Things I teach that are not true

Image: Tribolium castaneum (red flour beetle), Peggy Greb USDA-ARS, released to public domain.

Teaching undergraduates is an enormous pleasure (most of the time), and getting paid to do it is a privilege.  Along with that privilege, of course, comes responsibility: I should work to teach my students things that are relevant; things that are important; and of course, things that are true.

Except that sometimes I teach my students things that are not true.

Please don’t write my Dean and insist on my firing until I’ve explained.  Why would I teach my student something that isn’t true?  Well, it depends, because there are at least four kinds of things I teach that are not true.

First: exceptions.  I teach entomology (among other things), and one of things I say on the first day of class is that nearly everything else I say will be an overgeneralization.  You see, there are about a million insect species known to science, and somewhere between 2 million and 50 million more yet to be discovered.  Among these are species doing anything you can think of (and quite a few things you’d never think of*).  So any statement of the form “Insects do X” (or even “Insect family Y does X”) is a lie, unless tediously – and endlessly – hedged.  And yet we have to teach some kind of organized body of knowledge, so we teach generalities and give occasional reminders that there’s always a counterexample.  I don’t think I’m in the only field for which this is true.

Second: models.  We use simple models to represent, and communicate, our knowledge of the natural world.  In ecology, for example, the immigration-extinction balance underlying the theory of island biogeography is an abstraction, an oversimplification – and its depictions in textbooks and lecture notes are thus in a sense not true.  (For one thing, we normally ignore within-island speciation.)  But it’s useful to think about, and teach with, simple conceptual models, even knowing these simple models are not “true”.  It’s not just us.  Classical mechanics isn’t “true” either, but it’s an extremely useful approximation in many situations.  So even the physics that ecologists are said to envy teaches things that are not true.

Third, I teach things that are not true – but that we don’t yet know are not true.  Science progresses, and things once thought true get overturned.  We once taught students that dinosaurs are extinct, but we now understand that modern dinosaurs flap and soar and perch among us, very much alive but rechristened “birds”.  We once taught students that the continents don’t move.  We once taught students that DNA can be transcribed to RNA, but not the other way around.  It’s completely certain that among the things I’m teaching today are things we’ll discover to be false tomorrow.  There’s nothing wrong with this, of course, unless we fail to alert our students to the possibility.  That we overturn previous understanding is the very definition of science: its acknowledged fallibility and its self-correction separate science from superstition.

And that’s why there’s a fourth category: I sometimes, knowingly but temporarily, teach things that are not true.  Let me give you an example. In the 1960s, Thomas Park and colleagues ran some now-classic experiments on the outcome of competition in flour beetles.  Two species of beetles (Tribolium castaneum and T. confusum; the former is pictured above) can be reared easily in small vials of flour.  Under some environmental conditions, T. castaneum predictably drives T. confusum extinct, and other under conditions, it’s the reverse.  That’s easily understood.  But under certain other conditions, one species always “wins” – but which of the two species wins depends on their initial frequencies.  This would be a puzzling result in the absence of theory, but it’s actually a clear prediction of the Lotka-Volterra competition model.  That model, a very simple piece of math describing two species competing for shared but limiting resources, is a centrepiece of undergraduate ecology courses (and a building block for many more complex models).  We want our students to understand it, and it’s enormously helpful that Park’s flour beetles provide an example of its least intuitive outcome.

So I’ve always taught about Park’s flour beetles – but I’ve just learned (from a paper by Shigeki Kishi) that in fact, the frequency-dependent outcome of flour beetle interactions probably doesn’t have anything to do with resource competition**.  Instead, it probably arises from reproductive interference.  In brief, T. confusum males in mixed culture attempt to mate with females of either species, and they damage the genitalia and reduce fecundity of T. castaneum females***.  If there are enough T. confusum, this effect counters the competitive superiority of T. castaneum – but this is not at all what frequency-dependent outcomes in the Lotka-Volterra model are about.

So what to do?  Well, the next time I teach competition, I’m still going to teach Park’s flour beetles as an example.  But once having finished, I’m going to step back from the board a bit and say “OK, but actually, I have a confession to make.  That was a great illustration of Lotka-Volterra competition – or rather, for a long time we thought it was.  But it turns out…”.  When I do that, what I’ll be teaching is not that the Lotka-Volterra model isn’t useful, and not that the flour beetles aren’t a helpful way to think about it – but rather, that this is what science does: changes its mind, moves forward, and so spirals ever inward, closer and closer to truth.

But here’s what I’m not sure of.  We don’t always have time to teach the full complexity.  Are there times when I should teach something that is not true, without then owning up to the real story, simply because it’s a good illustration of an important concept?  Roughly, that is, something that just ought to be true, even if it isn’t?  How different is this from the simplifications and generalizations of my first two categories of things that are not true?  Should I teach Park’s Tribolium experiments because they’re a great illustration of conditional outcomes in the Lotka-Volterra competition model – even if I’m not going to follow up with the lesson that they aren’t actually that?

I don’t know the answer to that.  Would it help, or hurt, my students if they were sometimes settling for mostly true?

© Stephen Heard  December 4, 2017

Thanks to Beren Robinson for steering me to Kishi’s paper.

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*^Like traumatic insemination in bedbugs. Or kleptoparasitism of nuptial gifts in hangingflies.  Or Pez-dispenser reproductive behaviour in the springtail Sminthurides.   (Google them, I dare you).  I could go on, and on, and on, and it wouldn’t even all have to be about sex.

**^Actually, we’ve known since the 1960s that the Tribolium interaction is driven not by direct resource competition but by intraguild predation.  Resource competition and intraguild predation look pretty similar dynamically, though, so maybe ignoring that wasn’t an example of teaching something that is not true.  I think.

***^It’s tempting to think that this cluelessness on the part of T. confusum males is responsible for their Latin name.  Unfortunately, it’s more mundane than that.  Although the species description doesn’t quite say so explicitly, the name seems to refer to the common confusion, in collections, of this species with T. ferrugineum.