One question is does there necessarily exist a simple model for a given biological question, the other is, is there a unique model? And taking that one step further, given two models that are equal in all regards except that one is more complex, why should we favour the more simple model? This argument, that we should prefer simpler explanations, is Occam’s razor.
William of Ockham. This picture is attributed to the following source.
Here’s the definition of Occam’s razor from Wikipedia:
It is a principle urging one to select, among competing hypotheses, that which makes the fewest assumptions and thereby offers the simplest explanation of the effect.
In fact, the Wikipedia page on Occam’s razor, for me, made for inspired reading. Here are some of the highlights*:
Justifications for Occam’s razor
- Aesthetic: nature is simple and simple explanations are more likely to be true.
- Empirical: You want the signal; you don’t want the noise. A complex model will give you both, e.g. overfitting in statistics.
- Mathematical: hypotheses that have fewer adjustable parameters will automatically have an enhanced posterior probability because the predictions are sharper (Jeffreys & Berger, 1991)
- Practical: it is easier to understand simple models.
Alternatives to Occam’s razor
- Popper (1992): For Popper it can all be cast in the light of falsifiability. We prefer simper theories “because their ecological context is greater” and because they are testable.
- Elliot Sober: simplicity considerations do not count unless they reflect something more fundamental.**
And yet my initial reaction to the definition of Occam’s razor was that it sounded a bit strange: simple explanations and few assumptions? Yikes, I can give you your simple explanation, but it’s going take a lot of assumptions to get there. I think my confusion could be due to a difference in bookkeeping (and the phrasing ‘simple explanation of the effect‘). In the Occam’s razor definition, you score only assumptions that contribute to the explanation. In biology, if the true explanation consists of n things-that-matter, the theoretician will say that the observation can be reproduced by only considering k < n of those things. Here, biologists are used to scoring the number of assumptions as the number of things that are suspected to matter but that are neglected, i.e. n – k. This difference would seem to suggest that, although in biology we do value simplicity, we also value explanations that incorporate known contributing factors over explanations that ignore these. These types of values are reflected in Elliot Sober’s view on Alternatives to Occam’s razor as described above.
However, even given that caveat, I think we still often prefer simple models in biology. Why? Here’s Ben Bolker (p7)*** with some insight:
By making more assumptions, (mechanistic models) allow you to extract more information from your data – with the risk of making the wrong assumptions.
That does kind of sum it up from the data analysis perspective: simple models make a lot of assumptions, but at the end of it you can conclude something concrete. Complex models still make assumptions, but they are a less restrictive type of assumption (i.e., an assumption about how a factor is included rather than an assumption to ignore it). All this flexibility in complex models means that many different parameter combinations can lead to the same outcome: inference is challenging, and parameters are likely to be unidentifiable. Given Wikipedia’s list of different justifications of Occam’s razor this seems to be an example of ‘using the mathematical justification to practical ends’. That is to say, this argument doesn’t seem to fit well into the list of justifications, but elements of the mathematical and the practical justifications are represented. Or perhaps it fits with Popper’s alternative view?
For the theoretical ecologist, another reason that parsimony is often favoured is certainly the practical justification: because simple models are easier to understand.
What do you think? Is parsimony important in biology? And why?
Jeffreys and Berger (1991) Sharpening Ockham’s Razor on a Bayesian Strop. [pdf] Alternatively, if that isn’t satifying this might do the trick:
Quine, W (1966) On simple theories in a complex world. In The Ways of Paradox and Other Essays. Harvard University Press.****
*okay, so maybe the actual highlight for me was learning a new expression. The expression is ‘turtles all the way down’ and the best way to explain it is by using it in a sentence. Here goes: sometimes people say ‘yes, but that’s not really a mechanistic model because you could take this small part of it and make that more mechanistic, and then you could take parts of that and make those more mechanistic.’ And to that, I would say ‘yes, but why bother? It’s just going to be turtles all the way down‘.
**fundamental = mechanistic, i.e. biological underpinning. This is a quote from Wikipedia and I need to chase down the exact reference for the statement. I have Elliot Sober (200o) Philosophy of Biology but he doesn’t seem to say anything quite this definitive.
***Ben suggests the references: Levins (1966) The strategy of model building in population biology; Orzack and Sober (1993) A critical assessment of Levin’s The strategy of model building in population biology; and Levins (1993) A response to Orzack and Sober: Formal Analysis and the fluidity of science. [I’ll read them and let you know.]
****I haven’t read either, I just list the references in case anyone wants to follow up.