Celebrating simple models

Amy Hurford’s excellent blog Just Simple Enough: The Art of Mathematical Modelling alerted me to a post on Joan Straussman’s blog titled “The Trouble with Theory”  This post is well worth reading, along with the comments that address questions about the role of theory and models.

But one sentence in Joan’s post caught my attention in particular: “Theories do not always prove to be true.” In fact, it can be argued that theory and models are never true – they are not meant to be. Models are supposed to be imperfect. What level of imperfection is suitable? This question underlies many of the comments in Joan’s post.

The first chapter of Hanna Kokko’s book Modelling for Field Biologists and Other Interesting People has an excellent example of the value of imperfection. If you were lost in a forest, a map would be helpful to navigate out of the forest. Such a map would need to have sufficient detail, and be at the correct scale, to be useful. A map of the world with too little detail, or the wrong sorts of details, would be unhelpful.

A map of the world might not help someone lost in a forest.

But too much detail would make it impossible to see the big picture. In fact, in the extreme, the map would have all the detail of the real world – and be just as big. But the real world is too detailed to be allow you to see the way out. One needs a happy medium.

If your map has too much detail, it starts to look too much like the real thing. If you are lost, you already have too much of the real thing.

So, how closely should models be tied to reality (and data)? The answer to this question depends on the purpose of the model. For example, the other maps, such as a map of the world, might be useful for other purposes even if it is useless for finding your way home.

Models have a wide range of purposes, and the required detail for these models will usually vary depending on their purpose. But some models can be entirely data free and very simple if the aim is to simply illustrate logical consequences.

For example, during my PhD I read about models of natal dispersal in the presence of competition for breeding territories. The models developed to that point predicted increasing dispersal distances as the level of competition increased (all else being equal). However, these models were based only on the movement of a single disperser across a landscape of territorial vacancies. As soon as multiple dispersers were considered, very simple models (straight line dispersal by individuals moving at the same time) illustrated that dispersal distances might increase or decrease with competition (McCarthy 1997). This simple model1 clearly falsified the notion that dispersal distances should increase with competition.

If you think that is counter-intuitive (the reviewers certainly did), then you should read the paper. And you might think about games of musical chairs. But it illustrates how models, in the absence of data (or even much reality) can clarify one’s thinking. I love that about models.

Reference

McCarthy, M.A. (1997) Competition and dispersal from multiple nests. Ecology 78: 873-883.

1. OK, the mathematics took me a year or so to figure out, but that reflects my ability rather than the complexity of the model.

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About Michael McCarthy

I conduct research on environmental decision making and quantitative ecology. My teaching is mainly at post-grad level at The University of Melbourne.
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7 Responses to Celebrating simple models

  1. feingc says:

    I agree, different model serves different purpose. For me, a model is just a tool to solve certain question. My favourite model is game theory. The main reason it is so famous was because it is simple, yet has hundreds of applications across social science, economics, politics, etc. I think of this model, as building a multi-purpose tool that can be applied to a gazillion of cases. I wish I had Von Neumann’s brain cell to come up with something like that, simple yet powerful. I just read an article about how not to build a bad model, quite interesting. http://theartofmodelling.wordpress.com/2012/04/15/how-to-not-make-bad-models/

  2. Pingback: Tuesday at #ESA2012 | Michael McCarthy's Research

  3. skiptoniam says:

    Great post! It’s driven me to purchase Hanna Kokko’s book.

  4. wkmor1 says:

    Nice post Mick Mc. I’ve always been a fan of you’re and other’s simple models crusade, on a certain level. But sometimes it can go too far. Sometimes things are complicated and ‘complicated things require complicated models’. Here is Andrew Gelman on the subject. http://andrewgelman.com/2012/06/occam-2/

    • For sure, some models can be too simple for their particular purpose. Simple models are valuable, but we don’t want them to be too simple. That is easy to say, but it can be hard to find the balance. That’s why this paraphrasing of Einstein is insightful – because it captures one of the trade-offs in modelling very succinctly. And sometimes the comparison of complicated and simple models is instructive – it’s not as though there is always a sharp point of balance.

      I don’t think I’m on any particular crusade for simple models. While I like to build simple models, I’m not suggesting that others should avoid more complicated models (the comparison is interesting). It’s just I get most excited when simple models give unexpected insights.

      Thanks for providing the link to Gelman’s post.

      • wkmor1 says:

        Perhaps crusade is going to far. But I reckon you and others in SDM crowd like Walshe, Runge and Wintle like to promote the virtues of the simple model a fair bit.

        My feeling is that simplicity doesn’t need to be an objective of a model or the modeller. Tractability, sure. But the two aren’t the same thing. It makes us much sense to me, to aim for as simple model as possible, as it does to aim for as complicated model as possible. I like Gelman’s idea that a simple model is the best place to start—an infinitely better approach than the intellectual void that is ‘backwards stepwise selection’, yuk!

        To stretch your map metaphor to breaking point. Yeah a map with all the roads and important landmarks is useful. But how much better (and freaking cooler!) is that map on an tablet computer with a button that switches to satellite mode or street-level view!!

      • “As simple as possible” is a very different aim from “as complicated as possible”. In aiming to find something as simple as possible (but still fulfill the task that is required), the trade-off between realism and simplicity is quite stark, and intellectually challenging. When seeking a model that is as simple as possible but no simpler, one might end up with a complicated model if that is what is required to fulfill the task. It is just we don’t want a complicated model for the sake of it. But there are benefits of using models with a range of complexity (see my comment about a table on Jean Straussman’s post).

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