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This blog will cover a diversity of topics, but will heavily feature evolutionary biology, particularly topics relating to population genetics and genomic imprinting.

Jon Wilkins
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  • March 4, 2013
  • 09:13 PM
  • 146 views

How Many English Tweets are Actually Possible?

by Jon Wilkins in Lost in Transcription

So, recently (last week, maybe?), Randall Munroe, of xkcd fame, posted an answer to the question "How many unique English tweets are possible?" as part of his excellent "What If" series. He starts off by noting that there are 27 letters (including spaces), and a tweet length of 140 characters. This gives you 27140 -- or about 10200 -- possible strings.

Of course, most of these are not sensible English statements, and he goes on to estimate how many of these there are. This analysis is based on Shannon's estimate of the entropy rate for English -- about 1.1 bits per letter. This leads to a revised estimate of 2140 x 1.1 English tweets, or about 2 x 1046. The rest of the post explains just what a hugely big number that is -- it's a very, very big number.

The problem is that this number is also wrong.

It's not that the calculations are wrong. It's that the entropy rate is the wrong basis for the calculation.

Let's start with what the entropy rate is. Basically, given a sequence of characters, how easy is it to predict what the next character will be. Or, how much information (in bits) is given by the next character above and beyond the information you already had.

If the probability of a character being the ith letter in the alphabet is pi, the entropy of the next character is given by

– Σ pi log2 pi
If all characters (26 letter plus space) were equally likely, the entropy of the character would be log227, or about 4.75 bits. If some letters are more likely than others (as they are), it will be less. According to Shannon's original paper, the distribution of letter usage in English gives about 4.14 bits per character. (Note: Shannon's analysis excluded spaces.)

But, if you condition the probabilities on the preceding character, the entropy goes down. For example, if we know that the preceding character is a b, there are many letters that might follow, but the probability that the next character is a c or a z is less than it otherwise might have been, and the probability that the next character is a vowel goes up. If the preceding letter is a q, it is almost certain that the next character will be a u, and the entropy of that character will be low, close to zero, in fact.

When we go to three characters, the marginal entropy of the third character will go down further still. For example, t can be followed by a lot of letters, including another t. But, once you have two ts in a row, the next letter almost certainly won't be another t.

So, the more characters in the past you condition on, the more constrained the next character is. If I give you the sequence "The quick brown fox jumps over the lazy do_," it is possible that what follows is "cent at the Natural History Museum," but it is much more likely that the next letter is actually "g" (even without invoking the additional constraint that the phrase is a pangram). The idea is that, as you condition on longer and longer sequences, the marginal entropy of the next character asymptotically approaches some value, which has been estimated in various ways by various people at various times. Many of those estimates are in the ballpark of the 1.1 bits per character estimate that gives you 1046 tweets.

So what's the problem?

The problem is that these entropy-rate measures are based on the relative frequencies of use and co-occurrence in some body of English-language text. The fact that some sequences of words occur more frequently than other, equally grammatical sequences of words, reduces the observed entropy rate. Thus, the entropy rate tells you something about the predictability of tweets drawn from natural English word sequences, but tells you less about the set of possible tweets.

That is, that 1046 number is actually better understood as an estimate of the likelihood that two random tweets are identical, when both are drawn at random from 140-character sequences of natural English language. This will be the same as number of possible tweets only if all possible tweets are equally likely.

Recall that the character following a q has very low entropy, since it is very likely to be a u. However, a quick check of Wikipedia's "List of English words containing Q not followed by U" page reveals that the next character could also be space, a, d, e, f, h, i, r, s, or w. This gives you eleven different characters that could follow q. The entropy rate gives you something like the "effective number of characters that can follow q," which is very close to one.

When we want to answer a question like "How many unique English tweets are possible?" we want to be thinking about the analog of the eleven number, not the analog of the very-close-to-one number.

So, what's the answer then?

Well, one way to approach this would be to move up to the level of the word. The OED has something like 170,000 entries, not counting archaic forms. The average English word is 4.5 characters long (5.5 including the trailing space). Let's be conservative, and say that a word takes up seven characters. This gives us up to twenty words to work with. If we assume that any sequence of English words works, we would have 4 x 10104 possible tweets.

The xkcd calculation, based on an English entropy rate of 1.1 bits per character predicts only 1046 distinct tweets. 1046 is a big number, but 10104 is a much, much bigger number, bigger than 1046 squared, in fact.

If we impose some sort of grammatical constraints, we might assume that not every word can follow every other word and still make sense. Now, one can argue that the constraint of "making sense" is a weak one in the specific context of Twitter (see, e.g., Horse ebooks), so this will be quite a conservative correction. Let's say the first word can be any of the 170,000, and each of the following zero to nineteen words is constrained to 20% of the total (34,000). This gives us 2 x 1091 possible tweets.

That's less than 1046 squared, but just barely.

1091 is 100 billion time the estimated number of atoms in the observable universe.

By comparison, 1046 is teeny tiny. 1046 is only one ten-thousandth of the number of atoms in the Earth.

In fact, for random sequences of six (seven including spaces) letter words to total only to 1046 tweets, we would have to restrict ourselves to a vocabulary of just 200 words.

So, while 1046 is a big number, large even in comparison to the expected waiting time for a Cubs World Series win, it actually pales in comparison to the combinatorial potential of Twitter.

One final example. Consider the opening of Endymion by John Keats: "A thing of beauty is a joy for ever: / Its loveliness increases; it will never / Pass into nothingness;" 18 words, 103 characters. Preserving this sentence structure, imagine swapping out various words, Mad-Libs style, introducing alternative nouns for thing, beauty, loveliness, nothingness, alternative verbs for is, increases, will / pass prepositions for of, into, and alternative adverbs for for ever and never.

Given 10000 nouns, 100 prepositions, 10000 verbs, and 1000 adverbs, we can construct 1038 different tweets without even altering the grammatical structure. Tweets like "A jar of butter eats a button quickly: / Its perspicacity eludes; it can easily / swim through Babylon;"

That's without using any adjectives. Add three adjective slots, with a panel of 1000 adjectives, and you get to 1047 -- just riffing on Endymion.

So tweet on, my friends.

Tweet on.

C. E. Shannon (1951). Prediction and Entropy of Written English Bell System Technical Journal, 30, 50-... Read more »

C. E. Shannon. (1951) Prediction and Entropy of Written English. Bell System Technical Journal, 50-64. info:/

  • December 19, 2012
  • 11:39 AM
  • 350 views

Epigenetics and Homosexuality

by Jon Wilkins in Lost in Transcription

So, last week featured a lot of news about a paper that came out in the Quarterly Review of Biology titled "Homsexuality as a Consequence of Epigenetically Canalized Sexual Development." The authors were Bill Rice (UCSB), Urban Friberg (Uppsala U), and Sergey Gavrilets (U Tennessee). The paper got quite a bit of press. Unfortunately, most of that press was of pretty poor quality, badly misrepresenting the actual contents of the paper. (PDF available here.)

I'm going to walk through the paper's argument, but if you don't want to read the whole thing, here's the tl;dr:

This paper presents a model. It is a theory paper. Any journalist who writes that the paper "shows" that homosexuality is caused by epigenetic inheritance from the opposite sex parent either 1) is invoking a very non-standard usage of the word "shows," or 2) was too lazy to read the actual paper, and based their report on the press release put out by the National Institute for Mathematical and Biological Synthesis.

That's not to say that this is a bad paper. In fact, it's a very good paper. The authors integrate a lot of different information to come up with a plausible biological mechanism for epigenetic modifications to exert influence on sexual preference. They demonstrate that such a mechanism could be favored by natural selection under what seem to be biologically realistic conditions. Most importantly, they formulate their model into with clear predictions that can be empirically tested.

But those empirical tests have not been carried out yet. And, in biology, when we say that a paper shows that X causes Y, we generally mean that we have found an empirical correlation between X and Y, and that we have a mechanistic model that is well enough supported that we can infer causation from that correlation. This paper does not even show a correlation. It shows that it would probably be worth someone's time to look for a particular correlation.

As a friend wrote to me in an e-mail,

I found it a much more interesting read than I thought I would from the press it's getting, which now rivals the bullshit surrounding the ENCODE project for the most bullshitty bullshit spin of biology for the popular press. A long-winded-but-moderately-well-grounded-in-real-biology mathematical model does not proof make.
Exactly.

Okay, now the long version.


The Problem of Homosexuality

The first thing to remember is that when an evolutionary biologist talks about the "problem of homosexuality," this does not imply that homosexuality is problematic. All it is saying is that a straightforward, naive application of evolutionary thinking would lead one to predict that homosexuality would not exist, or would be vanishingly rare. The fact that it does exist, and at appreciable frequency, poses a problem for the theory.

In fact, this is a good thing to keep in mind in general. The primary goal of evolutionary biology is to understand how things in the world came to be the way they are. If there is a disconnect between theory and the world, it is ALWAYS the theory that is wrong. (Actually, this is equally true for any science / social science.)

Simply put, heterosexual sex leads to children in a way that homosexual sex does not. So, all else being equal, people who are more attracted to the opposite sex will have more offspring than will people who are less attracted to the opposite sex.

[For rhetorical simplicity, I will refer specifically to "homosexuality" here, although the arguments described in the paper and in this post are intended to apply to the full spectrum of sexual orientation, and assume more of a Kinsey-scale type of continuum.]

The fact that a substantial fraction of people seem not at all to be attracted to the opposite sex suggests that all else is not equal.

