Friday, 23 November 2012

Abe Lincoln Dragon Slayer – A True Story

There’s a lot to be thankful for on this (American) Thanksgiving weekend. Suppressing the dragon uprising for example...

[News: The Dragon Phylogeny is currently on sale ($9.99) at
Coming Jan 2013: Detailed analysis of the Dragon Phylogeny]

Lincoln Crushing the Dragon of Rebellion
David Gilmour Blythe, 1862
Oil on canvas, 18 x 22 inches
Abraham Lincoln was not just the 16th president of the United States, immortalized on the U.S. penny (yes they still have those for some reason) and over 50 postage stamps, a fictional vampire slayer, a patent holder (U.S. No. 6469), and the subject of a new Spielberg Movie. Good old Honest Abe can also add ‘dragon slayer’ to his considerable C.V.

In our ongoing search to build and expand the Dragon Phylogeny, we came across this gem by American artist David Gilmour Blythe (1815-1865). This oil on canvas painting from 1862 shows Lincoln about to lay the beat down on a nasty little dragon using nothing but a wooden maul. None of us have seen the Spielberg movie or read Doris Kearns Goodwin's biography yet, so we don’t know if this scene is mentioned, but it should be!

This painting is particularly interesting because it represents one of the relatively few cases of a New World dragon in a depiction predating 1923 – the cut-off date for inclusion the Dragon Phylogeny. There are also some morphological peculiarities that are not evident in most of the Old World dragons. In particular, the hoofed feet, fish-like or possibly serpentine scales, and brown patches resembling fur. It is within the average size of the European dragon of the same period and has a head morphology intermediate to the European and Oriental forms. Unfortunately this image was not included in the phylogeny because we weren’t sure whether it has four legs or just two – and number of legs is a key diagnostic characteristic in the analysis. But we thought it would be noteworth given the recent surge of interest in Lincoln’s life.

Apart from its physical appearance, this dragon has enormous strength, having just toppled a marble column with nothing but its tail. It also appears to have fire breath, given the burning building from which it has just emerged and the massive city fire in the background. Compared to Abe Lincoln’s chicken legs, the marble-smashing tail suggests that the dragon has vastly superior strength despite its size. Lincoln has the additional handicap of being chained to a wooden stump by Popeye the Leprechaun. Yet this dragon is about to get its ass handed to it. At least I presume this is the case since there is good historical evidence that Lincoln died <SPOILER ALERT> from a shot to the head </SPOILER> and not in the jaws of a dragon.

Actually, the painting is a sort of political commentary analogous to modern political cartoons albeit with more subtle critiques. The dragon represents the rebellion by the Confederate States, as suggested by the painting’s title “Lincoln Crushing the Dragon of Rebellion” and its destruction of the pillars of… I’m going to say America? The stump is also labelled with the inscription “democracy” and overlain with the Constitution. note how THEY ARE BOTH IN ALL-CAPS INDICATING THAT THEY ARE TO BE YELLED, maybe? Actually, this appears to be a critique of the constraints of the democratic process and the limits to presidential power that are perceived to be constraining Lincoln’s ability to supress the dragon of rebellion. The little Irish dude seems to be a caricature of the Irish immigrants, who at the time were criticized by the previously established WASPy immigrants. This is a bit awkward since the artist Blythe was himself a descendant of Scottish and Irish immigrants. The significance of the maul probably connects to Lincoln’s nickname ‘rail splitter’, which refers to his early job splitting logs to use as fence rails. It was a key title emphasizing Lincoln’s connect to the average American. Despite the connection, a massive sword would be a much better tool with which to smite a dragon.

Overall the painting has a rather odd aesthetic. Though the subject matter - dragon slaying - is inherently awesome, we are not really sure whether the Surrealism is intentional or a lack of attention to detail. On the other hand, we don't have any DFAs in our midst, so we could be wrong. But what is the significance of depicting Lincoln as albino-Skeletor with a crystal meth addiction? Well, let’s just say David Gilmour Blythe is no Jon McNaughton...

One Nation Under God
Jon McNaughton
Oil on Canvas, 2009

 Looking much better, Abe. Now tell that politician to get off his cell phone and talk to Jesus.

Tuesday, 6 November 2012

A Presbyterian minister, phylogenetic inference, and the next president of the USA

Political pundits are notoriously bad at predicting elections. Sabermetrician and statistical geek Nathan Silver is showing how science can succeed where pundits fail.

Editor’s note: Watch for the official launch of the Dragon Phylogeny Project and Blog in a few weeks. In the mean time we thought you might enjoy our take on the U.S. Presidential election.
Don’t believe the hype – the U.S. election tonight is likely to be a blow-out for the incumbent president. True, the popular vote is likely to be within 3-5%, but at this point in the race there is a good chance that Obama will win 300+ electoral college seats – many more than the 270 required to win the presidency.

