‘Hand waving‘ in science has a bad reputation; referring to an argument as ‘hand waving’ suggests a lack of rigor. But is hand waving always a bad thing?
If by hand waving we simply mean omitting assumptions or steps in an argument for no good reason (or worse, for a bad reason, such as the desire to mislead the audience), then yes, hand waving is bad. But there are often good reasons for such lack of rigor. For instance, presentational reasons: the time constraints of a seminar often oblige the speaker to gloss over technical details. More interestingly, there can be substantive reasons for hand waving (and the line between presentational and substantive hand waving isn’t clear cut). Ecology is hard, and hand waving makes it easier. In order to make progress, we are often faced with a choice, not between a rigorous argument and a hand waving argument, but between a hand waving argument and no argument at all. Hand waving can include heuristic arguments, approximations, and rough ‘back of the envelope’ calculations. I’d also include rigorous models of simple situations which can, via hand waving arguments, be used to develop hypotheses about, or interpret data from, more complex situations. The hope is that the simple model somehow ‘captures the essence’ of the complex situation. (What it means to ‘capture the essence’, and how it’s different from, say, ‘getting the right answer for the wrong reasons’, is a subject for another post…)
Indeed, since all models (mathematical and otherwise) have simplifying (i.e. false) assumptions, all models are in a sense hand waving arguments about what the real world might be like. Simplifying assumptions are a feature, not a bug, a point well-articulated by philosopher Bill Wimsatt and in an ecological context by Hal Caswell. A model with no simplifying assumptions would be like a map as big as the world itself, and equally useless.
Hand waving arguments are perhaps especially common in community ecology, where our theoretical models typically are much simpler than the natural communities to which they’re applied (although not inevitably so, as I’ve discussed in a previous post). At least, that’s the perception of community ecology; I wouldn’t venture to guess at how true the perception is, though I’m not above joking about it. My former colleague Ed McCauley and I used to joke that community ecology consists of theory on one side, data on the other, and a bunch of community ecologists in the middle frantically waving their arms (arm waving being a more extreme form of hand waving). In contrast, the best population ecology involves tight, rigorous connections between theory and data; population ecologists hold their arms stiff at their sides like Irish step dancers. This was certainly true in the case of Ed, one of the world’s best and most rigorous population ecologists. If Ed were stranded on a desert island, I doubt he’d wave his arms to attract a passing ship (which brings us back to the point that sometimes arm waving is a good thing, such as when the alternative is to be stranded).
Ed and I are of course not the only ones to get a chuckle out of hand waving:
(cartoon by Sydney Harris)
Of course, there are no hard and fast rules about what’s a good (or good-enough) approximation, or what’s an essential vs. inessential detail. So hand waving arguments always involve some judgment calls. There’s an art as well as a science to hand waving. But just because hand waving involves judgment calls doesn’t mean there aren’t better and worse hand waving arguments (much like there are better and worse judges). I think that some ecologists definitely are better at hand waving than others. Mathew Leibold and Jon Chase are great hand wavers. They’re really good at using simple, equilibrial food web models with just 2-4 species to think about complex phenomena like turnover in species richness and composition along natural environmental gradients. No, I’m not going to tell you who I think the bad hand wavers are…
(UPDATE: Jon responds by saying ‘Thanks…I think’. In case there was any doubt, I really do mean it as a complement when I call Mathew and Jon great hand wavers, although I suspect they may not think of themselves in that way.)
Oikos recently published a nice piece of handwaving from Graham Bell. Natural populations are always fluctuating in size, and we’d like to infer from the pattern of fluctuations something about the underlying ecological mechanisms driving them. Graham develops simple alternative models to predict the relationship between successive minimum population sizes (i.e. population sizes lower than any that came before), and the expected time before the next minimum occurs, and tests those models with data from a long-term marine plankton monitoring program. The data support a model in which population fluctuations are driven by trophic interactions, so that minimum abundance decreases exponentially over time. There’s hand waving going on at multiple levels here, not just in the development of the models (all except for the food web model are extremely simple, ‘capture the essence’-type models). What justifies the hand waving is that the answer that comes out is extremely clear cut. The whole point of a hand waving argument is to skim over inessential details, and one indication that you’ve done so successfully is by getting a clear cut answer at the end.
Feel free to recommend any really good (or really bad!) examples of hand waving ecology in the comments.