Peppered moth - Biston betularia
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Moth-eaten Statistics

A Reply to Kenneth R. Miller A response to Miller and Levine

British statesman Benjamin Disraeli is reputed to have said that there are “lies, damn lies, and statistics.” Statistics based on unbiased samples and rigorous analyses can point us in the direction of the truth; but statistics can also be unscrupulously manipulated to “prove” things that are patently untrue. Brown University biology professor Kenneth R. Miller demonstrates the latter in his most recent response to me:

The relative proportions of light-colored and dark-colored (“melanic”) peppered moths changed during the industrial revolution, supposedly because of camouflage and bird predation. In the early 1950s, British physician Bernard Kettlewell released captive moths onto nearby tree trunks and made observations that seemed to confirm this explanation. Many biology textbooks now use Kettlewell’s work on industrial melanism as the classic demonstration of Darwinian natural selection in action, and they typically illustrate the story with photos of moths on tree trunks. Yet biologists in the 1980s discovered that peppered moths rarely rest on tree trunks in the wild. The textbook photos are staged, and in 2000 I criticized this practice in my book, Icons of Evolution.

Now Miller — a co-author of one of the textbooks I criticized — claims that “observations done to date show that most moths have, indeed, been found on tree trunks,” so “Wells is just plain wrong when he claims that moths don’t rest on tree trunks.” As support for his claim, Miller cites data and statistics allegedly proving that 68% of moths “were found on tree trunks.” Yet it is obvious from the data that Miller has relied on statistical manipulations and a biased sample to prove his point.


Miller begins with data published by Michael M. E. N. Majerus, an expert on peppered moths at the University of Cambridge. The relevant data are found on page 123 of Majerus’s book, Melanism: Evolution in Action (Oxford, 1998):

Table 6.1 The resting positions of peppered moths found in the wild between 1964 and 1996.

Exposed trunks 6
Unexposed trunks 6
Trunk/branch joints 20
Branches 15

Table 6.2 Resting positions of peppered moths found in the vicinity of mercury vapor moth traps at various locations between 1965 and 1996.

Exposed trunks 48
Unexposed trunks 22
Trunk/branch joints 66
Branches 20
Foliage 22
Man-made surfaces 25

Miller claims that Table 6.1 shows that 68% of moths rest on tree trunks, while Table 6.2 shows 67%. Since the two statistics are similar, and since only Table 6.1 reports moths found under natural conditions, I will limit my comments to it.


Miller obtains his percentage by lumping together moths found on tree trunks with moths found hiding in “trunk/branch joints” where horizontal branches meet the trunk. Since moths in trunk/branch joints are obscured from view, this category is usually omitted even by other defenders of the classic story, who limit themselves to combining moths on exposed and unexposed trunks to come up with a figure of 26%. And even the 26% figure is questionable, because it is not at all clear that “unexposed trunks” are equivalent to exposed tree trunks in relation to the classic camouflage-predation story. If moths are hidden from view in cracks in the bark, does their color make any difference?

Nobody really knows. As Majerus himself wrote in his book: “If the relative fitness of the morphs [i.e., dark and light varieties] of the peppered moth does depend on their crypsis [i.e., camouflage], the resting position is crucially important to the estimation of fitness differences…. [Yet] experiments to show that the degree of crypsis of the different peppered moth forms does affect the level of predation inflicted upon them by birds have never been carried out.” (pp. 123-125)

Given this uncertainty, normal scientific caution would suggest that only the 6 moths reported on exposed tree trunks should be counted as clear support for the classic camouflage-predation story. In other words, 13% of the moths reported in Table 6.1, not 68%. But 13% falls far short of justifying Miller’s claim that “observations done to date show that most moths have, indeed, been found on tree trunks.”

Manipulating the data in Table 6.1, however, is not Miller’s most egregious misuse of statistics. It turns out that Table 6.1 is not — and does not purport to be —an unbiased sample representing peppered moths in general.


In the decades since Kettlewell’s experiments, scientists have counted tens of thousands of peppered moths. One 1977 paper alone listed data for 8,426 moths in southern Britain between 1952 and 1974. (R. C. Steward, “Industrial and non-industrial melanism in the peppered moth, Biston betularia,” Ecological Entomology 2, 1977, p. 236) Yet Table 6.1 reports only 47 moths found resting in the wild in 32 years. Does this tiny sample provide us with an accurate picture of peppered moths in general?

It turns out that it is extremely difficult to find resting peppered moths in the wild. Peppered moths fly at night (which is when tens of thousands have found their way into researcher’s traps over the years), and they rest during the day. In 1985 three scientists reported that “all we have observed is where the moths do not spend the day. In 25 years we have only found two betularia on the tree trunks or walls adjacent to our traps.” (C. A. Clarke et al., Biological Journal of the Linnean Society 26, 1985, p. 197) The reason resting moths have been so hard to find is that they probably hide beneath higher branches where they cannot be easily seen. According to one expert: “In nature, Biston betularia probably rest high up in the canopies, on the under surfaces of horizontal branches.” (Kauri Mikkola, Biological Journal of the Linnean Society 21, 1984, p. 409)

So how can we determine what percentage of peppered moths rest in exposed positions where camouflage is likely to affect their survival? Surely not by doing statistics only on those moths found resting where they were sufficiently exposed to be spotted from the ground. That would be a bit like trying to determine what percentage of fish in the sea are visible to predatory birds by doing statistics only on those that can be spotted from a boat.

Table 6.1 lists only 47 of the tens of thousands of peppered moths that have been studied in the past few decades. This sample is obviously biased toward moths that were easily spotted by observers on the ground, and biased against moths that were hiding in the canopies. Even if all the moths in Table 6.1 (not just 13% or 26% or 68%) had been found on tree trunks, they would still represent less than 1% of all peppered moths counted during the same period.

Majerus, of course, does not claim that Table 6.1 represents an unbiased sample. In fact, he concludes from his extensive knowledge of the data that “peppered moths do not naturally rest in exposed positions on tree trunks.” (p. 121)

But Miller ignores Majerus’s expert opinion and teases inflated numbers from an unrepresentative data set. Miller thereby proves not that peppered moths normally rest on tree trunks, but that Benjamin Disraeli was right: There are lies, damn lies, and statistics.

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Jonathan Wells

Senior Fellow, Center for Science and Culture
Jonathan Wells has received two Ph.D.s, one in Molecular and Cell Biology from the University of California at Berkeley, and one in Religious Studies from Yale University. A Senior Fellow at Discovery Institute's Center for Science and Culture, he has previously worked as a postdoctoral research biologist at the University of California at Berkeley and the supervisor of a medical laboratory in Fairfield, California. He also taught biology at California State University in Hayward and continues to lecture on the subject.