Classes are over, and that means I have more time to think…about my classes. So I’m on the lookout for ideas to improve my teaching, and gosh, look, Nature has an article on better ways to teach genetics. So I read it eagerly, and was left scratching my head. It’s a short news article, so it’s a bit thin on the details of how to teach genetics the way it recommends, but I’m also confused about how this approach would be useful.
The author, Gregory Radick, advocates teaching Weldonian genetics, rather than Mendelian genetics.
In a recent two-year project, we taught university students a curriculum that was altered to reflect what genetics textbooks might be like now if biology circa 1906 had taken the Weldonian rather than the Mendelian route. These students encountered genetics as fundamentally tied to development and environment. Genes were not presented to them as what inheritance is ‘really about’, with everything else relegated to ignorable supporting roles. For example, they were taught that although genes can affect the heart directly, they also affect blood pressure, the body’s activity levels and other influential factors, themselves often influenced by non-genetic factors (such as smoking). Where in this tangle, we ask them, is a gene for heart disease? In effect, this revised curriculum seeks to take what is peripheral in the existing teaching of genetics and make it central, and to make what is central peripheral.
More developmental and environmental influences? That sounds good to me. I already try to get some of that across in my course, but standard transmission genetics is the core concept, and I work hard to make sure they grasp that before we grapple with the complications.
But still, he’s promoting the idea that we roll back our understanding of genetics to 1906, and start fresh from there? That’s just weird. Somebody is maybe a little too infatuated with WFR Weldon, and wants to resume the Genetics Wars of the 1900s (which wasn’t as awesome as my title makes it sound, all steampunkish and ferocious — it was more of an academic argument). Shortly after the rediscovery of Mendel’s work in 1900, a heated debate arose in the literature.
On one side was William Bateson, who was really keen on Mendel. Bateson was predisposed to favor the guy’s method: in 1899, he wrote a prescription for a scientific approach to crack the problem of heredity that was practically a literal description of what Mendel had already done.
What we first require is to know what happens when a variety is crossed with its nearest allies. If the result is to have a scientific value, it is almost absolutely necessary that the offspring of such crossing should then be examined statistically. It must be recorded how many of the offspring resembled each parent and how many showed the characters intermediate between those of its parents. If the parents differ in several characters the offspring must be examined statistically, and marshalled, as it is called, in respect of each of those characters separately.
And then Mendel’s paper from 1865 was unearthed, and that’s exactly what he had done, and he had come up with several general rules of inheritance that could then be applied and tested. Bateson maybe got a little over-enthusiastic, and used Mendel’s result to argue for saltationism, the idea that evolution proceeded in sudden leaps. This side of the Genetics Wars was called the Saltationists, or the Mendelians.
The other side was the Biometricians, led by Weldon, Karl Pearson, and Francis Galton. They objected to Mendel’s genetics for a couple of reasons: it was way too simple to explain everything (they were right), that characters aren’t as discrete as Mendel suggested (they were also right), and that you needed to emphasize statistical analyses more (wha…? I know, really strange, since Mendel’s work was tediously statistical, and Bateson kept emphasizing the importance of statistical analyses).
Weldon’s 1902 paper criticizing Mendelism is actually historically interesting and he does bring up a number of important scientific points. But I wouldn’t use it in an introductory genetics class, because it would just confuse matters and I’m most interested in getting students to understand the practical answers. For instance, it starts with a summary of Mendel’s laws, and then as an objection, raises an argument built around a rudimentary understanding of population genetics (it’s good for 1902, not so good for any time afterwards). He points out that if you take the results of a hybrid cross, which will produce one pure breeding type for every two hybrids and every one of the other pure breeding type, and then produce many generations by selfing (no further hybridizing allowed), the frequency of they hybrids will steadily decrease, because purebreds will only produce purebreds, and hybrids will produce half hybrids and half purebreds of the two types.
It’s trivially true, but not particularly interesting because of the artificially limited nature of crosses after the first generation, and it’s also completely irrelevant to Mendel’s conclusions. It even uses Mendel’s rules to generate the frequency of different combinations in each generation, so it can hardly be used to argue against Mendel. It is an interesting early step in the development of population genetics, I guess.
