In his commentary on the Harvard President Lawrence Summers' speculations on the reasons why women are underrepresented in the sciences, Steve Pinker writes in The New Republic:
Since most sex differences are small and many favor women, they don't necessarily give an advantage to men in school or on the job. But Summers invoked yet another difference that may be more consequential. In many traits, men show greater variance than women, and are disproportionately found at both the low and high ends of the distribution. Boys are more likely to be learning disabled or retarded but also more likely to reach the top percentiles in assessments of mathematical ability, even though boys and girls are similar in the bulk of the bell curve. The pattern is readily explained by evolutionary biology. Since a male can have more offspring than a female--but also has a greater chance of being childless (the victims of other males who impregnate the available females)--natural selection favors a slightly more conservative and reliable baby-building process for females and a slightly more ambitious and error-prone process for males. That is because the advantage of an exceptional daughter (who still can have only as many children as a female can bear and nurse in a lifetime) would be canceled out by her unexceptional sisters, whereas an exceptional son who might sire several dozen grandchildren can more than make up for his dull childless brothers. One doesn't have to accept the evolutionary explanation to appreciate how greater male variability could explain, in part, why more men end up with extreme levels of achievement.
This argument leaves me feeling uneasy. I'm not sure I can put my finger on the reason why. The best I can do is as follows:
First, let us understand why the sex ratio is 1 or virtually 1. If there is a preponderance of females, then the average male is more likely to have offspring (and pass down genes to the next generation) than the average female. Likewise, if there is a preponderance of males, the female gets an advantage. Thus the unequal sex ratio is unstable, and evolution will quickly make sure that the ratio of sexes evens out.
Notice that what counts is the number of males (and females) that are able to produce offspring. Thus for humans, at birth boys outnumber girls by a small margin, about 105 male births to every 100 female births, and this is because fewer boys survive childhood than girls; and I expect that the male/female ratio at prime reproductive age reduces to unity. (At the high-age end of things, human evolution could not have been influenced by the modern fact of us routinely living to beyond 40, and we should not use that to study evolution-induced tendencies.)
Suppose next that male variability is extreme, and all males can be classified into one of two groups - fit and unfit to produce offspring. Evolution then will change the sex ratio, so that the ratio of fit males to fit females is unity, and thus the overall sex ratio of males to females will be greater than 1.
So I argue (and I'm not yet sure how to compute this) that increased male variability would reduce the number of fit males, and thus evolution's tendency to equalize the numbers of fit males and fit females would make the overall male/female ratio greater than 1. The more variable male offspring are, the more advantageous it is to produce somewhat more male than female offspring, because with increased variability, more of the males are duds (reproductively, that is).
Another way evolution induces variability is because more variability increases the chances of successful adaption. In a rapidly changing environment, what constitutes reproductive fitness will not remain fixed from generation to generation, and more variability means the chances are higher that one of the offspring will be able to adapt and be reproductively successful. Here, Pinker's argument works as stated, I think, male variability will be favored over female variability. But whether this actually happened in the case of human evolution is highly dependent on the nature of the world during man's million years of evolution.
Variability of a characteristic will also increase if there is no selection pressure on that characteristic; deviations from the mean do not confer an advantage or disadvantage on its possessor. It is amusing to think that there is no selection pressure on male mathematical abilities, and so they have a wider variance than the mathematical abilities of women, which supposedly are more tightly clustered at the mean, showing evidence of greater selection. Men really do love women for their brains; math is a survival skill for women.
Which brings me to another point. Articles widely cite the fact that in some study from the 80s of early takers of the Scholastic Aptitude Test - 13 year olds or thereabouts - boys outnumber girls by a factor of thirteen in those who score above 700. Less cited is the fact that among college-bound students who took the SAT in 2001, the boys outnumbered girls by a factor of two, in the 700+ scores, a far cry from the 13-fold advantage exhibited by the younger cohort. Thus, the difference in mathematical precociousness could be purely a developmental time difference. I'm sure in verbal ability among 1 year-olds, girls will handily outscore boys. But by adulthood, there is scarcely any difference between the sexes. Not to sneeze at a two-to-one advantage; the point is that our ignorance of what is happening is quite apparent.
Update: One has to know Fischer's (1930) argument for why the sex ratio is one - this is provided in comment #6.