“Parsimony be damned!”

Abstract

Ockham's Razors: A User's Manual. By Elliott, Sober. Cambridge University Press, Cambridge, UK, 2015. x + 314 pp. US $30.99 (paperback), ISBN 978-1-107-69253-4. Elliott Sober is a celebrated and prolific philosopher of science at the University of Wisconsin, who has devoted quite a bit of ink over the past 35 years to the problem of parsimony, both as a general philosophical principle, and as the optimality criterion of the cladistic method. Perhaps his first forays into the latter realm were a paper presented at the second Hennig meeting in 1981, subsequently published in the precursor of this journal, Advances in Cladistics, vol. 2 (Sober, 1983a), and also an Annual Review article (1983b). These were followed by a rather derivative paper in volume 1 of Cladistics entitled, “A likelihood justification of parsimony” (Sober, 1985). At the time, Sober's analytical conclusions seemed relatively sanguine towards cladistic parsimony: “Parsimony correctly records which cladistic groupings are best supported by observations” (Sober, 1983b; p. 356); “The alternative to parsimony methods will be agnosticism; no method will succeed if they won't” (Sober, 1983a; p. 46). However, he also clearly felt that maximum likelihood provided the analytical framework necessary to measure cladistic parsimony's success (cf. Felsenstein and Sober, 1986). In 1988, Sober published a synthesis of his ideas in an influential predecessor book to Ockham's Razors, entitled Reconstructing the Past: Parsimony, Evolution and Inference. In that book, Sober attacked the philosophical premise of parsimony by suggesting that neither simple nor common cause explanations are always to be preferred, argued that Popperian hypothetico-deductivism is not an appropriate logical framework for phylogenetic inference, and in developing a likelihood framework for phylogenetic inference, claimed that both synapomorphies and symplesiomorphies provide evidence of grouping. Although of central significance as an attack on the philosophical underpinnings of the cladistic method, Sober's first book about parsimony and systematics was overlooked (or deliberately shunned) by the Hennig Society's book reviewers of the day. So here, I will endeavour both to review Ockham's Razors, and to try to connect the dots back to Sober's prior works on this topic as they relate to cladistics. On the second page of the introduction, Sober provides a statement of the principle of parsimony: “a theory that postulates fewer entities, processes, or causes is better than a theory that postulates more, so long as the simpler theory is compatible with what we observe”. The central significance of this to cladistics is clear: under the parsimony criterion, synapomorphy is a better explanation for shared character states than convergent evolution (= Hennig's (1966) “auxiliary principle”), and the preferred tree is the one that minimizes observed instances of homoplasy. However, Sober warns us that it is not quite so simple: are simple explanations really better than more complicated ones, and crucially, if so, why? Chapter 1 is a historical review of the formulation of the principle of parsimony and various attempts by others to justify it on philosophical grounds. Sober notes that although long associated with the 13th century William of Ockham, the idea of parsimony is older, with roots going back all the way to Aristotle. In Aristotle's writings, a distinction may already be perceived between ontological and epistemological versions of parsimony: the assertion, “nature does nothing in vain” implies that nature IS parsimonious; by contrast, “we assume, basing our assumptions on what we see, that nature does nothing in vain” suggests that it is our understanding of nature that is perceived through a parsimonious lens, regardless of whether nature is actually parsimonious or not (Aristotle quotes from Sober, 2015, pp. 7–8). There is a lengthy discussion of planetary motion (as seems inevitable in works on philosophy of science), and the theistic parsimony of Descartes and Leibniz. Parsimony is central to Isaac Newton's Rules of Reasoning in Philosophy (his first rule is essentially the same as Ockham's dictum), reflecting the Enlightenment taste for an orderly clockwork universe. There is good discussion of Hume's skepticism about induction and of the views of other major philosophers, such as Kant, Whewell and Mill. Sober spends a few pages on “Morgan's Canon”, the idea that the mental experiences of animals should not be anthropomorphized (taken up further in Chapter 4). To conclude and set up the next chapter, Sober asks three questions: does the fact that a simple theory S is simpler than a more complicated theory C help to justify claims: that S has a higher probability than C of being true?; that S is better supported by the observations than C?; and that S will make more accurate predictions in the future than C? I think it is potentially interesting to contemplate these questions in the specific context of phylogenetics. The 90-page chapter 2, “The probabilistic turn”, is about frequentist and Bayesian efforts to justify (or dismiss) the epistemic relevance of parsimony. While Sober discusses the work of Harold Jeffreys, Karl Popper and Hans Reichenbach, much of the argumentation is his own—some of it parallelling Sober (1988) and subsequent works. A distinction between frequentism and Bayesianism, he