Weldon then criticizes Mendel for something I think we’re all familiar with: his results were too good to be true! He expected 3:1 ratios, and he got almost exactly 3:1 ratios in all of his published results, and statistically, Weldon points out that this is degree of correspondence is unlikely.
These results then accord so remarkably with Mendel’s summary of them that if they were repeated a second time, under similar conditions and on a similar scale, the chance that the agreement between observation and hypothesis would be worse than that actually obtained is about 16 to 1.
This is also true, but rather petty, and illustrating a flaw in the Biometrician’s approach. Nowadays, ideally, if we saw such a potentially damaging flaw in a core conclusion of a relatively easily replicated experiment, we’d repeat it, especially given that the rest of the paper is an intimately familiar discussion of the properties of a great many varieties of peas. But, to be mean about it, the biometrician’s specialty was statistical analyses of other people’s experiments. (Whew, I can be catty about someone who has been dead for 110 years. Impressive).
But still, the remaining chunk of the paper is much more interesting, in a dry sort of way, then the first part. He looks at peas of a great many readily available varieties, and find that seed color and shape, for instance, exhibit a much greater diversity than the pairs of contrasting traits Mendel analyzed. It’s clear that phenotype is much more complex than the simple binaries Mendel placed them in — and in today’s world where simplistic binary thinking seems to have become the standard cultural mode, that’s a valuable contribution. He also reviews the experiments with various crosses that were going on at the time, and finds that not all traits are passed on with that simple dominant/recessive relationship Mendel documented.
These facts show first that Mendel’s law of dominance conspicuously fails for crosses between certain races, while it appears to hold for others; and secondly that the intensity of a character in one generation of a race is no trustworthy measure of its dominance in hybrids.
(Do I need to remind everyone that a hundred years ago “race” was used in a broad and generic way for what we’d now call “varieties”?)
So I’m left wondering what “Weldonian genetics” I’m supposed to teach. I think I already do. We didn’t just throw everything Weldon mentioned in the trash bucket once he died, but incorporated it into our understanding of inheritance.
The thing is, I spend the first two weeks of my course teaching the history of genetics and reviewing basic Mendelian inheritance. Most of them come out of high school understanding dominant/recessive/simple monohybrid crosses, but I try to make sure they’ve got those simple quantitative relationships down cold. The important thing here is that Mendel enables us to give a quantitative foundation for understanding inheritance, and I’d be curious to know if Radick’s curriculum accomplishes that.
The rest of the semester is spent ripping up the simplifications. We talk about multiple alleles, codominance, epistasis, background effects, conditional alleles, expressivity and penetrance, etc., etc., etc., all the mechanisms that generate the complexity that Weldon appreciated so much, and that Mendel neglected in his simplifications. The Genetics Wars dribbled away because with greater understanding came the awareness that both sides were right, and Bateson and Weldon are rather easily reconciled now. I don’t understand the point of resurrecting an antique enmity when modern genetics is a synthesis.
I also honor Weldon in the lab. The very first lab of the semester is all about statistics and probability, and one of the exercises involves throwing dice a hundred times. I suppose if I wanted to really teach Weldonian genetics, I ought to have each of them throw 12 dice 26,306 times and then analyze the statistics of the distribution. Of course, then we waste the rest of the semester breeding flies, when we could have done more dice throwing, or read other people’s genetics papers and dissected their data tables. I think one Weldonian lab is enough.
One other thing I have to point out about Radick’s experiment in teaching: it doesn’t seem to have been appropriately designed.
Our experimental group consisted of second-year humanities undergraduates. First-year biologists, who were taught the conventional approach, acted as our control.
Whoa. I’m going to say right there is a huge flaw: these two groups are very different populations of students, with different backgrounds, and the goals of those two classes are going to be very different. You can’t compare them adequately, much less claim the first year biologists are a “control”. I’m also wondering where these classes fit into their overall curriculum. We give our first year biology majors a brief overview of genetics in a class that also puts it into context and discusses the philosophy of science and evolution, but it is not a substitute for a full course in genetics. We only give them that in a third year course, after they got some cell biology and statistics under their belt, because first year students here are generally not ready for such an intensely quantitative course (some of our third- and fourth-years aren’t, either).