Evolutionary explanations for homosexuality are basically efforts to discover what that "all else" is, and why it is not equal.

There are two broad classes of possible explanation.

One possibility is that there is no biological variation in the population for a predisposition towards homosexuality. Then, there would be nothing for selection to act on. Maybe the potential for sexual human brain simply has an inherent and uniform disposition. Variation in sexual preference would then be the result of environmental (including cultural) factors and/or random developmental variation.

This first class of explanation seems unlikely because there is, in fact, a substantial heritability to sexual orientation. For example, considering identical twins who were raised separately, if one twin is gay, there is a 20% chance that the other will be as well.


Evidence suggests that sexual orientation has a substantial heritable component. Image: Comic Blasphemy.


This points us towards the second class of explanation, which assumes that there is some sort of heritable genetic variation that influences sexual orientation. Given the presumably substantial reduction in reproductive output associated with a same-sex preference, these explanations typically aim to identify some direct or indirect benefit somehow associated with homosexuality that compensates for the reduced reproductive output.

One popular variant is the idea that homosexuals somehow increase the reproductive output of their siblings (e.g., by helping to raise their children). Or that homosexuality represents a deleterious side effect of selection for something else that is beneficial, like how getting one copy of the sickle-cell hemoglobin allele protects you from malaria, but getting two copies gives you sickle cell anemia.

It was some variant of this sort of idea that drove much of the research searching for "the gay gene" over the past couple of decades.  The things is, though, those searches have failed to come up with any reproducible candidate genes. This suggests that there must be something more complicated going on.


The Testosterone Epigenetic Canalization Theory

Sex-specific development depends on fetal exposure to androgens, like Testosterone and related compounds. This is simply illustrated by Figure 1A of the paper:


Figure 1A from the paper: a simplified picture of the "classical" view of sex differentiation. T represents testosterone, and E represent Estrogen.



SRY is the critical genetic element on the Y chromosome that triggers the fetus to go down the male developmental pathway, rather than the default female developmental pathway. They note that in the classical model of sex differentiation, androgen levels differ substantially between male and female fetuses.

The problem with the classical view, they rightly argue, is that androgen levels are not sufficient in and of themselves to account for sex differentiation. In fact, there is some overlap between the androgen levels between XX and XY fetuses. Yet, in the vast majority of cases, the XX fetuses with the highest androgen levels develop normal female genitalia, while the XY fetuses with the lowest androgen levels develop normal male genitalia. Thus, there must be at least one more part of the puzzle.

The key, they argue, is that tissues in XX and XY fetuses also show differential response to androgens. So, XX fetuses become female because they have lower androgen levels and they respond only weakly to those androgens. XY fetuses become male because they have higher androgen levels and they respond more strongly to those androgens.

This is illustrated in their Figure 1B:


Sex-specific development is thus canalized by some sort of mechanism that they... Read more »

Rice, W., Friberg, U., & Gavrilets, S. (2012) Homosexuality as a Consequence of Epigenetically Canalized Sexual Development. The Quarterly Review of Biology, 87(4), 343-368. DOI: 10.1086/668167  

  • October 5, 2012
  • 10:52 AM
  • 303 views

The Psychology of that one line in Call Me Maybe

by Jon Wilkins in Lost in Transcription

So, like, I heard this song the other day. It was by this indie band called "Carly Rae Jepsen." You've probably never heard of them.

Actually *removes hipster glasses* while most of the appeal of "Call Me Maybe," the song that dominated the summer of 2012, comes from its earnest simplicity, there is one line in the lyrics that has some real texture to it:

Before you came into my life, I missed you so bad
This line captures something universal and not at all trivial, the way that our memories of past emotions are reshaped by our current knowledge.

The thing is, we tend to think of ourselves as objective observers. We trust that our perceptions bear a one-to-one correspondence to the world around us. But the information that actually makes it from the outside world into our brains is much more limited and impressionistic. Our brains construct most of the details based on expectations about how the world works.

As William Wordsworth, the Carly Rae Jepsen of his time, wrote:

                            Therefore am I still
A lover of the meadows and the woods,
And mountains; and of all that we behold
From this green earth; of all the mighty world
Of eye and ear, both what they half-create,
And what perceive;
While this perceiving-and-creating is a good description of our perceptions, it is even more true of our memories. When we attempt to recall how we felt about something in the past, it might feel like we are accessing internal CCTV footage, what we are actually doing is more like reconstructing those feelings on the basis of crayon sketch by a drunk three year old.

For those of you without drunk three year olds at home, what I mean is that there are a lot of details that need to be filled in. In the case of memories, one of the places we go for these details is our understanding of the world in the present.

Here's an example. In one psychology study (citation below), participants were asked to predict how they would feel if their team lost the Superbowl, and they were all like, "OH MY GOD THAT WOULD BE THE END OF THE WORLD!!!!11!1!!!" But then, when their team actually did lose the Superbowl, they were like, "Whatevs, dude."

That's maybe not too surprising, but the interesting thing is that when these people were asked to recall how they predicted that they would feel, they tended to remember feeling like it would not have been that big a deal. That is, their recollection of their emotional state in the past was anchored to their emotional state in the present.

Similar results were found for studies on the 2008 presidential election, satisfaction from completing a major purchase, and how much they would enjoy eating jellybeans, depending on the order in which jellybeans of different flavors were eaten.



While "recall of predicted hedonic sequence" sounds like a totally awesome study, in a hookers-on-mars-with-three-boobs sort of way, this study was actually about eating jellybeans.

In "Call Me Maybe," there are a couple of different ways to interpret the line "Before you came into my life I missed you so bad." One possibility is that Carly Rae is, in fact, a time traveler from the future. At the age of twenty four, she met her one true soulmate. Unfortunately, he was ninety-six years old and was unable to keep up with her sexually. So, she traveled back to the year 2009, and then waited for her ripped-jeans Adonis to show up in her life on that hot and windy night.

A second possibility is that her emotional state after having met this guy colored her recollection of her emotional state in the time before she met him.

Here's that video of the US Olympic Swim Team lip-syncing "Call Me Maybe." While you're watching it, I want you to try to remember how invested you were in the outcome of the Olympics back in July and August. Then notice how little you care about the Olympics in retrospect. Now, recognize that while you think you were all, "Olympics, Schmolympics!" at the time, you were actually all "USA! USA! Who is that nice Lochte boy?"

Don't you feel dumb?




Meyvis, T., Ratner, R. K., & Levav, J. (2010). Why Don't We Learn to Accurately Forecast Feelings? How Misremembering Our Predictions Blinds us to Past Forecasting Errors Journal of Experimental Psychology: General, 139 (4), 579-589 : 10.1037/a0020285

... Read more »

Meyvis, T., Ratner, R. K., & Levav, J. (2010) Why Don't We Learn to Accurately Forecast Feelings? How Misremembering Our Predictions Blinds us to Past Forecasting Errors. Journal of Experimental Psychology: General, 139(4), 579-589. info:/10.1037/a0020285

  • October 2, 2012
  • 09:06 PM
  • 321 views

The Genetical Book Review: The Mapmaker and the Ghost

by Jon Wilkins in Lost in Transcription

So, remember when not all kids books were about teenage wizards and sexy vampires? Well, it turns out that, if you know where to look, you can still find books like that. Enter The Mapmaker and the Ghost, by Sarvenaz Tash.

[Disclaimer: Sarv is a friend of my wife's. They got to know each other through the fact that both are in the New York area, and both had their debut middle-grade novels come out this year. If you are concerned that this may color the objectivity of this review, may I refer you to the Genetical Book Review's premise and guidelines.]

The Mapmaker and the Ghost is a story that I would say is of the same general flavor as something like From the Mixed-Up Files of Mrs. Basil E. Frankweiler. The setting is very much our world, and the adventure is on a human scale. In the Mixed-Up Files, a girl and her younger brother run off to the museum, and get caught up in a quest to discover the provenance of a statue. In Mapmaker, a girl (Goldenrod) and her younger brother (Birch) find adventure in the woods at the edge of town, and get caught up in a quest to find a legendary blue rose.



The Mapmaker and the Ghost, by Sarvenaz Tash. Want to buy it already?
Settle down there, sparky! Purchase links will be available at the bottom of the post.

For kids, I think, the human scale makes the story directly relatable to their own lives. At least, that seems to be one of the things that our kid loved about the book. (He was nine at the time he first read it, and has reread it multiple times.) The concerns that the characters have, about curfews and money and permission to go past a certain point in the street, etc., seem to resonate with the experience of childhood in a way that very few authors pull off.

Of course, as in any good adventure, there are exciting things that happen that go well beyond what most children actually experience. But those events have an emotional impact that derives from the realism of the novel. I mean, saving the world from the most evil villain of all time is, of course, exciting, but evading the gaze of a security guard can actually be even more emotionally tense and exhilarating, because it is a situation that a young reader can really embody.

Also, there's a gang of semi-feral kids with names like "spitbubble" and "snotshot," a mysterious old lady, a secret lair, and, of course, a ghost.

The book is appropriate for ages 7 through probably about 12. The main character is a girl, but the novel is strongly gendered, and will be engaging for boys and girls. (If you have a son who thinks that they should not read a book like this because it is about a girl, you should definitely buy it, thump him over the head with it, and then watch him enjoy it anyway.)

Now, on with the science!

As I mentioned, the central quest in the novel is the search for a blue rose that blooms in the woods at the edge of town once every fifty years. This is a big deal, because, you know, roses aren't blue. When you find a rose that is actually blue, it's blue because it has been dyed blue.

