May 25, 2013

Reflections on Chaos in Biological Evolution

As mentioned in my last post, this month is the 50th anniversary of the landmark paper by Ed Lorenz that inaugurated the scientific study of chaos (e.g. chaos theory). In this post, we will explore the potential contributions of chaos theory and dynamical systems (Figure 1) to the study of biological evolution from (hopefully) an intuitive perspective.

Figure 1. When people think of chaos theory, they generally think of something called a strange attractor. Two examples of these can be seen above. Figures are from [1] and [2].

Figure 2. LEFT: image from the Ian Malcolm novelty t-shirt. RIGHT: the butterfly effect as an attractor in phase space.

Coincidentally, this year is also the 20th anniversary of the movie "Jurassic Park" (based on the novel by Michael Crichton). The mathematician in the lost group (Ian Malcolm) was obsessed with chaos theory (Figure 2). The novel [3] features more extensive commentary by the fictional Dr. Malcolm, so go there if you want more insight than the movie offers.

The slant on chaos in "Jurassic Park" (or Crichtonian chaos) was on the unpredictablity of living systems: as Ian Malcolm said, "life finds a way". Unfortunately, the "Jurassic Park" argument from chaos was done using a populist, moralistic frame -- as in "ultimately, genetic engineering and otherwise screwing with natural processes is bad". This is unfortunate, since the chaotic and dynamical systems perspective can provide much insight into natural variation and evolution.

Figure 3. Here is a slide demonstrating what a fractal tree looks like (with a philosophical lesson attached). Notice its self-similar nature. Code for generating fractals can be found on OpenProcessing.

Stephen J. Gould wrote much about the role of chance in evolution [4], but did so in a qualitative fashion. While chaos is typically a memoryless phenomenon (and so does not account for historical contingency per se) [5], chaos does provide a tractable mechanism for chance events to unfold in a coherent fashion. Thus, chaos theory can bridge the gap between measurement and theory, which draws from the wide arc of natural history.

Besides the potential use of strange attractors embedded in phase space to characterize fitness landscape activity, there are interesting parallels between biological classification (e.g. phylogenies and gene genealogies) and fractal tree structures (Figure 3). There are also possible uses for Feigenbaum's logistic maps to characterize processes such as speciation and intraspecific population structure. In the second part of this post, I will focus on a number of examples that present an argument for why chaos is relevant to Darwinian evolution (Figure 4).

Figure 4. In [2], Motter and Campbell mention that chaos theory has helped replaced (for the most part) a mechanistic world-view. Here is what a non-chaotic world may look like (COURTESY: Co-axial World ad, Omega watches). For what its worth, the ad has a quasi-creationist theme, which hints at the critical underlying role of chaos in evolution.

The first of these is a set of papers by Robertson (an approach I will call Robertsonian chaos) that focus on the role of feedback on fitness [6, 7]. According to Robertsonian chaos, feedback acts upon the fitness and observed diversity of natural populations as a consequence of natural selection. In some cases, this feedback can actually decrease fitness. The important thing to remember is that the scenario of feedback leading to chaos is distinct from the ratchet mechanism for natural selection I covered in a previous Synthetic Daisies post.

As a chaotic (e.g. non-directional) mechanism, feedback can also act as a source of instability, and produce opportunities for evolutionary change. In [6], Robertson argues that due to its exponential effect, feedback dominates the dynamics of an evolutionary system. Using an electrical circuit as a metaphor, feedback provided by the action of natural selection acts as an amplifier (Figure 5).

Robertson's proposal for the role of feedback in evolution is fundamentally different from teleological, goal-oriented mechanisms. Instead, it enables "open-ended" evolution. This is also different from other mechanisms such as transgenerational epigenetic inheritance or facilitated variation [8] in that feedback is explicitly tied to outcome (e.g. evolutionary dynamics).

On the other hand, feedback does not seem to be a fundamental property of natural selection. That is, natural selection results in differential reproduction, but does not do so in a deterministic manner. One thing is certain: while feedback may act as an amplifier of natural selection, its mode of action is subtle [9].

Figure 5. Annotated version of Figure 1 from [6], which shows how the feedback mechanism works for a population embedded in a fitness landscape.