One last objection, and then I’ll stop muttering over this paper. Radick suggests that Weldon’s death in 1906 was responsible for the ultimate ‘defeat’ of the Biometricians, and even the wikipedia article on Weldon says the same thing. I don’t buy it. There are better reasons for the triumph of the Mendelians, and they are the series of positive results that followed on. I would point to the too-often neglected work of Walter Sutton, who linked abstract Mendelian “unit factors” to the behavior of chromosomes, and made a mathemical concept a biological reality. I’d also suggest that we can’t overlook the power of TH Morgan’s work on Drosophila. Even had Weldon lived, there would have been no change in the course of the science.
PZ: “Radick suggests that Weldon’s death in 1906 was responsible for the ultimate ‘defeat’ of the Biometricians”
http://www.nber.org/papers/w21788: “Overall, these results suggest that outsiders are reluctant to challenge leadership within a field when the star is alive and that a number of barriers may constrain entry even after she is gone”
Nope, still don’t buy it in this case. Galton and Pearson lived on. Weldon’s paper isn’t that convincing a case for a very different perspective, and Radick’s short article doesn’t actually explain how a Weldonian approach would be different from a modern genetic approach.
And really, Sutton & Morgan were a one-two punch that made the whole argument irrelevant.
The truth wins out in the end of course, but when? Removal of a strong champion can expedite this, but I don’t know if that was the case here. Still it’s an interesting observation.
lack of background knowledge led me stop reading at this bit of info:
Which sounds like a really good approach to the subject. To rebut the current mistaken idea that
– not tying to make a point. just illustrating what I’ve absorbed from past discussions here about “gene’s aren’t everything”. I’m open to read a little more about this field outside my skill level. sorry for showing how ignorant I am, and lacking of reading discipline to read the rest of this OP about the restoration of an intellectual battle between Mendel and Weldon. …carry on…
re 4: oops extra apostrophe escaped my control: gene’s ==> genes
Yep, that’s what I was taught, and it was pretty much all I was taught about genetics. Since the ‘one gene for trait X, another gene for trait Y’ meme is so pervasive, I suspect that is still pretty much all that is taught to most people.
I’ve never read Mendel’s paper, or anybody’s attempts at replication of his experiments, but isn’t it possible that Mendel looked for, and then used, traits that did follow closely the 3:1 result? It seems a logical thing to do.
Not only did Galton and Pearson live on, but Mendel had already been dead nearly 20 years before the Mendelian movement started.
moarscienceplz — the point of the criticism is that a 3:1 ratio should not come out of any study of dominant-vs.-recessive alleles exactly. Even if Mendel chose to study an allele with perfect 3:1 heritability, the actual numbers of offspring should not form an exact 3:1 ratio due to the nature of chance in genetic sorting.
Fisher’s 1936 paper in which he suggests Mendel fudged his data is available here, although fair warning: even though it’s a very interesting paper, it’s 23 pages with a lot of dense writing about numbers and statistics.
Fisher’s go-to examples start with Mendel’s 1829 figures of 5474:1850 and 6022:2001, which represent ratios of 2.96:1 and 3.01:1 respectively, and in Fisher’s view these were way too close to the expected values to have arisen by scrupulous experimental data collection. Fisher goes on to analyse more and more of Mendel’s data and argues that time and time again, the reported ratios are far too good to be true.
By way of example, I set up a 90×90 table in Numbers to give a total close to Mendel’s sample size, set the program to fill the table with random numbers from 1 to 4, and counted the ratio of 1:2-4. This should, of course, give a 3:1 ratio since that’s what I set up as the mathematical relationship, but you never get exactly 3:1. In 10 consecutive runs, I got ratios of 2.80, 3.10, 3.00, 3.06, 2.92, 2.99, 3.06, 3.08, 2.95, and 3.01. So when you see numbers like this, it’s easy to see that Mendel could easily have got his reported ratios (3 of the 10 were as good or better than Mendel’s). But the problem is that he keeps getting these numbers in trial after trial.