A few years ago, a Japanese company called Suntory made news when they produced the world's first non-dyed blue rose. They managed this through genetic engineering, taking a gene from a pansy and inserting it into a rose. [Insert juvenile and inappropriate joke here.]

Now, you're probably looking at this rose and thinking that you have to be pretty colorblind (or have a job in Suntory's marketing division) to call this "blue." Fair enough, but, that's the state of the art at the moment.



Suntory's "blue" rose, which, while lilac a best, is still pretty cool. As an aside, we could also interpret this as an example of what linguists call "collocational restriction," where the term "blue" has an idiomatic meaning in the specific context of the phrase "blue rose." In this case, it might be interpreted as "bluer than a rose normally is," much as "white coffee" is not actually white, but is at the white end of the distribution of coffee colors. (Image via Wired)

Here is Figure 1 from the publication of Suntory's work, which shows the biosynthetic pathways responsible for plant color. You don't find blue roses in nature because roses lack an enzyme in the pathway on the far right, which means that they lack any delphinidin-based anthocyanins.



Anthocyanins are the primary chemicals responsible for 

The gene that the researchers inserted into the rose is the one indicated by F3'5'H in the figure. This enzyme (flavonoid 3',5'-hydroxylase) is normally absent from roses, which is why they lack the bluish pigments.

Although only one blue rose cultivar has been brought to market (The Suntory "Applause" pictured above), they actually did the transformation with a bunch of different cultivars. Here are a few examples (from the same paper).



In each panel, the flowers on the left are without the F3'5'H gene, and the ones on the right are with it.

If you read Japanese (or trust Google Translate), you can check out more information at Suntory's dedicated blue-rose webpage, which features topics such as "Legend," "Brand Concept," and "Applause Wedding" (new!).

The authors note that there are various things one could imagine doing to make roses even bluer, including tinkering with the pH, getting other pigments in there, etc. How easy these next steps are going to be is less clear, though. It's hard to tinker without breaking stuff. Perhaps genuinely blue roses will continue to be the symbol of unattainability, and limited to great kids' books.

Katsumoto, Y., Fukuchi-Mizutani, M., Fukui, Y., Burgliera, F., Holton, T. A., Karan, M., Nakamura, N., Yonekura-Sakakibara, K., Togami, J., Pigeaire, A., Tao, G.-Q., Nehra, N. S., Lu, C.-Y., Dyson, B. K., Tsuda, S., Ashikari, T., Kusumi, T., Mason,... Read more »

Katsumoto, Y., Fukuchi-Mizutani, M., Fukui, Y., Burgliera, F., Holton, T. A., Karan, M., Nakamura, N., Yonekura-Sakakibara, K., Togami, J., Pigeaire, A.... (2007) Engineering of the Rose Flavonoid Biosynthetic Pathway Successfully Generated Blue-Hued Flowers Accumulating Delphinidin. Plant Cell Physiol., 48(11), 1589-1600. DOI: 10.1093/pcp/pcm131  

  • August 29, 2012
  • 03:45 PM
  • 297 views

The Case for Independent Scholarship #3: On Workaholic Scientists

by Jon Wilkins in Lost in Transcription

So, Sam Arbesman has a post up at Wired where he discusses a recent study on the work habits of  scientists in around the world. As a proxy for "working," the authors look at the pattern of downloads of papers or book chapters from Springer. The work makes use of a cool real-time mapping of IP addresses accessing those papers. If you want to see what it looks like, check it out here: http://realtime.springer.com/map.

They do a more detailed analysis of the top three countries (in terms of total number of downloads in about a week's worth of data), the US, Germany, and China. Correcting for time zone differences, they find these patterns:






On the left side, each line corresponds to a different day, with the more solid lines being weekends, and the thinner ones being weekdays. On the right, the weekends and weekdays are averaged.



A couple of things that will probably come as no surprise to most of the academics out there. 



(1) the daily hump starts picking up around 9 or 10 in the morning, and carries on until nine or ten at night.



(2) the weekday hump is bigger during traditional "working hours", but evening work hours are pretty consistent throughout the week.



Interesting cultural differences pop out that might not be as predictable. It looks like China has longer and/or more simultaneous breaks for lunch and dinner. (Although, given the common practice, at least in the US, of eating lunch at your computer, maybe the lack of those dips in the top panel are somewhat predictable.) Americans seem to be working a lot more in the middle of the night compared with their German and Chinese counterparts, while the Chinese seem to show less of a difference between weekday and weekend work habits.



The authors' conclusion, and one that is echoed in Sam Arbesman's commentary, is that this work pattern is consistent with what most academic scientists would probably tell you. Academia is a full-time job. And not a full-time job in the sense of a forty-hour work week, but a full time job as in, you sleep, eat, and work.



So is that a good thing or a bad thing? Well, on the one hand, you've got all of these highly trained, highly educated people working really hard and getting paid not a whole awful lot on a per-hour basis. Good deal, right?



On the other hand, it leads to a really crappy lifestyle, where the long hours come at the expense of time spent with family, hobbies, or even taking an interest in subjects outside of the very narrow range defined by your research. If you care about a broader definition of human happiness,  one that treats people as an end rather than a means, this is not a great way to structure your industry. 



Beyond that, it is important to remember that science, like all academic fields, is a fundamentally creative enterprise, and working longer hours does not necessarily translate into better results. Creativity has to be fueled by experience, and a broader range of experience can lead to asking more interesting questions and coming up with more original answers to those questions. The pressures that lead people to download papers from Springer from morning till night don't necessarily lead to the best science.



I should note that Sam's coverage also includes a plug for the Ronin Institute, because Sam is a freakin' rock star!


Wang, X. W., Xu, S. M., Peng, L., Wang, Z., Wang, C. L., Zhang, C. B., & Wang, X. B. (2102). Exploring Scientists’ Working Timetable: Do Scientists Often Work Overtime? Journal of Informetrics, 6 (4), 655-660 DOI: 10.1016/j.joi.2012.07.003

... Read more »

Wang, X. W., Xu, S. M., Peng, L., Wang, Z., Wang, C. L., Zhang, C. B., & Wang, X. B. (2102) Exploring Scientists’ Working Timetable: Do Scientists Often Work Overtime?. Journal of Informetrics, 6(4), 655-660. DOI: 10.1016/j.joi.2012.07.003  

  • August 20, 2012
  • 12:08 AM
  • 251 views

Post-copulatory female choice in crickets and Missouri

by Jon Wilkins in Lost in Transcription

So, maybe you've seen the news today about Representative Todd Akin. He's the republican nominee for Senate in Missouri, running this year against Claire McCaskill. In an interview he said that he opposed abortion in all circumstances, with no exception for rape, because rape does not lead to pregnancy, see, because, "If it's a legitimate rape, the female body has ways to try to shut that whole thing down." (Quotes on Jezebel, video here.)

After realizing that he sounded like a complete shithead, even for a contemporary Republican (and probably after receiving a scolding from national Republicans), he issued a statement in which he claims that he "misspoke," which is politician speak for, "I accidentally said what I actually thought, and then discovered that it will negatively impact my election chances, so I'm going to lie now. No backsies!"

Although, to be fair to Akin, nowhere in his statement did he back down from the position that abortion should be outlawed without exception, merely that he would advocate for "justice." Also, jobs!

Setting aside for the moment the woeful state of politics, is it true, or even possible, that the female body could have "ways to try to shut that whole thing down"?

Actually, in a lot of non-human animals, something sort of like that does exist.

In species where polyandry (where females mate with multiple males) is common, there is often competition for reproductive access both before and after copulation, where one male may participate in a larger share of a female's reproduction. In many cases, this is going to be something like sperm competition, where differential reproductive success depends on traits associated with the sperm, and by extension, with the competing males. This is not really what we're talking about, though.

In a few cases, you can actually get "post-copulatory female choice," where it is clearly the female deciding whether or not to allow fertilization. One such set of cases occurs in some spiders and crickets, where the male transfers a spermatophore to the female. This is basically a bag full of sperm that is attached to the female during copulation. She may then modulate the success of the sperm through the amount of time she permits it to remain attached to her.

For example, here's a paper on field crickets that shows not only that females modulate spermatophore retention time in response to male song quality, but that this modulation is contingent on the female's prior experience. This is important because it emphasizes the aspect of female choice.

But what about humans? Well, actually, yes. Human females have the capacity to engage in post-copulatory female choice, such that they do not necessarily have to give birth to their rapist's child. It's called safe, legal abortion. It still exists in this country, but if too many more Todd Akins get elected, the American female body will no longer have "ways to try to shut that whole thing down."

Rebar, D., Zuk, M., & Bailey, N. W. (2011). Mating experience in field crickets modifies pre- and postcopulatory female choice in parallel Behavioral Ecology, 22, 303-309

... Read more »

Rebar, D., Zuk, M., & Bailey, N. W. (2011) Mating experience in field crickets modifies pre- and postcopulatory female choice in parallel. Behavioral Ecology, 303-309. info:/

  • August 2, 2012
  • 10:18 PM
  • 326 views

The selfish herd

by Jon Wilkins in Lost in Transcription

So, one of the most interesting questions in evolutionary biology is the origin of collective behaviors. This can be the complex division of labor that we see in social insects and human societies, flocking behavior in migratory birds, or microbial formation of biofilms. It can be predators engaging in collective hunting, or prey engaging in collective being hunted. It's this last one that we're going to be talking about today.