How is this possible when national polls and political commentators suggest such a tight race? The answer lies with statistical geek and five-thirty-eight blogger Nathan Silver, who predicts that Obama will likely win all of the key swing states: Colorado, Iowa, New Hamshire and Virginia, with Romney likely to win Nebraska and North Carolina. Only Florida remains a virtual toss-up at this point.

Silver’s predictions are not without its critics, particularly on the political right of the spectrum, but when the results are finalized tonight they will all face a collective moment of truth. The Dragon Phylogeny Project has a lot of confidence in Silver’s projections. The reason is not that we are politically biased but because we possess a staunchly conservative scientific mindset, and Nathan Silver uses a powerful yet flexible tool for predictive modelling – Bayesian statistics.

Presbyterian Minister and Statistical Revolutionary
Bayesian statistics are named for the Presbyterian minister Thomas Bayes, whose theorem completely turned statistical inference on its head. And this is precisely what makes Bayesian statistics so powerful for prediction. To understand why, consider the statistical cliché of flipping a coin 100 times.

Frequentist statistical inference is the most popular form of non-Bayesian inference and begins with a statistical model. In the coin-flipping example our model might be that each flip of the coin is independent with an equal probability of heads and tails. Count the number of observed heads and tails from our 100 coin tosses and compare the results with the prediction of our statistical model. We can then assign a probability of getting the observed result given our statistical model. If the result is unlikely (for example, if we get 99 heads and 1 tail), then we reject the model. In this case, we might conclude that the coin tosses are not independent or something about the coin or the tossing apparatus is biased. This probability of the data given the model – or P(data|model) as a convenient short-hand – is the P-value often reported in scientific literature. Typically, the statistical model is rejected when P < 0.05 – that is, when P(data|model) is less than 5%. This is what is usually what is meant when a scientific study finds ‘statistically significant’ results.

Bayesian statistical inference turns the process completely on its head, by evaluating a given statistical model based on the available data – P(model|data). Using the same coin-toss example, we begin with the data (99 heads and 1 tail) and then ask what is the probability of a given statistical model. For example, what is the probability that the coin is unbiased (50%) or biased toward 60%, 75% or 95% heads? A probability can then be assigned to each model.

The elegance and the power of Bayesian statistics are in its ability to continuously assess statistical predictions as new data become available. In the case of political forecasting, Nathan Silver asks “What is the probability that Obama or Romney win State X given all of the available polling data?”

Bayesian statistics are not just for political forecasting – they are having marked impacts in all areas of biology, including phylogenetic inference, which is really what the Dragon Phylogeny Project is all about.

Phylogenetic Inference
In phylogenetics, the power of Bayesian statistics lies with the ability to contrast the probability of alternative phylogenies. For example, we might build a phylogeny based on DNA sequences from NCBI GenBank for the first subunit of thee cytochrome c oxidase genes (COI) of humans, chimps, mice, rabbits, dogs and birds. Using a Bayesian framework, we can predict not only the most probable tree topology, but also assess the probability of other topologies.

For example, what is the probability that humans evolved from dog-like ancestors? A legitimate hypothesis given that many dog owners resemble their pets. However, this hypothesis is not even remotely supported by genetic data, which consistently group humans within the primates. It’s actually pretty spectacular that Darwin was right about this, even though he had absolutely no concept of genes or DNA. This is yet another example of the power of Darwin’s great thesis.

But while there may be no question about human origins, in statistical prediction one should always be careful not to put too much confidence into individual statistical models. All statistical models are based on assumptions and require unbiased data; garbage in = garbage out, as the saying goes. Nonetheless, two additional lines of evidence suggest that Nathan Silver’s projections are right on the mark.

The Invisible Hand of Las Vegas
First, it’s one thing for pundits to make predictions on the air, but how many are willing to bet money on their predictions? Like Free Market Capitalism, the invisible hand of gambling tends to converge on the statistical truth as many people making bets with incomplete information tend to balance around the ‘true’ odds. The Vegas money line is about -400 for Obama, meaning that a $4 bet will win $1. This translates to about a 75% chance of winning (i.e. you would have to win 1 out of 4 times to break even). This is slightly below Nathan Silver’s prediction of 90% probability of victory for the Democratic President, but still shows a strong advantage for Obama.

Second, there is the news of a last-minute change in the Romney strategy to shift its campaigning into Pennsylvania instead of Ohio. There are of course many potential explanations, but it is certainly consistent with the prediction that Romney’s advisors have concluded he has a low chance of winning Ohio and have decided that a last-minute play for Pennsylvania might provide the only chance of winning.