The second perspective is a book by Arun Holden called "Chaos" [10], which focuses on applications of chaos to physiology and biology. M. Holden contributes a chapter called "What is the use of chaos?", which lays out the functional roles of chaos in biological contexts.

The case is made for five potential functions: 1) diversity generation, 2) diversity preservation, 3) system maintenance, 4) the interaction of population dynamics and genetic structure, and 5) the dissipation of disturbances. Of these five candidates, two are particularly intriguing.

One of these is maintenance, which is referred to in the chapter as "disentrainment". Disentrainment is the an intentional lack of coordination among system components. For example, disentrainment in a social system among individual actors would impede cooperation or perhaps even competition (Figure 6). In neural systems, neurons are often entrained in small populations. If entrainment (see Figure 6 for visual aid) is too extensive and includes too many neural populations simultaneously, electrical activity can cascade out of control [11]. If entrainment is not extensive enough, there is no coherence to the system.

Thus, evolutionary order on the edge of chaos in the form of self-regulating population structure and diversity prevents evolving systems from responding to natural selection and other population processes with only an all-or-nothing [12] response. While such a response is occasionally useful (e.g. biochemical ultrasensitivity), chaos provides options to an evolutionary systems (at least the highly evolvable ones).

The other is the dissipation of disturbances, which may be compared to robustness in evolving biological systems. The dissipation of disturbances involves a mechanism which keeps an evolving system from experiencing dangerous disruptions. This is particularly intriguing in light of the important role disturbances play in evolving ecosystems.

The role of chaos in dissipating disturbances seems to be counter-intuitive at first glance. However, a naturally chaotic system (e.g. a system that can visit a wider range of states in the course of its normal behavior) can recover from disturbances much more efficiently than systems that are more conservative. In conjunction with natural diversity, chaotic behaviors such as transience and itinerance [13] can actually save an evolutionary system from itself.

Figure 7. A more historical view of the "routes to chaos".......

There are likely other examples I have missed. I also have not discussed the differences between deterministic and stochastic chaos [14], which is important in the analysis of biological systems and is deserving of its own discussion. Hopefully, this post serves as inspiration for future work and discussion (see Figure 7). Long live chaos!


[1] Arbesman, S.   The Fiftieth Anniversary of Chaos. Social Dimension blog, May 17 (2013).

[2] Motter, A.E. and Campbell, D.K.   Chaos at Fifty. Physics Today, May, 27 (2013).

[3] Crichton, M.   Jurassic Park. A.A.Knopf (1990).

[4] Gould, S.J.   The Structure of Evolutionary Theory. Harvard University Press (2000).

[5] Kautz, R.   Chaos: the science of predictable random motion. Oxford University Press, Oxford, UK (2011).

[6] Robertson, D.S. and Grant, M.C.   Feedback and Chaos in Darwinian Evolution: Part I. Theoretical Considerations. Complexity, 10-14 (1996).

[7] Robertston, D.S.   Feedback theory and Darwinian evolution. Journal of Theoretical Biology, 152, 469 (1991).


[9] To frame this in terms of speculative mathematical modeling, another possible source of nonlinearity is the interaction (e.g. mathematical convolution) between the fitness value and selection coefficient functions over time sampled at every generation). As both of these functions are semi-independent, their interaction could produce nonlinear effects on a population's subsequent fitness.

See this Synthetic Daisies post from April for more information on the convolution of stationary noisy signals for more information.

[10] Holden, A.V.   Chaos. Princeton University Press, Princeton, NJ (1986).

For an introduction to the field (with relevance to chance and historical contingency), please see the following books:

[a] Ruelle, D.   Chance and Chaos. Princeton University Press, Princeton, NJ (1991).

[b] Smith, L.A.   Chaos: a very short introduction. Oxford University Press, Oxford, UK (2007).

[11] This is the mechanism behind epileptic seizures that originate in the medial temporal lobe of the brain. For more information, please see:

Litt, B., Esteller, R., Echauz, J., D'Alessandro, M., Shor, R., Henry, T., Pennell, P., Epstein, C., Bakay, R., Dichter, M., and Vachtsevanos, G.   Epileptic seizures may begin hours in advance of clinical onset: a report of five patients. Neuron, 30(1), 51-64 (2001).

[12] All-or-nothing responses resemble step-functions. On the other hand, critical responses (or first-order phase transitions, which rely on thresholds that resemble step functions) may be useful for evolving systems as well.