As with many questions in evolutionary biology, there are a couple of dimensions that people are interested in untangling: proximal and ultimate causation. Proximal explanations focus on the "how" part of the solution, as in, "what are the molecular, genetic, etc. mechanisms and environmental cues that result in this behavior?" Ultimate explanations focus on "why," in the evolutionary sense of "what were the selective pressures that led to the evolution of this behavior?"

Herding or flocking behavior is a classic case. For example, why do sheep hang out in a big group, in contrast to say, leopards, which tend to be pretty solitary? There are a number of possible (and not mutually exclusive) ultimate explanations, but the most talked about one is probably defense against predators.



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Back in the mid-twentieth century, it was common for biologists to talk in fairly loose terms about collective behaviors having evolved as a result of their benefits to the group. Then, in 1966, G. C. Williams published Adaptation and Natural Selection, which dropped a lot of truth into the community. In particular, it emphasized the gene-centered view of natural selection that hit the public consciousness with Richard Dawkins's 1976 book, The Selfish Gene, and which has remained the dominant paradigm in evolutionary biology ever since.

Williams demonstrated that group selection, while possible, will generally be a much weaker force than selection acting on the individual. Therefore, it is good practice to look for evolutionary explanations at this lower level. Given plausible adaptive stories at the individual and group levels, one should favor the individual-level story. While the two stories might not be mutually exclusive, individual-level selective pressures are more likely to have played an important role in  the evolution of any particular trait than group-level selective pressures (all else being equal, of course).

In 1971, W. D. Hamilton published a theoretical analysis that brought this individual-level perspective to herding behavior. Hamilton argued that all you need is for animals to be trying to evade predators as individuals. If there are other individuals of their type around, they just need to try to position themselves between other individuals. Here's how Hamilton draws it:



This frog wants to position itself between the two frogs on the right. That way, when the sea snake comes up, it will eat one of the frogs at the edge, and the one in the middle will be safe.

All you need is for everyone to follow one simple rule: when a predator comes, position yourself between two other individuals. What you get then is a tight cluster of individuals.

You can actually try this at home. You probably need about eight or ten people. So, most of you might not be able to try this at home, but you could maybe try it at school or work. Have each person pick two other people in the group (but don't tell who your picks are). Then, everyone tries to get between the two people they picked. What you'll get is something a lot like a cluster of frogs climbing all over each other to get away from a sea snake.


Frogs maneuvering to get between other frogs results in the formation of a clusterf**k of frogs. I know, right? I was surprised, too, but my herpetologist friends assure me that "clusterf**k" is the official collective noun for a group of frogs. Don't even ask about sea snakes. You don't want to know.

Bonus activity: after you've disentangled yourselves from the frogpile, try this one. Each person picks two people again, labeling them "A" and "B" (in your head). Again, no one needs to say whom they picked. Now, each person should position themselves so that their "A" person is between them and their "B" person. If it helps, imagine that "A" is Mitt Romney, that "B" is the American People, and you are Mitt's tax returns. Your job is to position yourself so that Mitt keeps the American People from seeing you. I won't spoil how it comes out.

So, Hamilton's model provides a nice, simple model that can produce the observed behavior. The model is attractive because (1) it requires selection only at the level of the individual, and (2) it requires each individual only to follow a very simple behavioral rule. The collective behavior is an emergent property requiring no coordination at the group level.

Now, there's a new paper out that is attempting to look at this empirically, in sheep. The study involves strapping adorable GPS backpacks on a bunch of sheep (Figure 1c, below) and then letting a sheepdog chase them around.




You can look at the movies here. It's only a brief communication, and does not really nail anything down, but the authors interpret their results as broadly consistent with the selfish herd model. In particular, they are able to see that individual sheep seem to be trying to get to the center of the flock.

The cool thing is more the potential for this type of experiment. Yes, Hamilton's model is attractive and parsimonious, but if we want to understand the rules that actually govern the behavior of sheep when they are faced with a predator (or, in this case, an annoyator), we will need to get good quantitative data on individual behaviors in a variety of contexts.

Plus, look at that little GPS backpack!

I'll leave you with this.



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King AJ, Wilson AM, Wilshin SD, Lowe J, Haddadi H, Hailes S, & Morton AJ. (2012) Selfish-herd behaviour of sheep under threat. Current biology : CB, 22(14). PMID: 22835787  

Hamilton, W. D. (1971) Geometry for the Selfish Herd. Journal of Theoretical Biology, 295-311. DOI: 10.1016/0022-5193(71)90189-5  

  • May 3, 2012
  • 10:45 AM
  • 596 views

Blue-eyed-people-are-all-related zombie news

by Jon Wilkins in Lost in Transcription

So, you know how sometimes at night you're lying in bed when you burp, but then the burp turns out to actually be you throwing up into your mouth just a little bit, and it tastes like a combination of whatever you ate for dinner and evil? Well, this is sort of like that.

Four years ago, a group of researchers from the University of Copenhagen published a nice paper on the genetics of blue eye color. In that paper they look at a bunch of Danish families in which some people have blue eyes and some have brown eyes (or, combination blue-brown eyes, which, for purposes of this study, are treated as non-blue). They also look at a small sample of non-Danish blue-eyed folks: five from Turkey and two from Jordan.

The paper makes a compelling case that the pure blue eyes phenotype depends on a particular nucleotide substitution that alters regulation of the gene OCA2. Furthermore, there is an extended haplotype around the key mutation that is shared by everyone in their sample (a few people have additional nucleotide substitutions that most likely post-date the key functional mutation). This suggests that, while there are many genes that contribute to eye color variation and to pigmentation in general, there may be a single critical mutation responsible for all of the blue eyes out there. Which is pretty cool.

For reasons that I still don't understand, this study has popped back into the news recently. In particular, an article that looks to have been written back in 2008 in USA Today was "updated" in February, and has resurfaced on AOL, which describes it as a "study from USA Today," and warns people with blue eyes about the dangers of falling in love with another blue-eyed beauty. Presumably because of incest (also shown is a clip from HLN -- the artist formerly known as CNN Headline News -- featuring the anchor doing a whole "ick" thing).

In worst-of-media-coverage-of-science fashion the reports that I have found (both from 2008 and from 2012), coverage focuses on stuff from the paper that is tangential, irrelevant, or wrong.

First, "all blue-eyed people are related." Where to start. The researchers suggest that the mutation might have arisen 6000-10000 years ago in the Black Sea region, prior to the Neolithic agricultural expansion into Europe. If we assume a generation time of, say, 25 years, that is 240-400 generations. If we look back that far in the past, even just to the 6000 year mark, each of us has 2^240 ancestors. That's 1.7 x 10^72, which, you will notice, is not just much larger than 7 x 10^9 (the current population of the whole world), but is close to the ballpark of the total number of atoms in the universe.

The fact is, once you go back more than a few hundred years, each of us has a list of ancestors that features the same people over and over again. Not only are we all related, we are all related over and over and over again. While your brother may not be your cousin, your tenth cousin is quite likely to be your seventh cousin as well.

So, yes, all blue-eyed people are related, but there is not really anything here to suggest that they are significantly more closely related than any two people.

Second, both the 6000-10000 year timeframe and the Black Sea origin of the mutation -- both of which featured heavily in press coverage of the paper -- are completely unsupported by anything in the data. What the authors actually say is this:


The mutations responsible for the blue eye color most likely originate from the neareast area or northwest part of the Black Sea region, where the great agriculture migration to the northern part of Europe took place in the Neolithic periods about 6–10,000 years ago (Cavalli-Sforza et al.1994).

The high frequency of blue-eyed individuals in the Scandinavia and Baltic areas indicates a positive selection for this phenotype (Cavalli-Sforza et al. 1994; Myant et al. 1997). Several theories has been suggested to explain the evolutionary selection for pigmentation traits which include UV expositor causing skin cancer, vitamin D deficiency, and also sexual selection has been mentioned. Natural selection as suggested here makes it difficult to calculate the age of the mutation.

That is, we don't know how old the mutation is, and have not tried to perform any sort of analysis to ask the question. That's fine, because what the paper actually does is provide us with a basis for asking these sorts of questions, although that will require more extensive sampling.

The supposition here is based solely on the fact that there was this expansion of agriculture (along with, to a not-fully-characterized extent, an expansion of the genes of the people who developed that early agricultural technology), and that stuff in Europe probably came with that.

The actual way to ask the question would be to go and sequence the DNA of a bunch of folks from all across Europe. To first approximation, we might assume that the mutation first arose in the region where the blue-eyes haplotype shows the greatest within-haplotype genetic diversity. For example, if the mutation first arose near the Black Sea, we should see more genetic variation right around the key mutation among blue-eyed people near the Black Sea. If the allele arrived more recently in Sweden, blue-eyed Swedes would be more genetically similar to each other in the same genomic region, simply because there would have been less time for differences to accumulate.

All else being equal, we might expect the geographical origin of a particular mutation to be at the central point of its range, or near the place where the mutation has reached its highest frequency. That supposition would place the origin somewhere near the Baltic (rather than the Black) Sea. But, there is good reason to believe that this mutation may have been subject to selection. The blue-eyes allele also affects other aspects of pigmentation, and lighter coloring is thought to have been favored at higher latitudes due to the reduced incidence of sunlight.

The fact that we think that natural selection would have pushed the mutation northward means that that its origin was probably somewhere to the South of its current center. Exactly how far depends on a bunch of details, like the strength of selection, and how that strength of selection changes as you move from South to North.