I’m still not convinced either way. Although Mendel’s numbers are better than I would have expected, it’s also true that he was working in a methodology that predated the modern statistical method (which is hugely indebted to Fisher, by the way, and if done correctly influences the experimental method and not just the analysis). And it’s not like Fisher was systematic in his approach either as he specifically focusses on those results of Mendel’s that were closest to expected…which will of course tend to bias the result towards finding suspicion. And having said all that, Fisher wasn’t trying to debunk Mendel since he essentially agreed with Mendel’s theory.
There can only be one obvious conclusion. Mendel was a time traveling alien who was attempting to further human understanding of genetics. :P
I think the idea of the Genetics War should be folded into some popular webcomics. And not in the obvious giant monsters battling for geopolitical supremacy, but in the giant monsters fighting for academic supremacy. “As you can see, my rebuttal includes particle beam firing eyestalks and can fly. My proposed modes of inheritance are vastly superior. “
Weldon was an interesting guy. But, as you correctly point out, not one who pointed a way forward from Mendelism, but rather someone who was trying to argue that there was some other scheme of inheritance, based on the statistical formulas of Galton and Pearson. (I’m impressed that you learned this history). He also was probably responsible for some of the heat in the argument between the Biometricians and the Mendelian, because it is recorded that after his untimely death a lot of the heat went out of the argument.
There continues to be a Weldon Medal awarded by Oxford University for advances in biometry.
I was not aware of the doubt of the distribution ratio (3:1) exactness before interesting and thinking along similar lines of thought to @6
He did these experiments in a monastery in fact I think it may have been only possible to do such a long controlled experiment in a monastic setting at the time at all.
I suspect that there had been going on some sort of unintentional selection process going on for many years before he arrived on the scene. Monasteries and the monastic life is nothing if not constrained, methodical and highly disciplined. Everything is controlled few things are random. That they would have been selecting seed to retain by some criteria as “good seed” leading to some greater degree of homogeneity than would be found in normal farming methods and practices seems possible to me. It could have also been the observation of the difference between the peas that the monastery was growing and the peas that Mandel knew from before he joined or that the local peasants were growing that might have led to his curiosity as to why and how that was so.
uncle frogy
chrislawson @#8
That’s a very good post, and thanks for digging out Mendel’s actual numbers. It is of course quite possible Mendel cherry-picked his data to support his conclusions, but I’m not super convinced that a sequence of numbers generated with the RND() function can demonstrate that. “Random” computer numbers are actually picked from an array of numbers that are hard-coded into the software. I’d like to try to replicate your experiment using two coins, but I doubt I’ll be able to get more than 2 or 3 runs, so even that will not be good enough to convince me either way.
#10: Why surprised? I learned genetics at your university!
I suspect that Mendel did select the data that best illustrated his point. But it doesn’t matter: those 3:1 ratios have been repeatedly confirmed. My class did fly crosses all semester long, and we saw solid 3:1 ratios from hybrid crosses, and 1:1 ratios from test crosses, and also the usual sex linkage distributions. These are pretty robust conclusions.
unclefrogy #11:
Thinking more on this, I’m sure Mendel himself must have done a lot of pre-selection of his seeds before he started counting them officially for his data set. He wanted data that allowed only two states for each trait he studied, such as smooth pea/wrinkled pea and green pea/yellow pea, so he had to cull all offspring that he could not definitely put into his 2 categories per trait. Even then he surely would still have some ambiguous results, and that may be where the fix was in. He may well have (possibly even unconsciously) assigned ambiguous results to the category that best supported his pre-existing conclusion.
Yeah, I’m starting to lean towards the “too good to be true” camp.
I recall reading either Asimov or Gould, who speculated that while Mendel may have been thoroughly honest with the data he was given, the monks doing the actual field work may have indulged in a little data selection prior to presenting it to Mendel as he liked to see the whole number ratios.
sez moarscienceplz @12: “‘Random’ computer numbers are actually picked from an array of numbers that are hard-coded into the software.”
Citation needed. Your use of the phrases “picked from an array” and “hard-coded into the software” suggests that you have a confused concept of how computers actually do handle random numbers.
Computers generate (pseudo-) random numbers by means of an algorithm that accepts one number as input, and produces as output another number which is exceedingly difficult (if not downright impossible) to predict ahead of time.