[13] For various perspectives on these concepts, please see:

[a] Zimmermann, M.   Transient Behavior. ZhurnalyWiki, 1999.

[b] Tsuda, I.   Chaotic itinerancy. Scholarpedia, 8(1), 4459 (2013).

[14] Casdagli, M.   Chaos and Deterministic versus Stochastic nonlinear modeling. Santa Fe Institute Working Paper, 1991-07-029.

May 20, 2013

Short Threads of Reading Queue

Here are some academic papers, articles, and blog posts I have put into my reading queue over the past few weeks that I have found interesting and/or comment-worthy. I have organized them into threads (e.g. streams of consciousness) here:

Short thread on cell biology and genomics:

[1] Xie, J.   Autocrine signaling based selection of combinatorial antibodies that transdifferentiate human stem cells. PNAS, doi:10.1073/pnas.1306263110 (2013).

[2] Williams, R.B.H.   The influence of genetic variation on gene expression. Genome Research, 17, 1707-1716 (2007).

In [1], the researchers use a combination of receptor antibodies to reprogram a cell's fate. Yet more evidence that cellular reprogramming is not only possible, but involves more than just a few transcription factors or a spontaneous transformation. The science in [2] is a pre-RNA-seq study on the effects of standing genome variation on steady-state gene expression. A good early review, although there is now more current/specific work available.

Short thread on economics, markets, and technology:

[1] Yglesias, M.   Who gets rich when robots take our jobs. Moneybox blog, May 13 (2013).

Mr. Spacely from "The Jetsons". He's rich and George Jetson is not.

[2] Falk, A. and Szech, N.   Morals and Markets. Science, 707, 340 (2013).

After reading [1], I come away with the impression that the only thing that can be economically gained from automation is a bolstering of the arbitrary claim (e.g. Russian roulette) to genius (e.g. even patent trolling qualifies). Apparently, it is more relevant (and fleeting) than ever. This is part of a trend that has lead to productivity gains of the last 40 years becoming locked up in corporations and/or an executive elite. Again, automation has helped this trend along, although automation does not always result in this outcome.

In [2], a curious finding is reported. If you are part of a market, you are more likely to let a mouse die for a lower amount of money. A novel addition to the experimental moral philosophy field. Not quite sure if this is an exercise in mutually-assured moral behavior (e.g. bystander effect), or a call to make judgments about economic value in isolation. Is there more than meets the eye to this simple set of experiments? As an aside, how does this relate to the psychology of auctions?

Short thread on subjectivity in the brain:

[1] Wittmann, M.   The neural substrates of subjective time dilation. Frontiers in Human Neuroscience, doi:10.3389/neuro.09.002.2010 (2010).

[2] Schurger, A.   Reproducibility distinguishes conscious from nonconscious neural representations. Science, 327, 97 (2010).

Apparently, 2010 was a good year for investigating subjectivity in the brain. How do we measure engagement with a piece of art or the practice of culture? In [1], changes in activity patterns among the "cognitive control" and "default activity" brain networks mediate subjective responses to visual motion. In [2], neural activity related to conscious, neural correlates of subjectivity must be both of a certain duration and intensity as well as being reproducible. While subjective experiences can be transient and unique, their neural correlates are not.

Happy 50th birthday, Chaos theory!


[2] Lorenz, E.N.   Deterministic Nonperiodic Flow. Journal of Atmospheric Science, 20, 130-141 (1963).


This feature got a pretty decent response on my micro-blog, Tumbld Thoughts: happy 50th birthday to the study of chaos [1]. A worldview first proposed (in formal fashion) by Edward Lorenz in a landmark paper on weather prediction called “Deterministic Nonperiodic Flow” [2]. Later, the field would grow to encompass analytical strategies such as nonperiodic attractors, bifurcation maps, and fractals.

As a new way to describe physical phenomena and complex systems with a high degree of nonlinearity and subtle unpredictabilities (e.g. the butterfly effect), chaos shattered the notion of a clockwork universe [3]. As a paradigm shifting concept, chaos theory has the potential to enrich all areas of science [4].

Image on left is from [1], and image at the right is from [3]. For the latest work in the field, check out the journal “Chaos: an interdisciplinary journal of nonlinear science”.