The problem is that, to do it right, you would have to build a model that explicitly incorporates the agricultural expansion and natural selection acting on OCA2, with the strength of selection favoring lighter pigmentation depending on latitude. Maybe also the fact that there are other genes affecting pigmentation. It is something that is doable, especially now that we have a specific gene to focus on, but at this point what we have is a bunch of speculation.

So, to recap, 1) Cool paper. 2) Sex between blue-eyed people is not incest. 3) We have no idea when or where this mutation came from, but it is now conceivable that we could ask the question. 4) Embarrassingly bad science reporting spontaneously rises from the grave four years later and tries to eat your brain.


Eiberg, H., Troelsen, J., Nielsen, M., Mikkelsen, A., Mengel-From, J., Kjaer, K., & Hansen, L. (2008). Blue eye color in humans may be caused by a perfectly associated founder mutation in a regulatory element located within the HERC2 gene inhibiting OCA2 expression Human Genetics, 123 (2), 177-187 DOI: 10.1007/s00439-007-0460-x

... Read more »

Eiberg, H., Troelsen, J., Nielsen, M., Mikkelsen, A., Mengel-From, J., Kjaer, K., & Hansen, L. (2008) Blue eye color in humans may be caused by a perfectly associated founder mutation in a regulatory element located within the HERC2 gene inhibiting OCA2 expression. Human Genetics, 123(2), 177-187. DOI: 10.1007/s00439-007-0460-x  

  • January 5, 2012
  • 01:44 PM
  • 576 views

The Genetical Book Review: The Postmortal

by Jon Wilkins in Lost in Transcription

So, welcome to the first Genetical Book Review of 2012, where we're going to talk about The Postmortal, by Drew Magary. As the book starts, Science!™ has developed a cure for aging, so that people can live forever. What follows is an exploration of the psychological and sociological consequences of immortality.



I love this picture. You can almost hear Death going, "D'oh."

I don't think I'm giving anything away when I tell you that the book winds up being predominantly dystopian. Basically, if you are the sort of person who frets about the future of humanity, who is prone to think things like, "How could I possibly bring a child into this world," well, don't read this book. At least, don't read it in bed after a spicy take-out meal.

If you do enjoy the occasional sci-fi dystopia, this one is of the variety where you make only a small technological (or, in this case, medical) change, and explore the implications in a world that is otherwise very much like our own. One of the interesting things that the author gets to do with this particular premise is to follow history over many decades through the eyes of a single, first-person narrator. So, the protagonist experiences technological and societal changes that would normally take place over the course of generations.

The book is presented as a series of blog posts, some of which are personal, narrative entries, and some transcripts of news reports, others link roundups, and so on. Magary is a contributing editor at Deadspin, and his reporting / media background shows through in the writing. The whole book is engaging, but the writing really shines in the news bits, which are pitch-perfect.

In the book, the cure for aging is achieved through gene therapy, targeted at a single locus, which seems to be closely linked to MC1R, the gene most commonly responsible for redheadedness. What we're going to use this as a jumping-off point to talk about different evolutionary theories of aging, and the extent to which each might be consistent with the existence of a single gene serving as a master control over the aging process.



In The Postmortal, the cure for aging is discovered serendipitously as a byproduct of research aimed at changing hair color. In our actual dystopia, it would have gone differently. Benjamin Button would have been indefinitely detained under NDAA and selectively bred with normal humans. A series of backcrosses would have been used to isolate the gene responsible for his aging reversal. 

But first, a couple of quibbles.

Quibble number 1. There are two biologists who feature prominently in the book: father and son Graham and Steven Otto. Now, I'm not going to argue sexism on the basis of a sample of two, since, even in a world with full gender equality, a random sample of two scientists would both be male about 1/4 of the time (p = 0.25). However, Graham Otto's devoted wife (and Steven Otto's loving mother) is (apparent) non-scientist Sarah Otto. It just so happens (presumably unbeknownst to Magary) that there is a real-life Sarah Otto, a prominent biologist who was just awarded a Macarthur "genius" grant. So, that's . . . unfortunate.

Quibble number 2. The "cure for aging" as presented in the book arrests an individual at whatever age they are when they receive the cure, whether it is three or eighty-three. This actually conflates two different processes: development and senescence. My biological intuition is that, even in the simplest conceivable case, there would be at least two distinct master switches controlling these very different processes. (Actually, possibly a third switch as well, controlling puberty and the onset of secondary sexual characteristics, as distinct from growth to adult size and shape.)

In talking about evolutionary theories of "aging," I will focus on evolutionary theories of senescence, which is really the most important aspect of "aging" with respect to this book.

[Note: none of this should be interpreted as a criticism of the premise or execution of the book, which I loved. The inherent power of science fiction comes from the idea that you build a world that differs from our own. Rather, as always with The Genetical Book Review, the book's premise serves as an excuse and a specific context for talking about evolution.]

Basically, there are three major classes of ideas about the evolutionary origins of senescence, which have different implications for how much and how easily natural selection or medical intervention might be able to extend our lifespans. As is often the case, these different theories are not necessarily mutually exclusive or incompatible, but rather have different emphases. Most consistent with the premise of the book are theories that propose a positive adaptive value to senescence and mortality. Somewhat less consistent are theories that focus on senescence as a byproduct of the fact that natural selection becomes weaker for traits that are expressed later in life. Least consistent are theories suggesting that senescence and lifespan are profoundly constrained by biological universals. We'll take each of these in turn.



Just as youth is wasted on the young, discounts are wasted on the elderly.

1) Senescence as an adaptation.

The idea that there could be a single genetic master switch controlling senescence is most plausible under models where aging and death are specifically adaptive. How would that work, you ask. I mean, after all, the whole idea behind natural selection is that is favors surviving and reproducing, right? Well, in some models, you can actually identify conditions where it makes sense beyond a certain age for adults to go ahead and die. One particular model (cited below) describes an adaptive benefit (at the group / inclusive fitness level) to senescence from limiting the spread of disease.

Perhaps somewhat more generally applicable are models in which senescence is selectively favored as part of a trade off. The idea is that it would be possible to construct a human who lived to be, say, 150, but that it could only be achieved through some sort of compensatory change in another trait. Candidate examples would be size or reproductive output. In fact, all else being equal, smaller humans do tend to live longer than larger ones. Similarly, there are a handful of studies purporting to show that abstaining from reproduction extends lifespan.

In this sort of case, it is easy to see how natural selection might actually favor earlier senescence. To first order, what matters to evolution is how many offspring you produce. If you can grow big and have lots of kids, you're going to win the evolutionary race, even if it means that you drop dead of a heart attack at thirty-five.

Under one of these models, it is easy to imagine the existence of one or a few genes that function as controllers, or strong modifiers, of senescence. Under the strongest version, you can even imagine a gene affecting only senescence. Under the weaker, trade-off version, it might be possible to dramatically extend lifespan, but not without side effects. Maybe the immortals would all weigh eighty pounds and have dramatically – or indefinitely – delayed onset of reproductive capacity.


... Read more »

Glazier, D. (2008) Effects of metabolic level on the body size scaling of metabolic rate in birds and mammals. Proceedings of the Royal Society B: Biological Sciences, 275(1641), 1405-1410. DOI: 10.1098/rspb.2008.0118  

Mitteldorf J, & Pepper J. (2009) Senescence as an adaptation to limit the spread of disease. Journal of theoretical biology, 260(2), 186-95. PMID: 19481552  

Williams, G. C. (1957) Pleiotropy, Natural Selection, and the Evolution of Senescence. Evolution, 11(4), 398-411. info:/

  • November 19, 2011
  • 08:05 AM
  • 634 views

Inequality and Occupy Wall Street

by Jon Wilkins in Lost in Transcription

So, I just discovered the blog of Miles Corak, an Economics Professor at the University of Ottawa (via this short piece in The Atlantic Wire). He has been doing a series of posts about wealth and income inequality that are really interesting and accessibly written. At this time, there are five posts in the series (here, here, here, here, and here).

If you're interested in a thoughtful, nuanced, and readable discussion of the economic factors underlying the Occupy Wall Street protests, check it out.

The most striking image comes from the post on nepotism, where Corak presents a graph from one of his own papers from the Journal of Labor Economics (accessible version available here) that shows the fraction of sons who work in the same firm as their fathers, as a function of income percentile. (Data for Canada)



Corak notes:


Connections matter. And for the top earners this might even be nepotism. This is not a bad thing if parents pass on real skills to their children, skills that might even be specific to particular occupations, industries, or even firms. If this is the case then it makes economic sense to follow in your father’s footsteps.

Wayne Gretzky often talked about the role his father played in developing his skating and stick handling skills. He spent hours and hours with Walter on the backyard rink. But not all top earners got to where they are because of this sort of good nepotism. I somehow doubt that James Murdoch is the Wayne Gretzky of the publishing world.

Bad nepotism promotes people above their abilities by virtue of connections, and it erodes rather than enhances economic productivity.

But there is even a larger cost. If the rich leverage economic power to gain political power they can also skew broader public policy choices—from the tax system to the education system—to the benefit of their offspring. This will surely start eroding the belief that labour markets are fair, and that anyone can aspire to the top.

He also notes that the United States is among the most unequal of the world's rich countries, as well as one of the most elastic. Elasticity, in this context, is the extent to which a person's income is determined by the income of their parents.




Corak goes on to write:


These facts are finally starting to percolate into the American consciousness. Joseph Schumpeter, the Harvard University economist who taught during the 1930s, is often cited as saying that recessions are like cold showers: they clear the economy of inefficiencies, make the existing structures more apparent, and set the conditions for change.

