In his wonderful old essay on the many uses of false models, William Wimsatt notes that one can use multiple false models to bracket, and thus give insight into, a more complicated reality:

Two false models may be used to define the extremes of a continuum of cases in which the real case is presumed to lie, but for which the more realistic intermediate models are too complex to analyze, or too special in their application to be of any general interest, or for which the information available is too incomplete to guide their construction or determine a choice between them.

Wimsatt gives the example of Haldane’s two alternative (phenomenological) models of crossing-over in genetics, one of which assumed that chromosomes are infinitely flexible, and the other of which assumed that they’re completely rigid. Reality is in the middle: data on crossover frequency is intermediate to what you predict from Haldane’s two models, suggesting that chromosomes can be thought of as somewhat flexible.

Question: What are some good examples of ecologists using multiple false models in this way?

I feel like there must be many good examples of this use of false models in ecology. But the ecological examples that come to my mind are all cases where this approach *wouldn’t* work, because the real case does not in fact lie on a continuum between the extremes. I’m thinking for instance of metapopulation models. Imagine trying to bracket the dynamics of real metapopulations by studying two limiting cases: completely isolated populations with no dispersal, and a bunch of populations interconnected by such high rates of dispersal as to effectively comprise a single large well-mixed population. You wouldn’t get any insight into the intermediate case of colonization-extinction dynamics solely by studying those two limiting cases. Colonization-extinction dynamics comprise a distinct dynamical regime that requires intermediate dispersal rates, but isn’t “intermediate” between “no dispersal” and “high dispersal” in any other sense. For instance, expected metapopulation persistence time generally is higher at intermediate dispersal rates than with either no dispersal or high dispersal.

But surely there must be good ecological examples I’m just not thinking of? Help me out! 🙂

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This is interesting on a mathematical/theoretical level (and something which I have some papers vaguely related to even). For linear models, or more generally ones which have continuous and monotonic dependence on parameters, the alternate limits of a parameter going to 0 and the parameter going to infinity should exactly bracket all possible behaviours. But for most nonlinear interactions, this won’t be true (and presumably most real phenomena are at least in some regimes nonlinear).

I suspect when the bracketing models contain most of the interesting dynamics, or if the real system satisfies some constraints, then this approach works, though I don’t personally know of any good examples. My intuition is that this can’t happen in most cases, though “false models” are often unreasonably effective in the right hands.

We made such an argument in our model for phytoplankton N:P stoichiometry (Klausmeier et al. 2004, Nature 429: 171-174). The extreme scenarios were unlimited resources, where the optimal strategy maximizes the exponential growth rate, leading to a high N:P, and resource competition to equilibrium, where the optimal strategy minimizes R*, leading to a low N:P. In-between cases were hand-waved away as either leading to intermediate strategies or coexistence of the two extremes. Glad to have a reference for this approach now!

But as you say, there are plenty of examples where intermediate cases don’t lie between the end-points.

Aha, thank you! Somehow, I knew the first example commenters suggested was going to be one I should’ve remembered on my own…

I’ve always considered the debate between Clements and Gleason as being an example of this type. Community structure generally exhibits some degree of biotic determinism AND stochasticity…

Also, Liebig’s Law of the Minimum vs the Multiple Limitation Hypothesis provide useful models for instruction, but real systems can demonstrate either (or both)…

Yes, Clements vs. Gleason is an example, though a bit different in some ways from the sorts of cases I was thinking of when I wrote the post. Clements vs. Gleason involved verbal models rather than mathematical ones. And it was a debate between two opposing sides, rather than one person intentionally using two oversimplified false models to bracket a more complicated reality.