The exception that proves the rule

I first learned a more useful meaning of the expression “the exception that proves the rule” from the essay “Death Before Birth, or a Mite’s Nunc Dimittis” in The Panda’s Thumb, a 1980 collection by paleontologist Stephen Jay Gould. (I would link to the full version of the essay, but it seems the only website freely hosting it is an archive dedicated to Ted Kaczynski, so, uh, yeah.)

In common parlance, this expression is often used to dismiss a counterexample to a supposed principle. Gould’s formulation for the “exception that proves the rule” uses an older meaning of “prove”, from the Latin probare, meaning to test or to try.

The essay begins with the observation of statistician R.A. Fisher that the ratio of males to females is roughly equal across many sexual species. Fisher’s explanation for this phenomenon goes something like this:

• Suppose there were more females born than males.
• Males will now, on average, leave more offspring than females, since males will impregnate more than one female on average.
• Thus, genetic factors causing parents to leave more male offspring will gain an evolutionary advantage.
• Over time, these genetic factors will become more common in the population, pushing the sex ratio toward 50/50. However, their advantage diminishes toward zero as the sex ratio approaches 50/50.
• The same argument applies should males come to predominate rather than females.

This is a tidy explanation for the roughly equal sex ratio in most species. But beyond this, how do you actually test the idea if most species conform to the 50/50 ratio?

Why, you look at the exceptions, the exceptions that “prove” the rule.

In the essay, Gould recounts the sad life of the male mite of the genus Adactylidium, which is doomed to emerge, do nothing, and die within hours. Why? Because all of the action has already occurred in the relative safety of the mother’s body. These mites display an extreme sex imbalance: a single male, with all other siblings being female. The larvae literally eat their mother alive as they develop. Before emerging, the lone male mates with all his sisters, and the siblings then collectively chew their way out of their mother’s spent carcass. The females, already pregnant, leave to seek out a food source, while the male, his duty done, simply dies.

This tests Fisher’s hypothesis by changing the initial circumstances and thus the predicted outcome. In the case of exclusive sibling mating enclosed within the mother’s body, it would indeed be evolutionarily advantageous to produce a single male and as many female offspring as possible. And that is what we observe.

The exception proves the rule.