For examples from brain science, see the following two articles and book:

* Robson, D.   Disorderly genius: How chaos drives the brain. New Scientist, June 29 (2009). YouTube video.

* Kitzbichler, M.G., Smith, M.L., Christensen, S.R., Bullmore, E.   Broadband Criticality of Human Brain Network Synchronization. PLoS Computational Biology, 5(3), e1000314 (2009).

* Freeman, W.J.   Neurodynamics: an exploration in mesoscopic brain dynamics. Springer, Berlin (2006).

Intriguing evolution stuff:

Zimmer, C.   Enlisting a virtual pack, to study canine minds. New York Times, April 22 (2013).

The Dognition website.

This is a story about Dr. Hare, the Anthropologist (the study of humans) interested in canine cognition. Can we throw any more species in there? Oh yes -- apparently dogs are more intelligent than their wolf wild-type cousins (determined by something called the "pointing test"). So to make this assessment more scientific, Dr. Hare came up with a test for dog intelligence. He also founded a company called Dognition, which is collecting data from dogs worldwide. But there's no such thing as a Dog IQ just yet. It will be interesting to see how intelligence corresponds with breed and degree of artificial selection for specific traits.

Evolutionary "gut check":

Burger, O.   Human mortality improvement in evolutionary context. PNAS, doi:10.1073/ pnas.1215627109 (2013).

This is a paper that I could not quite figure out. My gut says that something is not quite right/being accounted for here. Are they using ethnographically-observed hunter gatherer populations to derive an evolutionary baseline? If so, can they truly demonstrate that these populations actually represent such a baseline? Also, it seems to me that increases in life expectancy may involve the elimination of early mortality (due to warfare, violence, and disease) rather than a biological or cultural adaptation (particularly one on the order of those that distinguish between sister taxa, as the one that distinguishes human hunter-gatherers and chimps).

...and, finally, actual robots!

ICRA 2013 Conference website. Held in Karlsruhe, Germany, and sponsored by IEEE.

Erico Guizzo reports for IEEE Spectrum from ICRA (Robotics Conference), and brings us (among many other interesting things) a feature on Entropica:

LEFT: Screenshots of Entropica configurations (social network interactions and a pole balancing task). RIGHT: real-world (e.g. Primate) behaviors (termite dipping/tool use and stock market trading).

Wissner-Gross, A.D. and Freer, C.E.   Causal Entropic Forces. Physical Review Letters, 110, 168702 (2013).

Hewitt, J.   The emergence of complex behaviors through causal entropic forces., April 22 (2013).

Using a robotic model, it can be demonstrated that general intelligence (in the form of causal generalization) may be amplified or otherwise result from entropy maximization. This is related to work done on ant trails, showing that they conform to Fermat's principle of least time.

May 15, 2013

Lecture to BEACON Center, Michigan State

On May 17th (Friday) at 3:30pm (EST), I will be giving a lecture entitled "Adventures in Quasi-Evolution" [1] to the BEACON Center [2]. The audience is Thrust Group 1 (Genomes, Networks, and Evolvability).

The first half of my talk will be on computational models of cellular reprogramming (e.g. evolutionary modulus, or the engineering on the remnants of evolutionary and developmental variation). The second half is some emerging work I am doing on the cultural evolution of economic value (e.g. evolutionary through the looking glass, or how evolutionary models [3] may explain current economic puzzles).


[1] "Adventures in Quasi-Evolution". Figshare, doi:10.6084/m9.figshare.701463 (2013). I define quasi-evolution as "changes over time not due to reproductive fitness or generational inheritance".

[2] For those who are unfamiliar, the BEACON Center (an NSF-funded center) is a multi-disciplinary, multi-University group interested in the intersection of biology and engineering with relevance to evolution. Catch the lecture at one of these locations:

Michigan State University: Biomedical and Physical Sciences Building, Room 1441 (BEACON seminar room), 3:30pm.

North Carolina A and T University: McNair Hall, Lecture Room 4, 3:30pm.

University of Idaho: Life Sciences South (LSS), Room 144, 12:30pm

University of Texas, Austin: Service Building (SER), Room 321H, 2:30pm.

