Thursday, August 1, 2013

Dulling Occam’s razor - or the perilous principle of parsimony



In science, multiple possible explanations always exist for any particular phenomenon. In ideal situations, we can design and perform definitive experiments that conclusively discriminate between alternative explanations, and thus allow us to conclusively reject all competing hypotheses save one. This is the best approach for zeroing in on the true cause of a phenomenon of interest. In many cases, however, definitive experiments are difficult or impossible to perform or - even if they can be performed - remain saddled with considerable ambiguity. That is, multiple competing hypotheses often remain and cannot be conclusively ruled out through experimental elimination. In such cases, it is customary for investigators to differentially support alternative hypotheses based on circumstantial evidence and assertions as to their plausibility.

A fashionable way to use plausibility to support a given inference is to invoke parsimony, also known as Occam’s Razor – the idea that (here citing Wikipedia) “among competing hypotheses, the hypothesis with the fewest assumptions should be selected. In other words, the simplest explanation is usually the correct one.” In scientific inference, then, the idea is to figure out which explanation is the simplest and to then express the greatest confidence in that hypothesis. To me, this whole enterprise – and the presumption behind it – is nonsensical, and I have long looked for a venue to express this opinion. A recent visit to Dalhousie University to be an external examiner for a thesis provided the impetus for me to use this blog as a soap box.

I was the examiner for the thesis of Njal Rollinson, a PhD student of Jeff Hutchings. Njal had constructed a wonderful thesis using salmonid fishes to test various adaptive explanations for variation in egg size. Njal's thesis was one of the better ones that I have examined, with five excellent chapters – all of them already published in good journals (Ecology, American Naturalist, Oecologia, EER, and CJFAS). I had a great time reading the thesis because I had studied this topic in the past and felt that Njal’s work was a great improvement on previous efforts - including my own. Until I got to the final concluding chapter, that is. In that chapter, Njal took the courageous approach of arguing that (contrary to the rest of the thesis) many aspects of egg size variation were not adaptive but instead reflected constraints caused by hard-to-escape genetic correlations. Reading with raised eyebrows, I then saw that dreaded word – parsimony. In essence, Njal argued that the simplest argument was that egg size variation (especially in relation to female size) was not adaptive but rather a result of genetic correlations between body size and egg size. He felt that parsimony provided a good basis to make this assertion and to thereby put adaptive explanations on the back-burner.

Newly-hatched salmon from my days of studying egg (and offspring) size.

So, why would I think this argument was nonsense?

1. Who decides which explanation is the simplest – and by what criteria? What usually happens is that investigators have a favorite explanation already in mind and find ways to argue that it is the simplest. But someone else could easily have a different interpretation regarding simplicity. For instance, genetic drift is often invoked as a more parsimonious explanation than selection – kind of like a null model that needs to be rejected before one can invoke the more “complicated” interpretation of selection[1]. I would argue precisely the opposite. As far as I can tell, no study has conclusively confirmed genetic drift (as opposed to selection) as a driver of among-population variation in functional traits – the only sorts of traits for which we would try to infer adaptation anyway[2]. By contrast, countless studies have found strong evidence for adaptive divergence in such traits. Moreover, adaptation by natural selection is a simple logical (mathematical) outcome when genetically based traits are related to organismal fitness. Natural selection thus seems to me a much more parsimonious explanation than drift, which additionally requires very small population sizes and very weak selection! To paraphrase Bret Weinstein as quoted in The Tapir’s Morning Bath (p. 300): Adaptation is a better explanation than God, but God is a better explanation than drift.

2. Who’s to say that nature is parsimonious anyway? Consider for a moment the frequent use of parsimony as a formal method for considering the evolution of traits on phylogenetic trees. In essence, the model of evolution that requires the fewest transitions between character states is assumed to be the correct one - and this is certainly the simplest (most parsimonious) model. To me this idea seems crazy as a general assumption. Many cases are known of all sorts of strange, variable, and contradictory evolutionary changes in a given group of organisms. That is, evolution does not follow a simple linear progression through a set of states but is instead rife with all sorts of fits and starts and reversal. So, in this sense, it seems certain that parsimony will give you the wrong answer. (Although it isn’t guaranteed that any other methods will give you the right answer).

