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Probability, Statistics, Evolution, and Intelligent Design

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Probability, Statistics, Evolution, and Intelligent Design Probability, Statistics, Evolution, and Intelligent Design Peter Olofsson n the last decades, arguments against Darwinian evolution An ID Hypothesis Testing Challenge to Evolution have become increasingly sophisticated, replacing Cre- In his book The Design Inference, William Dembski introduces ationism by Intelligent Design (ID) and the book of Genesis I the “explanatory filter” as a device to rule out chance expla- by biochemistry and mathematics. As arguments claiming to nations and infer design of observed phenomena. The filter be based in probability and statistics are being used to justify also appears in his book No Free Lunch, where the description the anti-evolution stance, it may be of interest to readers of differs slightly. In essence, the filter is a variation on statistical CHANCE to investigate methods and claims of ID theorists. hypothesis testing with the main difference being that it aims at ruling out chance altogether, rather than just a specified Probability, Statistics, and Evolution null hypothesis. Once all chance explanations have been ruled The theory of evolution states in part that traits of organisms out, ‘design’ is inferred. Thus, in this context, design is merely are passed on to successive generations through genetic mate- viewed as the complement of chance. rial and that modifications in genetic material cause changes To illustrate the filter, Dembski uses the example of in appearance, ability, function, and survival of organisms. Nicholas Caputo, a New Jersey Democrat who was in charge Genetic changes that are advantageous to successful repro- of putting together the ballots in his county. Names were to be duction over time dominate and new species evolve. Charles listed in random order, and, supposedly, there is an advantage Darwin (1809–1892) is famously credited with originating in having the top line of the ballot. As Caputo managed to and popularizing the idea of speciation through gradual place a Democrat on the top line in 40 out of 41 elections, change after observing animals on the Galapagos Islands. he was suspected of cheating. In Dembski’s terminology, Today, the theory of evolution is the scientific consensus cheating now plays the role of design, which is inferred by concerning the development of species, but is nevertheless ruling out chance. routinely challenged by its detractors. The National Academy Let us first look at how a statistician might approach the of Sciences and Institute of Medicine (NAS/IM) recently Caputo case. The way in which Caputo was supposed to draw issued a revised and updated document, titled “Science, names gives rise to a null hypothesis H0 : p = 1/2 and an alter- Evolution, and Creationism,” that describes the theory of native hypothesis HA : p > ½, where p is the probability of evolution and investigates the relation between science and drawing a Democrat. A standard binomial test of p = 1/2 religion. Although the latter topic is of interest in its own based on the observed relative frequency pˆ = 40/41 ≈ 0.98 right, in fairness to ID proponents, it should be pointed out gives a solid rejection of H0 in favor of HA with a p-value of that many of them do not employ religious arguments against less than 1 in 50 billion, assuming independent drawings. A evolution and this article does not deal with issues of faith statistician could also consider the possibility of different and religion. values of p in different drawings, or dependence between How do probability and statistics enter the scene? listings for different races. In statistics, hypotheses are evaluated with data What then would a ‘design theorist’ do differently? To collected in a way that introduces as little bias apply Dembski’s filter and infer design, we need to rule out as possible and with as much precision as all chance explanations; that is, we need to rule out both possible. A hypothesis suggests what we H0 and HA. There is no way to do so with certainty, and, to would expect to observe or measure, if the continue, we need to use methods other than probability hypothesis were true. If such predictions calculations. Dembski’s solution is to take Caputo’s word that do not agree with the observed data, the he did not use a flawed randomization device and conclude hypothesis is rejected and more plausi- that the only relevant chance hypothesis is H0. It might sound ble hypotheses are suggested and evalu- questionable to trust a man who is charged with cheating, but ated. There are many statistical as it hardly makes a difference to the case whether Caputo techniques and methods cheated by “intelligent design” or by “intelligent chance,” let that may be used, us not quibble, but generously accept that the explanatory and they are all filter reaches the same conclusion as the test: Caputo cheated. firmly rooted in The shortcomings of the filter are nevertheless obvious, even the theory of in such a simple example. probability, the In