But recessions have social as well as economic consequences. The current recession has shaken some people awake, and Occupiers signal the decline of the American Dream in our consciousness, a manifestation of underlying realities, and the demand for a change in the way of doing business.

Here's hoping that there will be many more installments coming in this series.

Corak, M., & Piraino, P. (2011). Intergenerational Transmission of Employers Journal of Labor Economics, 29 (1), 37-68 : 10.1086/656371

... Read more »

Corak, M., & Piraino, P. (2011) Intergenerational Transmission of Employers. Journal of Labor Economics, 29(1), 37-68. info:/10.1086/656371

  • November 12, 2011
  • 08:14 PM
  • 547 views

What power laws actually tell you about wealth and the 1%

by Jon Wilkins in Lost in Transcription

So, there's an article published in yesterday's Guardian titled, "The mathematical law that shows why wealth flows to the 1%," which is fine, except for the fact that the "law" is not really a law, nor does it necessarily show "why" wealth flows anywhere.

To be fair, it's a perfectly reasonable article with a crap, misleading headline, so I blame the editor, not the author.

The point of the article is to introduce the idea of a power law distribution, or heavy-tailed distributions more generally. These pop up all over the place, but are something that many people are not familiar with. The critical feature of such distributions, if we are talking about, say, wealth, is that an enormous number of people have very little, while a small number of people have a ton. In these circumstances it can be misleading, or at least uninformative, to talk about "average" wealth.

The introduction is nicely done, and it represents an important part of the "how" of wealth is distributed, but what, if anything, does it tell us about the "why"?

To try to answer that, we'll walk through three distributions with the same "average," to see what a distribution's shape might tell us about the process that gave rise to it: Normal, Log Normal, and Pareto.







The blue curve, with a peak at 300, is a Normal distribution. The red curve, with its peak around 50, is a Log Normal. The yellow one, with its peak off the top of the chart at the left, is a Pareto distribution.
In each case, the mean of the distribution is 300.

The core of the issue, I think, is that there are three different technical definitions that we associate with the common-usage term "average," the mean, the median, and the mode. This is probably familiar to most readers who have made their way here, but here's a quick review:



The mean is what you usually calculate when you are asked to find the average of something. For instance, you would determine the average wealth of a nation by taking its total wealth and dividing it by the number of people.



The median is the point where half of the distribution lies to the right, and half lies to the left. So the median wealth would be the amount of money X where half of the people had more than X and half had less than X.



The mode is the high point in the distribution, its most common value. In the picture above, the mode of the blue curve is at about 300, while the mode of the red curve is a little less than 50.



The Normal (or Gaussian, or bell-curve-shaped) distribution, represented in blue, is probably the most familiar. One of the features of the Normal distribution is that the mode, median, and mean are all the same. So, if you have something that is Normally distributed, and you talk about the "average" value, you are probably also talking about a "typical" value. 



Lots of things in our everyday experience are distributed in a vaguely Normal way. For instance, if I told you that the average mass of an apple was 5 ounces, and you reached into a bag full of apples, you would probably expect to pull out an apple that was somewhere in the vicinity of 5 ounces, and you might assume that you would be as likely to get an apple that was bigger than that as you would be to get one that was smaller. Or if I told you that the average height in a town in 5 feet, 8 inches, you might expect to see reasonable numbers of people who were 5'6", fewer who were 5'2", and fewer still who were 4'10".



So what sorts of processes lead to a Normal distribution? The simplest way is if you have a bunch of independent factors that add up. For example, it is thought that a large number of genes affect height, with the specific variants of each gene that you inherited contributing a small amount to making you taller or less tall, in a way that is close enough to additive.




What would it mean, then, if we were to find that wealth was Normally distributed? Well, it could mean a lot of things, but a simple model that could give rise to a Normal wealth distribution would be one where the amount of pay each person received each week was randomly drawn from the same distribution. Maybe you would flip a coin, and if it came up heads, you would get $300, while tails would get you $100. Pretty much any distribution would work, as long as the same distribution applied to everyone. After many weeks, some people would have gotten more heads, and they would be in the right-hand tail of the wealth distribution. The unlucky people who got more tails would be in the left-hand tail. But most people's wealth would be reasonably close to the mean of the wealth distribution.




Image from Alex Pardee's 2009 exhibition "Hiding From The Normals"


Now, it's important to remember that just because a particular mechanism can lead to a particular distribution, observing that distribution does not prove that your particular mechanism was actually at work. It seems like that should be obvious, but you actually see a disturbing number of scientific papers that basically make that error. There will typically be whole families of mechanisms that can give rise to the same outcome. However, looking at the outcome (the distribution, in this case) and asking what mechanisms are consistent with it is an important first step.



Alright, now let's talk about the Log Normal distribution (the red one). Unlike the Normal, the Log Normal is skewed: it has a short left tail and a long right one. This means that the mean, mode, and median are no longer the same. In the curve I showed above, the mean is 300, the median is about 150, and the mode is about 35. 



This is where talk about averages can be misleading, or at least easily misinterpreted. Imagine that the wealth of a nation was distributed like the red curve, and that I told you that the average wealth was $30,000. What would you think? Well, if I also told you that the wealth was Log Normally distributed, and I gave you some additional information (like the median, or the variance), you could reconstruct complete distribution of wealth, at least in principle.



The problem is that we tend to think intuitively in terms of distributions that look more like the Normal. In practice, we hear $30,000 average wealth, and we say, "Hey, that's not too bad." We probably don't consciously recognize that (in this example), half of the people actually have less than $15,000, and that the typical (i.e., modal) person has only about $3500.



What type of process can give rise to a Log Normal distribution? Well, again, there are many possible mechanisms that would be consistent with a Log Normal outcome, but there is a class of simplest possible underlying mechanisms. We imagine something like the coin toss that we used in the Normal case, but now, instead of adding a random quantity with each coin toss, we multiply.



This is sort of like if everyone started off with the same amount of money invested in the stock market. Each week, your wealth would change by some percentage. Some weeks you might gain 2%. Other weeks you might lose 1%. If everyone is drawing from the same distribution of multipliers (if we all have the same chance of a 2% increase, etc.), the distribution of wealth will wind up looking Log Normally distributed.




Vilfredo Pareto, who grew a very long b... Read more »

Clauset, A., Shalizi, C., & Newman, M. (2009) Power-Law Distributions in Empirical Data. SIAM Review, 51(4), 661. DOI: 10.1137/070710111  

  • November 3, 2011
  • 11:55 AM
  • 525 views

Mutational Analysis in Poetry and Biology

by Jon Wilkins in Lost in Transcription

So, Robert Pinsky wrote a cool little piece in Slate the other day titled "In Praise of Memorizing Poetry – Badly." In it he argues for a particular benefit to be gotten from misremembering a poem: that it brings into focus the choices that were made in the poem, the the consequences of using one word rather than another. He illustrates his argument with Yeats's "On Being Asked for a War Poem," which he presents like this:
“On Being Asked for a War Poem” I think it better that in times like these
A poet's mouth be silent, for in truth
We have no gift to set a statesman right;
He has had enough of [something] who can please
A young girl in the indolence of her youth,
Or an old man upon a winter's night.He talks about misremembering the [something] as "glory" or "indolence" or "striving" before rediscovering Yeats's original "meddling."

In the case of "meddling," the result of the exercise is to highlight the historical context in which Yeats was writing. Yeats was an Irish poet writing about World War I in 1915. At the time, Ireland was still part of the United Kingdom, and was actively involved in the war. However, some Irish nationalists used the war as an opportunity initiate a rebellion against English rule. And, in fact, the Irish War for Independence began pretty much as soon as World War I ended.



During Easter week of 1916, Irish rebels seized control of several key buildings
in Dublin and declared independence from England. Yeats wrote a poem about it.
Yeats's poem was written in response to a request by Henry James, and was originally titled "To a friend who has asked me to sign his manifesto to the neutral nations." In all of this context, the choice of "meddling" seems to point to a degree of ambivalence towards the war, even presaging Ireland's own neutrality in World War II.

Now, of course, all of this information is, in principle, available to anyone who has both the original text and access Wikipedia. However, for Pinsky, it is this forgetting, the substitution of "meddling" with "glory," that serves as the catalyst for this particular close reading. And I doubt that, in the absence of some similar impetus, very many people would have focused on this particular aspect of the poem.

In biology, similar mistakes, in the form of mutations, provide one of our most important windows into the structure and function of biological systems. These mutations are sometimes the product of targeted mutagenesis, but can also result from naturally occurring mutations.

A lot of our coarse-grained knowledge of many systems comes from loss-of-function, or knockout mutations, where a mutation removes a particular gene, or renders it nonfunctional. For example, in 1976, Sharma and Chopra first described a recessive mutation in the fruitfly Drosophila melanogaster. Flies inheriting two copies of the mutation exhibited various developmental defects, the most obvious of which involved wing formation. So, the mutation, and later the gene, became known as "wingless."

This is typical in genetics, where a gene will be given a name based on the phenotypic consequences of losing that gene. So, a gene required for wings becomes "wingless," a gene required for heart formation might be called "heartless," and so on.



Kim Jong Il relaxes with some brews.
Due to the nature of the discovery process in biology, many genes wind up with names that are more like the opposite of what the gene actually does. This is sort of like how the least democratic countries always wind up with the word "Democratic" in their names, or how Citizens United succeeded in dramatically curtailing most citizens' abilities to control their own government.
More subtle mutations, which alter the behavior of a gene or its gene product without completely eliminating it function, are more closely analogous to the misremembering that Pinsky is talking about, however. In a way, a knockout mutation of an important gene is more like just removing one whole line from Yeats's poem, without regard for grammar, rhyme scheme, coherence, etc. What you would wind up with is a mess that fails in many ways, and is probably not terribly instructive – just like in biology.