As a simple example of such, there’s the “middle of the square” algorithm; start with an N-digit number, square it, and pick the N middlemost digits of that square. If you start with (let us say) the 12-digit number 140023458317, what will the middle 12 digits of its square be? Good luck figuring that out by any means other than squaring 140023458317 and taking the middle 12 digits of that square.
If you want more than one PRN (pseudo-random number), no problem; take the output from that first use of the PRN algorithm, and use that as input to your PRN algorithm. Lather, rinse, repeat.
Now, if you start with some particular number X, you’ll always end up with the same sequence of PRNs, and this is why computer geeks talk about “pseudo-random” numbers. So it could be said that PRNs are, in a metaphorical sense, “hard-coded into the software”. But it’s not like there’s a chunk of memory in the machine which had a collection of pre-set numbers loaded into it in the factory, and you’re just grabbing one of those pre-set numbers!
“Wait a second,” some of you may be saying. “What happens if your PRN generates, at some point in the series of numbers it’s making, the original number you started with? Wouldn’t that mean it repeats itself from then on?” Yes, it would, and this is a known thing about PRN algorithms. The “period” of a PRN algorithm is the number of PRNs it can generate before it starts repeating itself. The most commonly-used PRN algorithm is called “Mersenne twister”, and its period is (2^19937 – 1).
Obviously, it makes a difference how you choose the ‘seed number’, the number which starts your PRN algorithm off. One way computers can pick a seed number is to use the computer’s clock, which can typically measure time down to the millisecond, and often to a greater degree of precision than that. Record the exact (down to the millisecond) time at which the computer’s user clicked their mouse button, and that’s a seed which is vanishingly unlikely to ever be repeated.
I’m not sure what that alternative course is like, but the fact remains that genes are real, and not just as a convenient concept. They even have a physical interpretation. Mendel may or may not have fudged his data. My guess is that he threw out any result too far from what he expected but not for nefarious reasons. He probably figured that there had been some contamination or other confounding factors. It’s like tossing a coin ten times and figuring that if you ever get a 1:4 heads to tails ratio, then the coin is probably rigged or damaged except with a lot more statistical naivete.
If you start by hypothesizing that there are atomic, inheritable elements that can control certain characteristics, you can develop a fertile theory that leads to all sorts of discoveries. If you hypothesize that these elements have a physical interpretation, you can get to chromosomes and DNA. You can recognize “jumping genes”. You can hypothesize about regulation. You can even use the hypothesis practically in breeding new plant and animal varieties. Try developing modern hybrid maize without a simple gene theory. It would be like trying to understand chemistry without atoms or music without notes.
I think a lot of the argument is against reductionism. There are a lot of good reasons to avoid oversimplification. After all, the real world is complicated. Despite this, reductionism is a useful tool, particularly when things are complicated.
PZ@13: Puzzling … I don’t think I ever taught it to you, and no one else here would have done so then. Remarkable that you would have remembered it, anyway.
As for Mendel’s ratios, there has been a fairly large literature on the fact that they are too good to be true, focusing on what unconscious manipulations might have occurred, what conscious but well-intended cleaning up might have been done, and to what extent Mendel might have knowingly falsified them. Here is a review by Edward Novitski in Genetics in 2004, available as a free PDF, which tends to defend Mendel but does cite much of the literature analyzing the departure from expectation.
moarscienceplz —
As cubist says, that’s not how random number generators in computers work. The model you’re referring to is sometimes used by DMs in tabletop RPGs like D&D where the DM will roll a thousand dice (or buy a pre-rolled dice sheet) prior to the game and check off the random numbers as the game progresses. The purpose of this is to speed up gameplay and to prevent players from knowing when the DM is rolling for some random event (sometimes even knowing the DM is making a roll can give the players hints about the game that the DM would prefer to keep secret).
For the purposes of doing Monte Carlo trials on your computer, the internal random number generator (RNG) is perfectly acceptable. One of the defining features of a good pseudorandom RNG is that its output is statistically indistinguishable from a true random generator. So when you’re just trying to see what happens with large arrays of numbers, you’re fine to go. The people who worry about pseudorandom generators are cryptographic security people because they’re trying to protect against attackers finding one particular random-generated sequence. It’s a very different problem to experimenting on the frequencies in large random arrays.
