Monday, March 14, 2005

Does evolution result in more male variability?

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.


Lumo said...

Steve Pinker's argument is definitely a very powerful one...

A sad day for Harvard

Lumo said...

Concerning the counting, I am not sure what are the right assumptions.

There are almost certainly species in which the male:female ratio is not 1:1. It may well be just a biological necessity that if the genders are determined via the XX/XY chromosomes, then the probability simply will always be 1:1 for the genders regardless of the natural selection.

Once you accept it, you may return to Pinker's argument.

TripleIntegral said...

700+ is not far enough out the distribution curve. As you approach say 780 the ratios on the test go to something like 5:1. Even a 780 on the math SAT does not com e close to measuring the type of mathematical aptitude that someone needs to be a theoretical physicist or mathemeticina these days.

Your other argument on the gene stuff is just plain wrong. One reason is that no matter the actual ratio of surviving males/females, the birth rate is 1:1 or so. The reasons for higher variability in male atttributes are atttributed not so much to genetics per se as hormonal influences on brain plasticity and other factors in early development, as well as possibly genes.

Anonymous said...

The 1 to 1 ratio argument seems wrong to me. Consider two tribes, one tribe has a sex determining gene which causes 2 men to be born for every woman. The second tribe has 1 man for each woman.

Out there on the veldt, for some reason, tribes with a preponderance of men enjoy an evolutionary advantage - more hunters or something - the reason doesn't matter.

Wouldn't the first tribe reproduce more and eventually overwhelm the second tribe? In that case the 2 to 1 sex gene would predominate.

rafinlay said...

If each tribe started with (say) 100 women, the tribe with a 2:1 male birth ratio would produce fewer children each generation than the tribe with a 1:1 ratio. If there is any overwhelming going on due only to the birth-sex ratio, it would be the other way around. The real question should be: why hasn't there been an evolutionary advantage favoring a higher proportion of females?

Arun said...

Here is a link that gives the standard evolutionary biology argument for 1:1 sex ratios, and the cases when there are exceptions.

I'm reproducing the text here:
A population of nearly all females with just enough males to allow fertilization has the highest possible intrinsic growth rate. So -- Why so many males?


- All offspring have one male parent and one female parent

- If males are rare, than males will have a high fitness relative to females (males would contribute more of the genes of the next generation

-Same in reverse, if females are rare

Fisher showed that this causes an equal sex ratio

Subsequently it has been shown that this result holds regardless of the mechanism of sex determination (e.g. chromosomal sex determination, genic sex determination, environmental sex determination)

More precisely, mothers will equalize investment in reproductive male and female offspring

(which resolves the apparent contradictions in the Hymenoptera)


If mating occurs among close relatives before mixing with the general population, this selects for female-biased sex ratios

This is called local mate competition

e.g. fig wasps, Nasonia parasitic wasps

Arun said...

And here is a link to an experiment that validates Fischer's theory:

Most sexually reproducing species have sexual proportions around 1:1. This major biological phenomenon remained unexplained until 1930, when FISHER proposed that it results from a mechanism of natural selection. Here we report the first experimental test of his model that obeys all its assumptions. We used a naturally occurring X-Y meiotic drive system—the sex-ratio trait of Drosophila mediopunctata—to generate female-biased experimental populations. As predicted by FISHER, these populations evolved toward equal sex proportions due to natural selection, by accumulation of autosomal alleles that direct the parental reproductive effort toward the rare sex. Classical Fisherian evolution is a rather slow mechanism: despite a very large amount of genetic variability, the experimental populations evolved from 16% of males to 32% of males in 49 generations and would take 330 generations (29 years) to reach 49%. This slowness has important implications for species potentially endangered by skewed sexual proportions, such as reptiles with temperature sex determination.