Point mutations, which might alter a single amino acid in a protein, provide a more targeted and interpretable set of changes. Such a mutation might cause a small shift in the binding behavior of the protein, or might cause a slight change in the timing of the gene's expression.

Like in the poetry case, these mutations are more likely to be revealing of the fine tuning part of the creative process, where mutations of small effect arise and are subjected to natural selection. In some populations – things like certain viruses, which have a very large population size and strong selective constraints – it might even be reasonable to think that these alternate, mutant forms have been explored and rejected by past natural selection. In other cases (e.g., large mammals, with relatively small effective population sizes), the most common form we find in nature might not represent some finely tuned optimum, but may simply be a form that works well enough.

Similarly, when we read a Yeats poem, we are inclined to assume that every single word has been chosen with extreme care, that a host of plausible alternatives were considered and rejected by the poet before he settled on just exactly the right word, in this case, "meddled." I think we are inclined to agree with Pinsky's final assessment, that "by memorizing his poem imperfectly, I had received a creative writing lesson from a great poet."

However, a lot of poems in the world, even very good ones, are probably more like large mammals, with many of the word choices working well enough, but not necessarily representing some optimum, even a local one. (There is of course, the question, in biology and in poetry, of to what extent one can talk coherently about optima, but that's a post for another day.) But this process, deliberate or accidental tinkering, is critical both to the creation of great things, and to understanding how greatness is created.

Sharma RP, & Chopra VL (1976). Effect of the Wingless (wg1) mutation on wing and haltere development in Drosophila melanogaster. Developmental biology, 48 (2), 461-5 PMID: 815114

... Read more »

Sharma RP, & Chopra VL. (1976) Effect of the Wingless (wg1) mutation on wing and haltere development in Drosophila melanogaster. Developmental biology, 48(2), 461-5. PMID: 815114  

  • October 16, 2011
  • 10:18 PM
  • 617 views

I owe Martin Nowak an apology

by Jon Wilkins in Lost in Transcription

So, if you're an Evolutionary Biologist, you're already familiar with the dust-up prompted by a Nature paper published in 2010 by Martin Nowak, Corina Tarnita, and E. O. Wilson.  If not, I wrote about the paper, and the response from the community, here and here.

Briefly, the article attacked one class of approaches to modeling the evolution of traits affecting social interaction: models based on kin selection and inclusive fitness. The authors made strong claims about the effectiveness of such models, claiming that they were useless or even wrong for thinking about eusociality (e.g., in species of bees and ants). The paper prompted a number of written responses, in blogs and in letters to Nature, one co-authored by 137 prominent biologists, refuting many of the claims of the paper.

The paper comes with a weighty appendix, which contains a lot of calculations. Those calculations are not problematic. Rather, it is the main text (the only part most people will read) that triggered the vocal response. The main text made a bunch of unsupported (and wrong) claims, knocking down a straw-man caricature of kin-selection models. It was this straw-man caricature that people found so offensive, along with the failure to cite a huge body of literature (which would have undermined that straw man).

The disconnect between the careful, meticulous appendix and the swaggering, irresponsible main text led most readers to assume that we were looking at a frankenpaper, the imperfectly integrated product of multiple authors. In this sort of circumstance, the impulse is to partition blame among the authors.

My sense was that most people held Tarnita, a postdoc with Nowak at the time, blameless, a talented junior scientist in the wrong place at the wrong time.

The blame, in most people's eyes, fell primarily on Nowak, for a complex set of reasons that I tried to untangle here.  In particular, Nowak has a reputation for not being generous in attribution of credit to other scientists.


Wilson was not blamed. He is, after all, a living legend among evolutionary biologists. If anything, the discussion about Wilson was along the lines of, "Why is Wilson keeping such bad company?" Some people even speculated that he was perhaps being taken advantage of, that he had been roped into putting his name on the paper.

It now appears that I, along with all the other rumor-mongering evolutionary biologists, owe Nowak an apology.


Over the past year, Wilson has been on the warpath, giving various interviews in which he reiterates the major arguments presented in the paper. The most recent just appeared here in the Atlantic. This article, I think, makes it clear that Wilson was the ideological driving force behind all of the misrepresentation in the original Nature article. It also seems to indicate that the disingenuous argument will be expanded to book length in Wilson's forthcoming The Social Conquest of Earth.

The richest part of the Atlantic article comes in Wilson's trashing of Stephen Jay Gould. Trashing Gould is, of course, a popular pastime among evolutionary biologists.
“I believe Gould was a charlatan,” [Wilson] told me. “I believe that he was … seeking reputation and credibility as a scientist and writer, and he did it consistently by distorting what other scientists were saying and devising arguments based upon that distortion.” This is a valid enough criticism of Gould. It is also a dead-on description of what was wrong with the Nowak et al. paper. I suspect that the irony is lost on Wilson.

Nowak, M., Tarnita, C., & Wilson, E. (2010). The evolution of eusociality Nature, 466 (7310), 1057-1062 DOI: 10.1038/nature09205

... Read more »

Nowak, M., Tarnita, C., & Wilson, E. (2010) The evolution of eusociality. Nature, 466(7310), 1057-1062. DOI: 10.1038/nature09205  

  • September 29, 2011
  • 06:53 PM
  • 614 views

The Genetical Book Review: The Psychopath Test

by Jon Wilkins in Lost in Transcription

So, welcome back to the Genetical Book Review! This episode? The Psychopath Test, by Jon Ronon. Ronson is the author of The Men Who Stare at Goats, which the movie was based on.

Also, his name is what my name would be if I were from Iceland.

The Psychopath Test traces Ronson's exploration of psychopathy: what a psychopath is, how you identify one, the effect they have on society, and society's efforts to contain them. The book is written engagingly, and makes for a quick read, even if you're as slow a reader as I am. Ronson mixes historical and medical information with interviews of both psychopaths and the doctors who have sought to define and/or treat them. Some of the accounts, you can imagine, touch on some fairly gruesome events, but the light manner of the writing should make the material palatable even for those with weaker stomachs for that sort of thing.

One of the most interesting things about the book is the fact that the material is presented chronologically -- not in the order that things happened, but in the order that Ronson learned about and understood them (ostensibly, at least). The effect is a really interesting one, which fits well with what seems to be one of the books goals. By the end of the book, Ronson has deconstructed the whole notion of sanity/insanity, as well as the motives of doctors, pharmaceutical companies, police, the entertainment industry, and journalists, including himself.

He achieves the effect by writing in a sort of semi-gonzo, close first person, chronicling his own reactions and beliefs along the journey. First, he learns x, and so he believes X. Then, in the next chapter, he learns y, and starts to doubt his belief in X. And so on throughout the book. The result is a message that is fragmented, but also nuanced and faceted. This mixture of sometimes contradictory conclusions actually seems quite fitting, given the complexity of the phenomenon, and our limited understanding of it.

Even out of that complexity though, there are two big take-home messages that rise above the others.

First is the fact that psychopathy is not really a well-defined, discrete thing. There is a continuum not only of severity, but of type. Two people could both score high on the eponymous psychopath test (constructed by Bob Hare, who features prominently in the book), but actually exhibit quite different suites of behavior.

This, of course, is not news to anyone who has spent time studying psychiatric disorders (or any other sort of complex disease). Labeling is a necessary part of science and of medicine, as it is what allows us to communicate with each other in an efficient way. However, we need to keep reminding ourselves that these labels refer to abstractions, and that the thing we care about is typically a lot more complicated, and a lots less well understood, than a monolithic label implies.

Which is to say, while it might not be news, it is always good to be reminded of it.

Second is the idea that there are a lot of aspects of society that have a vested interest in reducing people to their maddest edges, as Ronson puts it. Reality television and daytime talk shows seek out people who have something going on that is crazy enough to be entertaining, and then edit out all the boring (read "sane") bits. Journalists do likewise, seeking out the extreme behaviors and personalities that will make for good quotations and compelling stories. Pharmaceutical companies benefit monetarily from the application of clinical labels to any behavior that lies outside the norm.

And so forth.
There are obviously a lot of very ill people out there. But there are also people in the middle, getting overlabeled, becoming nothing more than a big splurge of madness in the minds of the people who benefit from it.The other thing that struck me was the chapter on the DSM, the big book that defines all mental illnesses. I think I had always assumed that there was some sort of rigorous, evidence-based process by which disorders were included or excluded. It seems that, well, not so much. It seems more like it is a veneer of codification laid on top of a bunch of idiosyncratic opinions, passed through a filter of special interests. Sigh.

Basically, if you work in the field, you may already be familiar with many of the stories, and may already have internalized many of the punchlines. But, for most people, The Psychopath Test provides an entertaining, informative, and often troubling look at medicalization and exploitation of mental health in our society.

Ronson, Jon. The Psychopath Test. New York: Riverhead Books, 2011.

Hare, R. D. (1980). A research scale for the assessment of psychopathy in criminal populations Personality and Individual Differences, 1 (2), 111-120 : 10.1016/0191-8869(80)90028-8

... Read more »

Hare, R. D. (1980) A research scale for the assessment of psychopathy in criminal populations. Personality and Individual Differences, 1(2), 111-120. info:/10.1016/0191-8869(80)90028-8

  • August 1, 2011
  • 08:59 AM
  • 1,177 views

Why do we make odd faces when we orgasm? A romance in three parts

by Jon Wilkins in Lost in Transcription

So, Guillaume's Mailbag has continued on its mission to provide an adaptive explanation for every existing trait. The most recent trait Guillaume has been tackling was submitted by John Wilkins, who asked, "Why do we make odd faces when we orgasm?"

