Do simple models lead to generality in ecology? Opinion of a simpleton

By | September 25, 2013

Evans et al. have a paper in Trends in Ecology and Evolution with this abstract:

Modellers of biological, ecological, and environmental systems cannot take for granted the maxim ‘simple means general means good’. We argue here that viewing simple models as the main way to achieve generality may be an obstacle to the progress of ecological research. We show how complex models can be both desirable and general, and how simple and complex models can be linked together to produce broad-scale and predictive understanding of biological systems.

I noticed the paper because of Bob O'Hara's post. It took Bob three pages of complex text about giraffes and parrots to deal with the thing - the TREE paper is iffy and inspiring at the same time. But what surprises me is the complete absence of any statistical perspective in the original paper and in the post. So here is my take:

Of course simple models are not always more general. To get the obvious extremes and eccentricities out of the way: the simplest model is a constant (an 'invariant'). Surely not very useful in ecology which is nothing but variation. Also, some simple models are just completely off the context, which I guess is the Bob's example of modelling head-perching behavior of parrots with a model of giraffe (bi)cycling.

In statistical practice, models can indeed rely on simplifications that are too radical: fitting a line through a clearly hump-shaped data will almost always lead to wrong predictions and the model cannot be generalized. A more complex polynomial would be better. In contrast, making the model overly complex it is called overfitting, and it also leads to poor generality. An example is when one tries to capture stochastic variation by a deterministic model.

Importantly, neither simplicity alone nor model fit alone guarantee generality, but both together do. Evans et al. do not mention it (for unknown reasons), but statistics has a direct way to measure the presence of the simplicity-fit tandem. It is called out-of-sample prediction performance and it can be calculated by crossvalidation, or approximated by AIC, BIC, DIC and similar. In short, it measures how well can a model be generalized to data that were not used to fit the model. Accidentally, I happen to have a very simple post on that.

So to answer the question that Evans et al. have in their title: Generality of any model, measured by its out-of-sample prediction performance, may follow various relationships with complexity measured as the number of estimated parameters. What I usually observe is a hump-shaped relationship between generality and complexity. Simple models may not always be more general, but generality will always only decrease above a certain complexity threshold.

I believe that Albert Einstein got it right:

Make everything as simple as possible, but not simpler.

The last three words are absolutely crucial.

Reference

Evans MR, Grimm V, Johst K, Knuuttila T, de Langhe R, Lessells CM, Merz M, O’Malley MA, Orzack SH, Weisberg M, Wilkinson DJ, Wolkenhauer O, & Benton TG (2013). Do simple models lead to generality in ecology? Trends in Ecology & Evolution. DOI: 10.1016/j.tree.2013.05.022

One thought on “Do simple models lead to generality in ecology? Opinion of a simpleton

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