PNAS: We're only for "lab biologists"

Steve Evans, Ken Wachter, and I submitted our recent paper, developing a new mathematical model of mutation-selection equilibrium, to the Proceedings of the National Academy of Sciences (PNAS), a journal which purports to "span the biological, physical, and social sciences", but which has degenerated over time into a biology journal. It was reported that the editorial board desired to raise the journal's profile in applied mathematics.  We submitted the paper to the Applied Mathematics section.  It bounced back to us a week later from the "member-editor", with the lapidary remark that it was an original piece of work, with potentially useful new insights, but that it could not be published in PNAS because it was, in a word, mathematical, hence unlikely to be understood by many of their readers.  (Click here for the complete report.)  One imagines this reader -- call him Simple Simon Scientist -- breezing through a typical 500-page issue, from Agricultural Sciences to Zoology, and suddenly crashing into our paper, with its shameless exposition of the Feynman-Kac formula. Simple shoots bolt upright in bed, clutching his head in agony. Next day, in the office, he dictates a letter, cancelling his subscription. "Never did I think that the National Academy of Sciences would so assault me, S. Simon Scientist, by printing a paper that I do not understand."

While people lament "math phobia" as an infirmity of school children, it also seems to strike grownup scientists.  It has, perhaps, gone unrecognized because of the distinct symptomology: not the open "I hate math", but "That's too abstract", together with the suggestion that "others" would not understand.  The result is an invidious double standard.  Imagine that a team of experimenters were to develop original techniques to attack a problem that has already been considered to be of broad interest, or that they were to adapt techniques that had never before been applied to this sort of problem. Suppose that their experiments then showed that earlier approaches had been misleading, and that essential conclusions need to be revised.  Would their paper be rejected, with the comment that "the methods will be familiar to only a small fraction of readers", so that it would be suited to a more specialized journal?  On the contrary, one might say, this should be an inducement to more people to learn these techniques.  One would think, from the reactions we have garnered, that we had perversely elected to write the paper in an obscure dialect of Akkadian.

We appealed against this decision, as being contrary to the journal's official policy, and they did agree to send it out for review.  One month later, we got two referee reports.  One said that the paper is mathematical, hence unlikely to be understood by the majority of PNAS readers.  "It would go totally over the head of any lab biologist..."  ("Only the purest of pure probabilists would understand..."  This reference to "purity" suggests the mixture of inferiority complex and prejudice that we're up against.)  The other was from a mathematician: Our formulae, it was claimed, were really anticipated by others in a 1976 paper.  To the native Laputan, of course, God and the universe are mere special cases of your own favorite theorem.  (Or, as Steven Weinberg remarked in another context, "So might a carpenter, looking at the moon, suppose that it is made of wood.")

There are good reasons why one might consider this paper unsuited to PNAS.  It is unfortunate, though, that the journal clandestinely adopts a policy of treating mathematical approaches to science as though they were rituals of an esoteric cult -- "If we needed stochastic analysis, God would have given us stochastic fingers to count on" seems to be the motto,  if not "Everything we needed to know about mathematics, we learned as freshmen" -- rather than actually reading the paper, to decide whether the techniques might be appropriate to advance the common cause of science.


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