In just a few hours, political pundits and statistical projections will face the test of real-world voters. If Silver’s predictions turn out to be correct, you don’t have to let it shake your political leanings, but you should let it convince you of the awesome power of Bayesian statistical inference.

Monday, 27 August 2012

The Dragon Phylogeny - Introduction

The Dragon Phylogeny is an effort to map hypothetical evolutionary relationships among dragons. It’s true that these are mythical creatures, but the detail of their portrayal in historical art and literature makes them amenable to scientific analyses based on morphological variation.

This project began in the summer of 2009 as a diversion activity while writing my Ph. D. dissertation in Ecology and Evolutionary Biology at the University of Toronto, Canada. I collected images of 76 paintings, sketches, prints, and sculptures of dragons dating from the dark ages to the earliest 20th century, using images available on the internet. The most notable of these include prints of Asian dragons by Totoya Hokkei and Yashima Gakutei, Muslim depictions in Firdawsi’s Shahnama, a sketch by Leonardo Da Vinci, and a diversity of dragon species evident in various works featuring St. George’s dragon, the most famous of which are probably those by the Renaissance master Raphael.

What is a phylogeny? A phylogeny is a graphical representation of the hypothetical evolutionary relationships among different taxanomic groups, such as species, genera, families, etc. Most phylogenies today are based on DNA sequences, but dragon tissue is tough to acquire, and I think it’s also illegal under CITES or something. I could be wrong on that. Anyway, instead of DNA, I used the ‘old school’ approach that was used before the days of the polymerase chain reaction. It uses morphological instead of genetic variation.

How to build an ‘old school’ phylogeny: I identified 27 distinct traits that differentiated the 76 dragon art pieces (hereafter ‘species’) used in the study. These traits were then encoded into numbers so that they could be analyzed using a ‘neighbour-joining cluster analysis’. Just as the nucleotides of DNA (A,T,G and C) can be encoded as a single number (0-3), traits like skin texture, wing structure, and number of appendages can be numerically encoded. The neighbour-joining cluster analysis is a mathematical way of measuring the differences between the numbers representing the traits of interest, so that species with the fewest differences are joined together by the shortest branch distances. 

How to read a phylogeny: The output is sort of like a family tree, except that the tip of every branch represents a species and the lines joining the tips show how similar the species are to each other. The assumption is that species with more similar traits share a more recent common ancestor. The spatial arrangement of the tips doesn’t really matter – that’s why phylogenies can look like spirals, circles, or triangles. Instead, the length of the lines joining two species represents how distantly related they are. For example, in the phylogeny of mammals, the lines connecting humans and chimps are very short compared to the lines connecting humans and mice, because we share a common ancestor with chimps much more recently than we do with mice.

Key insights from the Dragon Phylogeny: The most obvious result is the evolutionary distance between the group that I’ve called Orientalia vs. the Eurasian dragons. Orientalia is an entire taxonomic class containing the Asian dragons or (a.k.a. lóng). If we follow the lines connecting all of the Orientalia species we see that they are more closely related to Mammalia than they are to the dragons found in Eurasia. This shows a deep evolutionary divergence with geography as the Asian lóng of the Eastern Hemisphere are biologically no more related to Eurasian dragons of the west than are unicorns and other mammals. It was therefore probably a mistake to translate ‘lóng’ as ‘dragon’, or at least there is no biological justification for this translation. If only those early western scholars had understood evolutionary phylogenetics as well as you do now.

To get to the common ancestor of Eurasian and Oriental dragons, we have to go way back to the time of the fish-like ancestors. If we follow the phylogeny down from Orientalia towards the center of the spiral we see three main branches. The first are the ancestral Actinopterygii, which include modern fish and are a distinct group from all of the land vertebrates. The second branch moving clockwise includes both mammals and lóng, indicating that they share the same tetrapod fish-like ancestor – something like the modern-day Coelacanth. In contrast, the Eurasian dragons must have shared an as yet unidentified hexapod fish-like ancestor, which gave rise to dragons with six appendages instead of four (i.e. four legs + two wings) – the Dracopteronidae and the Dracoverisidae. This assumes that complex appendages like wings or legs did not evolve out of nothing, which is probably a fair assumption. Continuing clockwise along the spiral we can see that the Wyvernidae gradually lost two legs and then two more legs in the Serpentidae ancestors, before losing wings in the more recently derived Serpentidae species at the top of the spiral. 

Conclusion: I know it’s a bit complicated but if you understand how to interpret these relationships you are already a step ahead of most first-year biology college students. Boom! you just learned all about phylogenetics.

This t-shirt design depicting the Dragon Phylogeny was submitted to
You can see it here: Dragon Phylogeny

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