University of Washington: UW Hutchinson Cancer Center, Building PAA Room 023D, 12:30pm

[3] The cultural evolutionary models used in my research are called Contextual Geometric Structures (CGSs). Contextual Geometric Structures (CGS) will never play chess well, or perhaps at all. They will never beat Ken Jennings on Jeopardy. That's not the point. They exist as soft or fuzzy (e.g. possibilistic, non-transitive) classifiers that capture (or at least reproduce) the structural features of cultural behavior. This is quite different from the dual inheritance models that are common in studies that focus on the geneaology of traits.

The "structure" of culture has been observed and pondered by many cultural anthropologists, from Claude Levi-Strauss to Pierre Bourdieu. Bourdieu used a construct called the "habitus" to characterize the relationship between individuals in a single generation and cultural structures that exist across multiple generations. CGSs provide a measure of computational precision (e.g. a kernel function)  to this and other conceptions of "cultural logic".

As a quasi-evolutionary phenomenon, CGSs are designed to capture neither the dual inheritance of genes and culture nor the connectionism of a traditional cognitive model. The outcomes of CGS agents are not geared towards optimal decision-making. Rather, they classify natural phenomena according to a set of discrete oppositions (or categories).

Some of these are based on premises (e.g. historically-determined preferences), while others are based on biological features of the organism. The CGS agents then use the classificatory state of other agents as a cue to either follow (conform) or disperse (dissent). What results is a form of social learning that can be used to update (or obliterate) the space between the lower-level categories.

CGS simulations can be run either in an liquid-like simulation, or independently. In the original conception, which maps CGSs to geographic and other spatial phenomena, a hybrid model was proposed. In experiments geared towards understanding the social construction of economic value, populations of CGS kernels and their agents are static with respect to spatial position. However, they exchange items and attach value to those items based on repeated interaction.

For more information, please see:

May 10, 2013

Celebrity Recurrence, Professional Graphs, and Nano-Self-Expression

This has been cross-posted to my micro-blog, Tumbld Thoughts:

First up, it’s time for internet memes to meet mathematical concepts. On the left is a conceptual piece I am calling “The Cage Recurrence”. This is based on the Nick Cage vampire urban legend [1]. The transformations in the image are based on the Poincare recurrence (inset A), originally developed by Henri Poincare [2].

A Poincare recurrence occurs when the state of a volume-preserving flow map (e.g. 2-D image) returns to a close approximation of the initial condition after a period of time (usually very long). Theoretically, this is related to ergodic theory and the evolution of Hamiltonian systems [3]. As such, the dynamics of a Poincare recurrence can also be illustrated as a chaotic Poincare map (inset B, left) or a deterministic Baker’s map (inset B, right).

Next up, LinkedIn has a new feature that allows you to visualize your professional social network. It plots all of your first-order connections on the basis of shared connections and other attributes.

The network tends to cluster by workplace/community, but my network includes a lot of people that do not fall into any one category (as do most, I would imagine). InMaps uses programming tools such as Hadoop for handling large datasets and Processing for visualization. Fun!

Finally, here is a feature on nanoscale movies. In 1990, Don Eigler and other researchers at IBM [4] were able to assemble the letters “I-B-M” out of Xenon atoms using scanning tunneling microscopy (STM) [5].

Now, similar techniques have been used to make the world’s first atomic-scale animated short film “A Boy and His Atom” [6]. A “Star Trek” logo is also possible [7]. 


[1] Google “Nick Cage vampire” for more information.

[2] Image/illustration is courtesy of the Max Planck institute for Complex Systems and Crutchfield, J.   Chaos. Scientific American, December (1986).

[3] it may also be the mechanism behind deja vu in “The Matrix” trilogy.

[4] Eigler, D.M. and Schweizer, E.K.   Positioning single atoms with a scanning tunnelling microscope. Nature, 344, 524-526 (1990).

[5] Johnson, D.   IBM Makes Smallest Movie Ever. IEEE Nanoclast Blog, May 1 (2013).

[6] Pachal, P.   IBM Manipulates Atoms to Create the World’s Smallest Movie. Mashable, May 1 (2013).

IBM Research, “A Boy and His Atom”. YouTube, April 30 (2013).

[7] Kramer, M.  IBM Warps Atoms into Crazy “Star Trek” Art., May 3 (2013).

