] or a neutral network [3].

In a hypercube representation, each node represents a specific genotype, while the edges represent pathways (or the accumulation of mutations) between genotypes. In short, the shortest paths are the most probable. In a highly-connected space, a long distance can be traveled across the space in a short number of mutations (or edges).

III. The safe and the risky.
How can the structure of a biological system make things safe for innovation? Certainly, blindly changing key components of a metabolic network or developmental scaffolding without regard for essential function can result in lethality. The presence of the building blocks and standards principles provides a failsafe means to tinker or change without lethal disruption. But there are two other principles at work: redundancy and connectivity. These principles are arguably more important in acting as gatekeepers for the fitness benefits reaped by innovations.

A machine finding its way through a maze. One way to search for novel solutions in a de novo fashion.

Redundancy involves the presence of multiple parts that play a similar or interchangeable role in the functioning of a system. For example, both genetic and metabolic networks can be robust to the removal of single components. When components get removed without having a consequence on function [4], we can say that such a component is redundant. Gene duplications can play a similar role: single copies can be knocked out without a large detriment to fitness. Related to redundant function is, of course, robustness. Robustness can be thought of as how much redundancy exists in a specific system. Wagner gives the example of phenocopying as a way in which developmental robustness can lead to redundant phenotypic configurations.

Connectivity is a less appreciated aspect of evolution. Yet in terms of functional and conceptual unity, connectivity is an essential component of evolving systems that produce innovation. Three aspects of connectivity are most important here: interaction type, density, and connection order. There are a number of interaction types in biological networks that can give rise to innovation. For example, we can look to genetic networks (interaction between genes), breeding networks (interactions between conspecifics), or even the aforementioned neutral networks (interactions between evolutionary configurations) for ways in which connectivity can yield pathways that lead to innovations of high fitness.

An example of a genetic (gene interaction) network. Sometimes this approach is called "hairball science". COURTESY: Figure 1 in [5].

Network density (or the number of interconnections between nodes) allows for a greater number of potential innovative solutions to be explored in a shorter number of steps. This can increase the number of potential solutions, which can be reached in a shorter number of evolutionary steps and/or time (depending on your perspective). In the neutral network, a number of "safe" pathways of equivalent fitness are created for the innovating pathway or organism to explore. While the network density is important in facilitating innovation, the connection order of the network is also important. In networks with a short connection order (e.g. small-world networks), even random paths through the network can yield large-scale, non-deleterious change.

An example of constituent genotypes in a neutral network with reference to robustness. COURTESY: Ricardo Azevedo, Wikipedia.

IV. Multiple origins, multiple solutions.
The final point of Wagner's book is to remind us that innovations can be achieved through multiple unique solutions, and that existing innovations may have had multiple origin points. While evolution also has no unique solution, innovation is particularly subject to parallel evolution. Since this book does not shy away from computational representations, Wagner applies the idea of evolution strategies [6] to illustrate how innovations can be modeled as a five-part process. Specifically, innovation involves trial-and-error, population-based exploration, solutions with multiple origins, a combinatorial structure, and a stochastic process with a mutation-selection structure. While these factors also define the evolutionary process, we might say that innovation is inseparable from evolution by natural selection. Thinking more broadly and considering social systems, cultural innovation might also be best characterized as an evolutionary process. Wagner's approach to innovation as evolvability is a useful and accessible introduction to the topic, and places this new set of concepts and terminology directly into the context of evolution by natural selection.

NOTES:
[1] For other, briefer reviews, please see: Hoppe, R.B.   Andreas Wagner: Arrival of the Fittest: Solving Evolution’s Greatest Puzzle. Panda's Thumb blog, November 4 (2014) AND Pagel, M.   The Neighborly Nature of Evolution. Nature, 514, 34 (2014).

[2] For an example, please see: Gavrilets, S. and Gravner, J.   Percolation on the Fitness Hypercube and the Evolution of Reproductive Isolation. Journal of Theoretical Biology, 184(1), 51–64 (1997).