says (p. 84), is that “Bayesianism is a philosophy for individual agents who each want to decide how confident they should be in various hypotheses. Likelihoodism is an epistemology for the public world of science; it aims to isolate something objective on which agents can agree despite the fact that they differ in their prior degrees of confidence in the hypotheses under consideration”. As is often the case with explanations of these methods, there is a lot of discussion of coin-tossing and other simple examples, as well as mention of the likelihood of common ancestry as an explanation for adaptive versus non-adaptive features. He calls “Darwin's principle” the idea that adaptive features are more likely to be convergent and therefore less weighty as evidence of common ancestry. This is seemingly sensible, but of course is contrary to Hennig's aforementioned auxiliary principle. From my perspective, any apparent synapomorphy is a synapomorphy unless there is contravening evidence to show that it is not, regardless of its adaptive value. Sober shows that you can invent circumstances under which common cause explanations are less likely than separate cause explanations, and argues that therefore such notions may be naive. As he says (p. 119), “there are many things to count, and many ways to count them”. Later on in chapter 2, Sober discusses model selection, using either the Akaiki or the Bayesian information criteria, both of which he says depend on parsimony, since all things being equal, a model with fewer parameters is preferred over one with more. Thus, he argues, parsimony is epistemically relevant both if it agrees with likelihood estimates [if it does not, then, as per the title of this review, “parsimony be damned!” (p. 149)], and because it bears upon estimating the predictive accuracy of models. He also suggests that it may bear upon the process of testing hypotheses—start with the simple ones. Finally, he rejects the idea that the relevance of parsimony in these two ways is dependent on the assumption that nature is simple. Chapter 3 is about phylogenetic inference, and I must say that some of Sober's argumentation seems wrong, or perhaps is incompletely explained. For example, he says of his figure 3.5 (a tree with three ingroup and “n” outgroup taxa) that if the outgroup taxa are all in the same state, then the ancestral state of the ingroup shares that state. I don't think that is correct—if, for example, the outgroup taxa all have state 0 and the ingroup taxa all have state 1, then it seems to me that the most parsimonious optimization of the basal node of the ingroup is 1. He also says (p. 159) that if ((A,B)C) is the true tree, then a ((1,0)1) character distribution must be an instance of homoplasy in A and C. But that is only potentially parsimonious if the ancestral state for the three taxa is 0 (which of course we cannot know), and even then, it is equally parsimonious to explain the character distribution by gain at the base and a reversal in B. Sober describes three applications of cladistic parsimony—inferring topologies, inferring ancestral character states and inferring the characteristics of a contemporary taxon from those of its relatives. He says the third is rare, but if we change “contemporary” to “terminal” (i.e. taxa that exist empirically, rather than hypothetical ancestral entities), then it is clear that that sort of inference is common in palaeontology—inferring parental care in non-avian dinosaurs, for example, and even in predicting life history characters of extant taxa that are not well known (e.g. restricting the hunt for caterpillars of a moth whose immature stages are unknown to host plants that larvae of its relatives are known to feed upon). Sober suggests that Hennig's justification of parsimony in systematics reflects the ideas of Hume and Kant, and that Hennig's assertions about synapomorphies being the only source of evidence of relationship are not necessarily true. To judge from his citations, Sober's interest in the efforts of subsequent cladists to explain or justify their approach seems to have dwindled in the early 1980s, perhaps stemming from his early commitment to his “likelihood justification for parsimony”. He seems to have a persistent (from 1988 to this book) lack of understanding of the meaning of symplesiomorphy, due to a reification of the symplesiomorphic states as “homologous” (as has been argued lately by Nixon and Carpenter, 2011, 2012). Thus, in Sober's models, “both synapomorphies and symplesiomorphies are evidence of genealogical relatedness” (p. 178). But as Brower and de Pinna (2014) have argued, symplesiomorphies are either synapomorphies of more inclusive taxa or complementary absences to neomorphic characters, have no independent existence qua “symplesiomorphies” and therefore provide no evidence of relationship, unless one is a pheneticist. Further, the quantity that is parsimoniously accounted for in cladistics is not character state identities but character state transformations (Brower, 2000), and in any event, the (0,0,1) character state distribution featured in Sober's arguments is more sensibly viewed as an autapomorphy. When symplesiomorphies are correctly recognized for what they are—”nothing” as per Brower and de Pinna (2014)—then Sober's “Smith/Quackdoodle theorem” is seen to be irrelevant (the theorem so-called because two people named Quackdoodle are more likely