And even if it really concerns you, you can always buy a true RNG in a USB stick that you can plug into your computer to provide a steady stream of quantum or thermal noise generated numbers. You can pick these up for as little as $20 and start doing your own true random Monte Carlo simulations!
People are still trying to find explanations for Mendel’s data: A Statistical Model to Explain the Mendel–Fisher Controversy. (Alas, a good fit of a model to a data set is not enough to verify that the process that generated the data set is well-described by the model.)
cubist #17
My information might be out of date, but it was true for a long time.
https://support.microsoft.com/en-us/kb/828795
The “million random numbers” thing may well indicate this is not a problem for what chrislawson did, and since my link was referencing Excel 2003, it may not even be an issue for a million numbers anymore.
Corey Yanofsky–
The authors of the paper you linked to must be very optimistic people. The last sentence in the abstract is: “This reconciliation model may well be the end of the Mendel-Fisher controversy.”
Ha ha ha! Very amusing. As if a controversy ever goes away…
Joe — that link is borked.
Here’s a currently working link to Novitski’s paper on the Mendel-Fisher issue. And yes, it is free to download.
Nobody teaches students that there is “a gene for heart disease”. That’s an insulting straw man.
Also, nobody teaches Mendel’s Laws and quits there, thinking that modern Genetics has been adequately covered. Everybody starts with Mendel, though, because his experiments were so simple and easily parsed*. The characters Mendel studied really did have only two trait alternatives determined by single genes with two alleles, one dominant to the other, that segregated independently of the other genes he studied. That’s why it’s possible in the first place to figure out (or explain) the gene-transmission patterns responsible. Punnett squares ftw!
But of course most phenotypic traits are not like that.( Mendel was either extremely lucky, or he tried other traits that didn;t make so much sense and didn;t report on them.) And so that’s always the next thing: oh. look, codominance; oh.look, sex linkage. Oh look, pleiotropy. Multigenic traits. Environmental effects. et cetera.
It sounds like this was a ‘nonmajors’ course in biology, a general education science requirement for humanities majors. These are usually survey courses; a necessarily condensed and, yes, simplified surf over the top of all of biology in 16 weeks with no prerequisites. I don’t know. In that setting, where genetics might be just one two- or three-week unit among many others, overemphasis on Mendel might indeed give the false impression that naive ‘gene-for’ determinism is a valid assumption. However, I don;t see how talking about this guy Weldon instead would help much.
*Also, it’s one of the few bits of the history of biology that survives most textbook editing (along with Darwin’s Youthful Voyage).
Speaking as a non-biologist: more posts like this, please! You keep saying how dry and tedious everything is, but this post, at least, was very interesting.
I was also a TA for Novitski at the UO, so who knows where I absorbed this stuff.
I think it’s highly likely that Mendel selected a subset of his data, and picked the experiments that most closely fit his expectations. That’s a naughty thing to do, but at this point, we really shouldn’t care. He’s dead, and Mendelian ratios work quite well for some traits.
#25: Yes, and that’s how I teach it. Start with Mendel because it works, and is good for practicing the basics of a cross. Then spend most of the semester building on that.
Then, of course, in the lab we do fly crosses, and it’s amazing: a bunch of naive students who didn’t even know how to sex a fly at the start of the term do crosses with simple traits, and they actually work just like Mendel said they did. Except that we throw in the sex linkage stuff, and then some simple recombination mapping, and it gets more complicated.
But how could you understand recombination mapping without first grasping Mendel’s law of independent assortment, so that you recognize that the ratios aren’t what you’d expect without linkage?
As a true Briton may I observe that the correct name for “Weldonism” is actually “Galtonism.”
Mind you, given that Galton was a particularly vocal proponent of eugenics, it’s probably a damn good thing that the Mendelian view won that early battle.
Still … Rule Britannia! Britannia waves the rules!
Very cringeworthy. Not the same original pool except for the fact that they were university underclassmen. Those who are predisposed to be quantitative/analytical versus those who may have more of a predisposition to be nuanced and more wholistic. This second group might certainly be predisposed to the different perspectives of looking at characteristics.