Popperian Corroboration and Phylogenetics

Starting with articles by Bock (1973) and Wiley (1975) in this journal, the field of systematic biology has a history, reviewed by Helfenbein and DeSalle (2005), of examining its methods in the context of the philosophy of science articulated by Karl R. Popper (e.g., 1959, 1962, 1983). Two main categories of debates have emerged in this literature. In one, Popper’s philosophy is assumed to be relevant, and it is used to promote some systematic methods and criticize others (e.g., Siddall and Kluge 1997; Kluge 2001), which has led to counterarguments proposing that the criticized methods are equally compatible with Popper’s philosophy (e.g., de Queiroz and Poe 2001, 2003). In a second category of debates, the relevance of Popper’s philosophy to systematics has been questioned (e.g., Rieppel 2003, 2005; Vogt 2008) and defended (e.g., Farris 2013, 2014). These debates can provide insights of at least two different kinds. Systematic biologists can gain a better understanding of how their methods and practices relate to general ideas about the nature of science, while philosophers can assess how well Popper’s ideas about the nature of science describe the methods and practices in a discipline other than the ones (primarily physics and astronomy) upon which those ideas were based. As part of the continuing debates about Popperian philosophy and phylogenetics, Farris (2013) recently argued that Felsenstein (2004) was incorrect in suggesting that Popper’s concept of degree of corroboration, C, relies on a Bayesian approach, that Helfenbein and DeSalle (2005) weremisguided in adopting Felsenstein’s suggestion as a justification for Bayesian approaches, and that Rieppel (2005) assigned an incorrect value to the term p(e|hb) in the defining formula of C. Here, I wish to call attention to an article regarding Popper’s philosophy and its relationship to phylogenetics (de Queiroz 2004) that is highly relevant to, but was not considered in, those disagreements. I will summarize some of the main conclusions of that article and then illustrate how the perspective developed in it and two earlier publications (de Queiroz and Poe 2001, 2003), which equates specific phylogenetic analyseswith specific components of C, clarifies issues discussed by Felsenstein (2004), Helfenbein and DeSalle (2005), Rieppel (2005), and Farris (2013). The article in question (de Queiroz 2004) focused on the concept of test severity, which is assessed using the term p(e|b) in the defining formula of C (e.g., Popper 1983, p. 238), the full definition of which is C(h|e|b)= [p(e|hb)−p(e|b)]/ [p(e|hb)−p(eh|b)+p(e|b)]. According to Popper, the data or evidence (e) used to test a hypothesis (h) may have a certain probability given that hypothesis and the background knowledge (b), thereby offering support for the hypothesis; however, the test can only be considered severe, and therefore the support meaningful, if the data have a much lower probability given the background knowledge (b) alone—that is, in the absence of the hypothesis being tested. In other words, the hypothesis can only be considered wellcorroborated if the probability of the evidence given that hypothesis in conjunction with the background knowledge, p(e|hb), is substantially greater than the probability of the evidence given the background knowledge alone, p(e|b). This idea is embodied in the numerator of the defining formula of C, which is the difference between these two quantities: p(e|hb)− p(e|b). In the context of phylogenetics, where e is a phylogenetic data set (e.g., a taxon × character matrix) and h is a hypothesis of phylogenetic relationships (e.g., a tree), b, the background knowledge, consists of those assumptions inherent to the method (model) used to analyze the data (de Queiroz 2004; see also de Queiroz and Poe 2001, 2003), including ordered versus unordered character states, rates (likelihood) or costs (parsimony) of change between states, and equal versus variable rates (likelihood) or weights (parsimony) among characters. One of the basic assumptions common to diverse phylogenetic methods is that the terminal taxa are related through common ancestry, which allows their relationships to be represented by a tree. In this context, the absence of h is the absence of the hypothesis of phylogenetic relationships under the assumption that those relationships are to be