It was interesting to me that these considerations were brought back to mind based on arguments about adaptation by natural selection – as opposed to some other scientific question to which parsimony might be applied. It reminded me of the dark ages of adaptation research – roughly a decade or so following the publication of Gould and Lewontin’s 1979 paper the “The spandrels of San Marco and Panglossian paradigm.”  That paper criticized evolutionary biologists for looking only at adaptive explanations rather than considering non-adaptive ones too. For instance, they pilloried the approach of “If one adaptive argument fails, try another.” Of course, this iterative adaptive approach is precisely what should be done if one wants to get the right answer. Since adaptation is clearly the most likely explanation for any particular functional trait, positing and testing one adaptive explanation after another is just the way to go. (Yes, non-adaptive explanations can be considered too - but certainly not as a null model.)

At this point, it will seem that I am more Panglossian than even the redoubtable Dr. Pangloss of Voltaire’s Candide, who felt that “everything was for the best in this best of all possible worlds."[3] This is certainly not the case as I recognize that constraints can play an important role. To take a caricature, offspring cannot be larger than their parents at the time of birth - so clearly offspring size is constrained in this inevitable way. Surely this is one case where we can dispense with all attempts at adaptive explanation and instead chalk up this organismal property to constraint. Or can we? I am reminded of the should-be-classic paper by Norm Ellstrand – following soon after Gould and Lewontin – titled “Why are juveniles smaller than their parents?” This paper suggested six adaptive hypotheses for the above-described juvenile small size (JSS) and marshaled support for each. Buoyed by their success in postulating adaptive reasons for a very widespread juvenile character, they suggested:

“Adaptive explanations can be sought for other juvenile characters as well. In particular, another juvenile character is even more widespread than JSS and deserves some thoughtful theoretical attention, the fact that juveniles always seem to be younger than their parents.”

All these thoughts were going through my head as I examined Njal and I couldn't help myself from going on a long diatribe along these lines. At the end, I asked Njal “So ... do you agree?” To which he responded “Well, now that you have brow-beaten me into it.” So, yes, I hope to have also now brow-beaten you into it too. Parsimony is a lousy approach on which to base scientific – and certainly evolutionary – inference, unless of course you believe that adaptation by natural selection is the most parsimonious explanation.




[1] Another manifestation of this idea is the testing in time series of phenotypic traits (e.g. fossil data) whether the observed pattern can be distinguished from a simple model of drift, more specifically a random walk process. The problem with this approach is that a random walk model can encompass a huge range of possibility that allows little opportunity for rejection. Moreover, selection is never consistently directional for extend periods of time and rather jumps around in fits and starts and reversals – to the extent that many clearly adaptive trends cannot be distinguished from drift. The solution, of course, is to compare - on an equal basis (neither model is the null but rather the two are competing hypotheses) - a drift model and a series of other models, including those based on adaptive mechanisms. Several papers by Gene Hunt show how this better approach supports adaptation over drift in many fossil time series. 

[2] I did once publish a paper where I argued that drift was the best explanation for among-population divergence in a trait normally thought to be a great example of adaptive divergence. I was able to draw this conclusion because I was studying a situation where selection on that trait was eliminated and so evolution would be able to proceed by drift. Otherwise, selection will almost always overwhelm drift. (This paper seems to have been cited only 7 times, when another paper on the same experiment positing adaptive explanations for other traits has been cited 64 times. Sadly, the aforementioned Ellstrand paper has only been cited 5 times.)

[3] For instance, Dr. Pangloss felt that syphilis was beneficial because it came from the New World and so was a necessary byproduct of access to New World wonders, such as chocolate. I can only concur given that I have not had syphilis but have enjoyed lots of chocolate – moreover I live in the New World.

2 comments:

  1. Nice post Andrew, with which I very much agree (http://dynamicecology.wordpress.com/2013/05/13/null-and-neutral-models-are-overrated/)

    Interesting to me as an ecologist to see an evolutionary biologist saying what you've said. From afar, I've always vaguely thought that evolutionary biologists were better than ecologists at developing and testing alternative process-based models that might have generated their data (e.g., models with vs. without selection). Perhaps that's just me seeing the grass as greener on the other side of the fence?

    -Jeremy

    ReplyDelete
  2. See Njal's response here: http://ecoevoevoeco.blogspot.ca/2013/09/normal-0-false-false-false.html

    ReplyDelete

Check your (taxonomic) biases at the door

Many of us like to believe that we are conceptually-oriented researchers; our particular study organism(s) are just means to an end, the en...