No Free Lunch, Dembski attempts to apply the filter “mathematics to a real biological problem: the evolution of the bacterial of chance.” flagellum, the little whip-like motility device some bacteria 42 VOL. 21, NO. 3, 2008 such as E. coli possess. Dembski discusses the number and A g e n e r a l types of proteins needed to form the different parts of the point of criti- flagellum and computes the probability that a random con- cism against ID figuration will produce the flagellum (using the analogy of is that it does not shopping randomly for cake ingredients). He concludes it is offer any scientific so extremely improbable to get anything useful that design explanations of must be inferred. natural phenomena, A comparison of Dembski’s treatments of the Caputo but merely attempts case and the flagellum is highly illustrative, focusing on two to discredit Darwin- aspects. First, in each case, Dembski only considers one ian evolution, aiming chance hypothesis—the uniform distribution over possible at inferring ‘design’ by sequences and protein configurations, respectively. He pres- default. Dembski’s filter is ents no argument as to why rejecting the uniform distribution streamlined to this approach; rules out every other chance hypothesis. Instead, he shifts by trying to rule out all chance the burden of proof to the “design skeptic,” who, accord- hypotheses, it attempts to infer ing to Dembski, “needs to explicitly propose a new chance design without stating any compet- ing design hypotheses. explanation and argue for its relevance.” In the Caputo case, Above, it was demonstrated how the fil- it may be warranted to test only one chance hypothesis, as ter runs into trouble, even when it is viewed there is only one such hypothesis that equates to fairness, entirely within Dembski’s chosen paradigm but the situation is radically different for the flagellum, where of “purely eliminative” hypothesis testing. nonuniformity in no way contradicts an evolutionary process Others have criticized the eliminative nature of of mutation and natural selection. Dembski routinely uses the the filter, claiming that useful design inference uniform distribution as a synonym for lack of knowledge, a must be comparative. In a chapter titled “Design dubious practice that has been gainfully exposed by proba- by Elimination vs. Design by Comparison” in his bilist Olle Häggström. book The Design Revolution, Dembski counters this Second, the one specific sequence of Democrats and type of criticism. He starts by doing a ‘reality check’ to Republicans that Caputo produced must be put together with conclude that “the sciences look to Ronald Fisher and not other comparable sequences to obtain the rejection region. Thomas Bayes for their statistical methodology,” referring to More specifically, we need to consider the set of 42 sequences the divide in the statistical community (to the extent that such that have at least 40 Democrats and compute its probability. a divide really exists) between the frequentist approach—in Dembski does this correctly in the Caputo case, but when it which unknown parameters are viewed as constants and are comes to the flagellum, he does not consider the rejection subject to hypothesis testing—and the Bayesian approach— region; he simply computes the probability of the outcome. in which unknown parameters are viewed as random variables Dembski’s way around this problem is to use his own term, described by their probability distributions. However, the “specification,” a vague concept that does not have a strict type of pure elimination he devises is not how statistical mathematical definition, but is intended to be a generalization hypothesis testing is done in the sciences. A null hypothesis of rejection region. In an essay titled “Specification: The Pat- H is not merely rejected; it is rejected in favor of an alterna- tern That Signifies Intelligence,” it is said that “Specification 0 tive hypothesis HA. Moreover, one can compute the likelihood denotes the type of pattern that highly improbable events of the data for various parameter choices specified by H to must exhibit before one is entitled to attribute them to intel- A conclude the evidence is, indeed, in favor of HA (so-called ligence.” In No Free Lunch, the index entry “Specification, power calculations). Hence, the statistical methodology of definition of” leads to a page where specification is used as a the sciences is eliminative and comparative. synonym for rejection region. The filter requires us at some One reason for Dembski to try to align with the frequentist point to compute a probability, so whatever “specification” camp is that there are indisputable problems with “Bayesian is, it must be possible to convert it into the mathematical design inference.” For example, to apply Bayesian methods, object of a set. one would have to assign a prior probability distribution over In the Caputo case, the two descriptions are easily inte- various chance and design hypotheses, which is obviously grated, as cheating can be described as patterns of the type a more or less hopeless task.
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