[3] For an example, please see: Wagner, A.   Robustness and Evolvability in Living Systems. Princeton University Press (2005).

[4] Li, J., Yuan, Z., and Zhang, Z.   The Cellular Robustness by Genetic Redundancy in Budding Yeast. PLoS Genetics, 6(11), e1001187 (2010).

[5] Magtanong, L. et.al   Dosage suppression genetic interaction networks enhance functional wiring diagrams of the cell. Nature Biotechnology, 29, 505-511 (2011).

[6] Evolution strategies assumes that evolution is an optimizing process that results from the iterative application of a mutation-selection model. For more, please see: Schwefel, H-P.   Numerical optimazaion of computer models. Wiley Press, Chichester (1981) AND Beyer, H-G. and Schwefel, H-P.   Evolution Strategies: A Comprehensive Introduction. Journal of Natural Computing, 1(1), 3–52 (2002).

Six Degrees of the Alpha Male: breeding networks to understand population structure

This post is part of a continuing series on ways to think more deeply about human biological diversity. In last month's post (One Evolutionary Trajectory, Many Processes), I discussed how dual-process models (such as the DIT model) might be used to include a new dimension to more traditional studies of population genetics. This example did not spend too much time on the specifics of what such a model would look like. Nevertheless, a dual-process model provides a broader view of the evolutionary process, particularly for highly social (and cultural) species like humans.

In this post, I will lay out another idea briefly mentioned in the "Long Game of Human Biological Variation" post. This involves the use of complex network theory to model the nature of structure in populations. To review, the null hypothesis (e.g. no structure) is generally modeled using an assumption of panmixia [1]. In this conception, structure emerges from interactions between individuals and demes (semi-isolated breeding populations). Thus, a deviation from the null model involves the generation of structure via selective breeding, reproductive isolation, or some other mechanism.

One way to view these types of population dynamics is to use a population genetics model such as the one I just described. However, we can also use complex network theory to better understand how populations evolve, particularly when populations are suspected to deviate from the null expectation [2]. Complex networks provide us with a means to statistically characterize the interactions between individual organisms, in addition to rigorously characterizing sexual selection and the long-range effects of mating patterns.

An example of a small-world network with extensive weak ties. Importantly, this network topology is not random, but instead feature shortcuts and extensive structure. Data represents the human brain. COURTESY: Reference [3].

Since attending the Network Frontiers Workshop (Northwestern University) last December, I have been toying around with a new approach called "breeding networks". The breeding network concept [2] involves using multilayered, dynamical networks to characterize breeding events, the creation of offspring, the subsequent breeding events for those offspring, and macro-scale population patterns that result. This allows us to characterize a number of parameters in one model, such as the effects of animal social networks on population dynamics [4]. This includes traditional network statistics (e.g. connectivity and modularity parameters) that translate into theoretical measures of fecundity, the diffusion of genotypic markers within a population, and structural independence between demic populations. But these statistics are determined by a meta-process, one that is explicitly social and behavioral.

Before we continue, it is worth asking why complex networks are relevant. No doubt you have heard of the "small-world network" phenomenon, which postulates that given a certain type of network topology, networks with many nodes and connections can be traversed in a very small number of steps [5]. This is the famous "six degrees" phenomenon in action. But complex networks can range from random connectivity to various degrees of concentration. This approach, which comes with its own mathematical formalisms, allows us to neatly characterize the behavior, physiology, and other non-genetic factors that result in the population dynamics that produces structured genetic variation.

An example of regular, small-world, and random networks, ordered by to what extent their connectivity is determined by random processes [6]. In breeding networks, non-random connectivity is determined by sexual selection (e.g. selective breeding). As sexual selection increases or decreases, it can change the connectivity of a population.