to be related to one another than two people named Smith). The theorem's conclusion (first developed in Reconstructing the Past, with intimidatingly extensive algebraic notation) is that “a synapomorphy deserves more weight than a symplesiomorphy precisely when apomorphies have a lower expected frequency than plesiomorphies” (Sober, 1988, p. 215). While I am sure the likelihood calculations are correct, the premise seems flawed, again based on the false reification of symplesiomorphies as evidence. Using Sober's logic, if you scored “presence of a nucleus” for all known taxa, the apomorphic state would be much more “frequent” than the plesiomorphic state. I don't think any biologist would say that “presence of a nucleus” is a less reliable or weaker synapomorphy than, say, “presence of mammary glands” because the former is found in all eukaryotes and the latter only in mammals. In cladistics, character state transformations are not differentially weighted based on where in the tree they are inferred to have occurred. Sober next raises the old Felsenstein (1978) bugaboo about parsimony and statistical consistency. Of course, likelihood models are also prone to statistical inconsistency if the model does not match the true pattern of evolution, and since the latter is unknowable, this criticism has no force whatsoever (Farris, 1999; Schuh and Brower, 2009; Brower, 2016). In addition, Sober notes that the property of consistency—convergence on the true parameter value with the addition of more data—is an instance of the “law of large numbers”, which he states elsewhere in the book is dependent on an assumption of the uniformity of nature, i.e. a metaphysical parsimony assumption. So in the end, we see that likelihood and other inductive statistical inference procedures, at least as far as phylogenetic inference from empirical data is concerned, depend upon parsimony assumptions, and the project to obtain a “likelihood justification of parsimony” seems to be a circular argument. Chapter 4 takes up the psychological question of whether chimpanzees can conceive of the mental states of others, which Sober introduces at the end of Chapter 3 as a “problem of phylogenetic inference”. I think this characterization is fundamentally wrong because, as posed, the question is a two-taxon statement and is really about the ambiguous optimization of the ancestral node. Even if we add in some other ape outgroups, the cognitive abilities in question are manifest only in humans, and so the character is on its surface an autapomorphy and the ancestral optimization is still ambiguous. Experiments to test whether chimpanzees have cognitive abilities akin to those of humans pose questions about similarity or evolutionary distance, not about relationship, and under such circumstances, what the experimenter views as “parsimonious” may coloured by a priori beliefs. Chapter 5, “parsimony in philosophy”, addresses a variety of applications of ideas about parsimony to longstanding metaphysical and epistemological problems in philosophy: naturalism, mind-body issues, morality, solipsism, etc. A lot of these vignettes evidently summarize previously published papers and chapters. The most interesting part to me is a discussion towards the end on the problem of induction. Sober agrees with Hume that it is impossible to provide a philosophical justification for the Principle of the Uniformity of Nature (that the future will necessarily resemble the past). Maybe so, but I think it is fair to say that if nature is not uniform to some degree, then science and the application of statistics to empirical problems are both rendered largely impotent to explain or predict. That does not mesh with experience. The book is generally well produced, although the complex nature of the argumentation makes it a tough read (as Sober says on p. 2, “This book is not simple”). The figures do not have legends, and often the axes of graphs are not labelled, which makes them somewhat inscrutable. Sober's citations are mainly of philosophical works, and the infrequent references related to systematics are almost all 30+ years old. The index is mostly to names of authors, but some subjects are listed too: birthday fallacy; employees unhappy with bosses; scrotum, evolution of; tourists, advice to. This review is by a systematist, for systematists, and is not intended to evaluate comprehensively every one of Sober's points. For example, I have not said anything about his distinction between the “razor of silence” and the “razor of denial” which is the reason that there is more than one razor in the title (these can be thought of as analogous to agnosticism versus atheism). Although Sober has written a lot about cladistic parsimony over the years, I think his major concerns are more about the correspondence of phylogenetic hypotheses to the “true tree” than they are about the coherence of the method itself. The fundamental take-home message for cladists is that if there is no rational basis for the principle of uniformity of nature, then statistical theory cannot provide a justification for parsimony or any other empirical method of phylogenetic inference. On the other hand, if nature is comprehensible (i.e. we can discern when it is uniform and when it is not, gather data and make inferences and predictions accordingly), then parsimony is a useful epistemological tool.

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