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.
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.
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.
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.