As complex networks are made up of nodes and connections, the connections themselves are subject to
connection rules. In some networks, these rules can be observed as laws of preferential attachment [7].
But in general, each node or class of nodes can have simple rules for preferring (or ignoring) association with one node over another. If this sounds like an informal selection rule, this is no accident. While complex network theory does not approach connectivity rules in such a way, breeding networks are expected to be influenced by sexual selection at a very fundamental (e.g. dyadic interaction) level.

The complex network zoo, and the three parameters (heterogeneity, randomness, and modularity) that define the connectivity of a network topology. Examples of specific network types are given in the three-dimensional example above, but breeding networks could fall anywhere within this space. COURTESY: Reference [8].

Another feature of breeding networks involves connectivity trends over time. For example, a founder population with a small effective population size might indeed be panmictic (in this case represented by a random network topology). However, as the population size increases and connectivity rules change, this topology can evolve to one with scale-free or even small-world properties. This is not only due to the selective nature of producing offspring, but difference in the fecundity of individual nodes.

Once you start paying around with this basic model, a number of alternative network structures [9] can be used to represent the null model. Types of configuration such as star topologies, hyperbolic trees, and cactus graphs can approximate inherent geographic structure in a population's distribution. These alternative graph topologies are the product of factors such as geography or migration, and may have pre-existing structure. The key is to use these features as the null hypothesis as appropriate. This will provide us with a better accounting of the true complexity involved in shaping the structural features of an evolving population.

A map showing the seasonal migration of shark populations in the Pacific, including aggregation points. COURTESY: The Fisheries' Blog.

NOTES:
[1] One model organism for understanding local and global panmixia is the aquatic parasite Lecithochirium fusiforme. For more, please see: Criscione, C.D., Vilas, R., Paniagua, E., and Blouin, M.S.   More than meets the eye: detecting cryptic microgeographic population structure in a parasite with a complex life cycle.
Molecular Ecology, 20(12), 2510-2524 (2011).

[2] The idea of breeding networks is similar to the idea of sexual networks, except that breeding networks are more explicitly tied to population genetics. This paper give good insight into how sexual selection factor into the formation of structured, complex networks: McDonald, G.C., James, R., Krause, J., and Pizzari, T.   Sexual networks: measuring sexual selection in structured, polyandrous populations. Proceedings of the Royal Societiy B, 368, 20120356 (2013).

[3] Gallos, L.K., Makse, H.A., and Sigman, M.   A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. PNAS, 109(8), 2825-2830 (2012).

[4] For more on animal social networks and their relationship to evolution, please see the following references:

a) Oh, K.P. and Badyaev, A.V.   Structure of social networks in a passerine bird: consequences for sexual selection and the evolution of mating strategies. American Naturalist, 176(3), E80-89 (2010).

b) Kurvers, R.H.J.M., Krause, J., Croft, D.P., Wilson, A.D.M., Wolf, M.   The evolutionary and ecological consequences of animal social networks: emerging issues. Trends in Ecology and Evolution, 29(6), 326–335 (2014).

[5] For a definition of network diameter in context, please see: Porter, M.A.   Small-world Network. Scholarpedia, 7(2), 1739 (2012).

[6] This classification of idealized graph models is based on the Watts-Strogatz model of complex networks. For more information, please see: Watts, D.J. and Strogatz, S.H.   Collective dynamics of 'small-world' networks. Nature, 393, 440-442 (1998).

[7] This property of idealized graph models is based on the Barabasi-Albert model of complex networks. For more information, please see: Barabasi, A-L. and Albert, R.   Emergence of scaling in random networks. Science, 286(5439), 509–512 (1999).

[8] Sole, R.V. and Valverde, S.   Information Theory of Complex Networks: On Evolution and Architectural Constraints, Lecture Notes in Physics, 650, 189–207 (2004).

[9] Oikonomou, P. and Cluzel, P.   Effects of topology on network evolution. Nature Physics 2, 532-536 (2006).