May 5, 2013

The significance of influence metrics: some fun with Klout and Google Scholar


Here is the main Klout interface with my personal Klout score and its trend over time. Klout is (please pick the one that is most applicable):

a) a popularity time-series, like brain electrical activity or stock market performance, and is probably (in an indirect fashion) related to each [1].

b) based on what exactly? I know, this puzzled me initially as well. Find out more here.

c) an excellent way to parlay your Facebook playtime into professorial tenure [2]. Not really. But it would not be at all surprising to me, given the almost-reflexive reverence paid to social media by business and journalistic culture.

d) a way to determine you personal worth, if your life is all about social media. And, really, what person’s life isn’t these days. It’s the new religion. Praise Zuckerberg [3]!

e) all of the above. Hope this raises my Klout score!

UPDATE: Since cross-posting this to Tumbld Thoughts, my Klout score has indeed increased by 8 (it is 40 as of May 5th). Looks like it is due to an increase in Facebook activity (or perhaps more targeted Facebook activity -- suggesting that the Klout score could be incredibly easy to manipulate). World domination, here I come!

Of course, this says nothing about my "official" academic research footprint. Or does it? Perhaps we can learn more about these types of metrics by looking at Google Scholar. Holly Dunsworth at the blog Mermaid's Tale has looked at what exactly constitutes her h-index measurement. In short, just because papers are cited does not mean that they are cited for the same reasons, and thus do not have a uniform degree of influence across citations [4].

My h-index [5] is 1 (across 27 papers -- some being Figshare documents), and is highly asymmetrical. A single Nature Reviews Neuroscience paper accounts for most of the citations taken into account. I'm actually not sure what database they are using to calculate citations (and thus influence), since it is not taking into account a number of peer-reviewed conference papers and book chapters (and blog posts, for that matter - [6]).

Does this dude abide? Apparently, I've only been influencing people in a significant manner since 2011. However, the analytics engine at does things a bit differently. Does this capture additional (and useful) information?

Okay, I have not reached a definitive opinion about this as of yet. It's just food for thought, so please discuss.

[1] Here is a fun paper (for theoretical physicists, at least) on this topic from Marcus Raichle's group: He, B.J., Zempel, J.M., Snyder, A.Z., Marcus E. Raichle, M.E.   The temporal structures and functional significance of scale-free brain activity. Neuron, 66(3), 353-369 (2011).

[2] a very apt April Fools' joke deftly executed by C. Titus Brown on his blog Living in an Ivory Basement.

[3] the classic "Microsoft buys the Catholic Church" internet meme is probably appropriate here.

[4] Here is another critical assessment of citation statistics: Adler, R., Ewing, J., and Taylor, P.   Citation Statistics. arXiv:0910.3529 (2010).

In addition, Audrey Watters at Hack (Higher) Education blog (hosted by Inside Higher Ed) has a post on the problems she's experienced with Google Scholar.

[5] Of course, the h-index is just one possible way to measure research output. But caveats of the h-index and then some apply to all alternative methods.

[6] This was a problem for Jonathan Eisen (Tree of Life blog) as well. At least Google tries to be accomodating in these cases.......

In general, "The Secret History of Rock" by Roni Sarig might enlighen this discussion a bit. In many cases, relatively (or in some cases absolutely) obscure bands such as the Dead Kennedys have served to influence much more popular (but perhaps less influential) musicians and bands. Influence networks serve as the mechanism for absolute vs. relative influence. While the h-index does not capture this phenomenon well, the Klout socre might be better at uncovering this.

May 3, 2013

Evolving the Tardis: Carnival of Evolution #59


I've passed the CoE torch yet again. Dirk Steinke from the University of Guelph and blog DNA Barcoding brings us this month’s “Carnival of Evolution” (#59). Continuing with the futuristic/fantasy theme of last month’s carnival, the theme this month is: Dr. Who, evolutionary biologist. Who knows, perhaps he can make sense of Dalek diversity. This edition features the recent Synthetic Daisies post "Replication, Model Organisms, and Evolutionary Signatures".

An analytics update to Carnival of Evolution #58: As of May 3 (since April 1), this version has received 630 hits. Not bad for an academically-oriented blog carnival. Enjoy this month's installment (it should get a fair number of hits as well), and if you wish to host a future edition, please contact Bjorn Ostman.