A book review in the January 11 issue of Science magazine begins with a wonderful line: “It is not often that mathematical theory is tested with a machine gun.”
The book under review is “How Species Interact: Altering the Standard View on Trophic Ecology,” by Roger Arditi and Lev R. Ginzburg (Oxford University Press, 2012). In it, according to reviewer Rolf O. Peterson at the School of Forest Resources and Environmental Science at Michigan Technological University, the authors argue in favor of a theory they developed in the 1980s, that predator-prey dynamics, which is classically viewed as principally depending on prey density, is better viewed as depending on the ratio of prey to predator. “I admit to being impressed by the immediate usefulness of viewing predation through ratio-dependent glasses,” Peterson writes.
The details of the debate lie within the equations, which Peterson, quoting from the classic essay, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” by Eugene Wigner, calls a “wonderful gift.” (Peterson ruefully adds that many of his colleagues in wildlife management “have an unfortunate phobia for all things mathematical.” “Trophic” ecology, by the way, is rooted in the Greek word “trophe,” for “nourishment.” It is basically the study of food chains, which are mathematical from top to bottom.) The two “sides” of the debate may actually lie at opposite ends of a spectrum, with prey density predominating when predators are rare and the prey-to-predator ratio taking over when predators become dense enough themselves to interfere or compete with one another. The best course mathematically may be to take a page from the fundamentalists and “teach the controversy.”
As for the machine gun, you’ll want to read Peterson’s review, which, if you subscribe to Science, is available here — suffice it here to say, it has something to do with wolves, Alaska, and aircraft. But the story predates Sarah Palin by a couple of decades.
Barry Cipra