In case you missed when I've plugged him before, JoHn Wilkins (no recent relation) is a philosopher of science in Australia. His most recent book is Species: A History of the Idea, and he runs an excellent blog called Evolving Thoughts. He recently concluded an excellent series of posts on "Atheism, agnosticism and theism" in which he discusses, among other things, what it means to have a belief. You can find the start of that series here.

But back to the face of orgasm. Guillaume took three full strips to answer this one, so I've waited until he was done to post them here. I think I've finally figured out how to make these full-page versions more readable on the blog, but it involved lowering the resolution of the JPEG, so, for higher-res versions of these three comics, head on over to Darwin Eats Cake. The first of the series of three can be found here.



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For those who are interested, a couple of vole and oxytocin citations are provided below to get you started. The vole literature is actually quite extensive and all interesting. I've included a relatively recent paper, which will contain citations to a lot of the other work. No peer-reviewed publications are yet available on the eating and mating habits of Ursus philorgasmii.
Ross HE, Cole CD, Smith Y, Neumann ID, Landgraf R, Murphy AZ, & Young LJ (2009). Characterization of the oxytocin system regulating affiliative behavior in female prairie voles. Neuroscience, 162 (4), 892-903 PMID: 19482070

Carmichael MS, Warburton VL, Dixen J, & Davidson JM (1994). Relationships among cardiovascular, muscular, and oxytocin responses during human sexual activity. Archives of sexual behavior, 23 (1), 59-79 PMID: 8135652

Although at least one study suggests that, in men, prolactin is actually more strongly correlated with orgasm than oxytocin is:

Krüger TH, Haake P, Chereath D, Knapp W, Janssen OE, Exton MS, Schedlowski M, & Hartmann U (2003). Specificity of the neuroendocrine response to orgasm during sexual arousal in men. The Journal of endocrinology, 177 (1), 57-64 PMID: 12697037

... Read more »

Ross HE, Cole CD, Smith Y, Neumann ID, Landgraf R, Murphy AZ, & Young LJ. (2009) Characterization of the oxytocin system regulating affiliative behavior in female prairie voles. Neuroscience, 162(4), 892-903. PMID: 19482070  

Carmichael MS, Warburton VL, Dixen J, & Davidson JM. (1994) Relationships among cardiovascular, muscular, and oxytocin responses during human sexual activity. Archives of sexual behavior, 23(1), 59-79. PMID: 8135652  

Krüger TH, Haake P, Chereath D, Knapp W, Janssen OE, Exton MS, Schedlowski M, & Hartmann U. (2003) Specificity of the neuroendocrine response to orgasm during sexual arousal in men. The Journal of endocrinology, 177(1), 57-64. PMID: 12697037  

  • July 1, 2011
  • 11:16 PM
  • 1,161 views

Wrinkly fingers for gripping?

by Jon Wilkins in Lost in Transcription

So, here's the latest in adaptationism:


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Hat-tip to Justin Blumenstiel, who is the king of transposable elements, which I think means that every time one of them transposes, they have to tithe to him.

Changizi M, Weber R, Kotecha R, & Palazzo J (2011). Are Wet-Induced Wrinkled Fingers Primate Rain Treads? Brain, behavior and evolution PMID: 21701145

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Changizi M, Weber R, Kotecha R, & Palazzo J. (2011) Are Wet-Induced Wrinkled Fingers Primate Rain Treads?. Brain, behavior and evolution. PMID: 21701145  

  • June 24, 2011
  • 08:54 PM
  • 1,129 views

Happy Belated Father's Day

by Jon Wilkins in Lost in Transcription

So, Farther's day was almost a week ago, but I wanted to share this video, which illustrates all the good-timey ho-down fun that led to your father becoming your father.

Did I just call your mom a ho?  It sure seems like it, doesn't it?



If you want to try this (or something like it) at home, check out the ideas in this article:

Joseph P. Chinnici,, Joyce W. Yue,, & Kieron M. Torres (2004). Students as “Human Chromosomes” in Role-Playing Mitosis & Meiosis The American Biology Teacher, 66 (1), 35-39

... Read more »

Joseph P. Chinnici,, Joyce W. Yue,, & Kieron M. Torres. (2004) Students as “Human Chromosomes” in Role-Playing Mitosis . The American Biology Teacher, 66(1), 35-39. info:/

  • June 23, 2011
  • 06:06 PM
  • 1,431 views

Happy 99th Birthday, Alan Turing

by Jon Wilkins in Lost in Transcription

So, today (June 23, 2011) marks the 99th anniversary of the birth of Alan Turing, British supergenius who played a critical role in winning World War II and is one of the founding fathers of computer science.

He was also gay, which was illegal Britain at the time. In 1952 he was prosecuted under the same law that had sent Oscar Wilde to gaol. He chose to undergo chemical castration (in the form of treatment with feminizing hormones) as an alternative to prison.

In 1954 he committed suicide in dramatic fashion. He died of cyanide poisoning, and was found lying in his bed with a half-eaten apple beside him. The speculation is that he had laced the apple with cyanide and was reenacting the apple scene from Snow White.

When Alan Turing was found on June 8, 1954, he had been dead for one day, and he looked exactly like this. Snow White by *VinRoc on deviantART
Turing's earliest major contribution was the hypothetical Turing machine, which consisted of a very long piece of tape and a set of rules for manipulating the symbols on that tape. Turing showed that such a machine was, in principle, capable of performing any mathematical computation that can be represented as an algorithm. The Universal Turing Machine (a Turing machine capable of simulating any other Turing machine) provided a sort of proof-of-principle for the idea of general-purpose computers, and the tape-and-manipulator structure of the Turing machine is often cited as the prototype of the separation-of-hardware-and-software structure that pervades our computer lives today.


A Turing machine consists of a tape with symbols on it and a machine with a set of rules for reading and manipulating those symbols. And a bell.
During World War II, Turing worked as a cryptanalyst and made major contributions to cracking the "Enigma" codes used by the German military. The success of Turing and his colleagues throughout the war gave the Allies a critical advantage, particularly during the early parts of the war, when the Germans had a significant military advantage.

After World War II, he introduced what we now call the "Turing test" for artificial intelligence. The idea is that a computer can be said to have achieved genuine intelligence if a human having a conversation with it could not tell that it was a computer. For the next forty-some years, this was considered to be the gold standard for the demonstration of human intelligence. Then came a flood of reality television, which demonstrated that many humans would not actually pass it.
During the last few years of his life, Turing turned his attention to certain problems in mathematical biology, including the curious fact that many plants seem to grow in patterns governed by the Fibonacci sequence. The whole phyto-Fibonacci thing is a weird and interesting phenomenon that will get its own dedicated post sometime soon.

In the meantime, happy birthday Alan Turing, and RIP.

Turing, A. M. (1950). Computing Machinery and Intelligence Mind, 59 (236), 433-460

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Turing, A. M. (1950) Computing Machinery and Intelligence. Mind, 59(236), 433-460. info:/

  • June 13, 2011
  • 11:59 AM
  • 823 views

Antibiotic resistance and corporate agriculture

by Jon Wilkins in Lost in Transcription

So, over the weekend, Nicholas Kristof wrote a nice piece in the New York Times in which he laid out the basic facts and statistics regarding the cavalier use of antibiotics in agriculture. His column is full of interesting (i.e., depressing) figures, one of the most striking of which is that the agricultural use of antibiotics in the state of North Carolina exceeds the medical use of antibiotics for the entire United States.

Anyway, the basic punchline is this: when someone in your family is hospitalized or killed by some food-borne, antibiotic-resistant pathogen, you can thank the huge agricultural corporations and the millions of lobbyist dollars they have spent blocking food-safety legislation.

Happy eating!

These full-page comics come out badly here on the blog, so to see a more readable version, go to the Darwin Eats Cake website.


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Sørensen SJ, Bailey M, Hansen LH, Kroer N, & Wuertz S (2005). Studying plasmid horizontal transfer in situ: a critical review. Nature reviews. Microbiology, 3 (9), 700-10 PMID: 16138098

... Read more »

Sørensen SJ, Bailey M, Hansen LH, Kroer N, & Wuertz S. (2005) Studying plasmid horizontal transfer in situ: a critical review. Nature reviews. Microbiology, 3(9), 700-10. PMID: 16138098  

  • May 26, 2011
  • 10:34 PM
  • 977 views

Traffic, preterm birth, and adaptationism

by Jon Wilkins in Lost in Transcription

So, here's a thing:


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This relates to a criticism that I made of evolutionary psychology, but which applies to many naive adaptationist arguments: it is easy to come up with a plausible-sounding adaptive explanation of just about anything. In most cases, it is equally easy to come up with an equally plausible-sounding explanation of the exact opposite phenomenon.

Barnett AG, Plonka K, Seow WK, Wilson LA, & Hansen C (2011). Increased traffic exposure and negative birth outcomes: a prospective cohort in Australia. Environmental health : a global access science source, 10 PMID: 21453550

... Read more »

Barnett AG, Plonka K, Seow WK, Wilson LA, & Hansen C. (2011) Increased traffic exposure and negative birth outcomes: a prospective cohort in Australia. Environmental health : a global access science source, 26. PMID: 21453550  

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