Evidence and evolution (3)
“To test a theory, you need to test it against alternatives.” (E&E, p.190)
After a gruesome (!) trek through Chapter 3 of Sober’s Evidence and Evolution: The Logic Behind the Science, I am now done with this chapter entitled “Natural selection”. The chapter is difficult to read (for someone like me) in that it seems overly repetitive, using somehow obvious arguments while missing clearcut conclusions and directions. This bend must be due to the philosophical priorities of the author but, despite opposing Brownian motion to Ornstein-Uhlenbeck processes at the beginning of the chapter —which would make for a neat parametric model comparison setting—, there is no quantitative argument nor illustration found in this third chapter that would relate to statistics. This is unfortunate as the questions of interest (testing for natural selection versus pure drift or versus phylogenetic inertia or yet for tree structure in phylogenics) could clearly be conducted at a numerical level as well, through the AIC factor or through a Bayesian alternative. The aspects I found most interesting in this chapter may therefore be deemed as marginalia by most readers, namely (a) the discussion that the outcome of a test should at all depend on the modelling assumptions (the author seems to doubt this, hence relegating Bayesian techniques to their dust-gathering shelves!), and (b) the point that parsimony is not a criterion per se.
“`Data! Data! Data!’ he cried impatiently, `I cannot make bricks without clay!” (Sherlock Holmes, The adventure of the copper beeches)
About the first point, the philosophical stance of the author is not completely foolproof in that he concedes that testing hypotheses without accounting for the alternative is not acceptable. My impression is that he looks at the problem from a purely dichotomous perspective, the hypothesis or [exclusive OR] the alternative being true. This is a bit caricatural as he integrates the issue of calibrating parameters under the different hypotheses, but there is a sort of logical discrepancy lurking in the background of the argument. Again working out a fully Bayesian analysis of a philogenic tree say would have clarified the issue immensely! And rejecting Bayesianism (sic!) because “there is no objective basis for producing an answer” (p.239) is a wee limited on the epistemological side! Even though I understand that the book is not trying to debate about the support for a specific evolutionary hypothesis but rather about the methods used to test such hypotheses and the logic behind these, completely worked-out example would have made my appreciation (and maybe other readers’) of Sober’s points much easier. And, again, I fail to see who could take benefits from reading this chapter. A biologist will most likely integrate the arguments and illustrations provided by Sober but could leave the chapter with a feeling of frustration at the apparent lack of conclusion. (As a statistician, I fail to understand how the likelihoods repeatedly mentioned by Sober can be computed because they never involve any parameter.)
“Parsimony does not provide a justification for ignoring the data.” (E&E, p.250)
Since I am interested in general by the negative impact of the “Ockham’s razor” argument, I find the warning signals about parsimony (given in the last third of the chapter) more palatable. Parsimony being an ill-defined concept, especially from a statistical perspective —where even the dimension of the parameter space is debatable—, no model selection is acceptable if only based on this argument.
“Instead of evaluating hypotheses in terms of how probable they say the data are, we evaluate them by estimating how accurately they’ll predict new data when fitted to old.” (E&E, p.229)
The chapter also addresses the distinction between hypothesis testing and model selection as paramount —a point I subscribed to for a long while before being convinced of the opposite by Peter Green and Jean-Michel Marin—, but I cannot get to the core of this argument. It seems Sober sees model selection through the predictive performances of the models under comparison, if the above quote is representative of his thesis. (Overall, I find the style of the chapter slightly uneven, as if the fact that some sections are adapted from earlier papers would make for different levels of depth.)
Statistically speaking, this chapter also has a difficulty with the continuity assumption. To make this point more precise, I notice there is a long discussion about reaching the optimum configuration (for polar bear fur length) under the SPD hypothesis, but I think evolution happens in discontinuous moves. The case about the local minimum in Section 3.4 is characteristic of this difficulty as a “valley” on a “fitness curve” that in essence takes three possible values over the three different types of eye designs does not really constitute a bottleneck in the optimisation process. Similarly, the temporal structure of the statistical models in Sections 3.3 and 3.5 is never mentioned, even though it needs to be defined for the tests to take place. The past versus current convergence to stationarity or equilibrium and hence to optimality under the SPD hypothesis is an issue (are we there yet?!) and so is the definition of time in the very simple 2×2 Markov chain example… And given a 2×2 contingency table like
testing for independence between both factors is a standard among the standards: I thus fail to understand the lengthy and inconclusive discussion of pp.240-243.