Sex ratios and the value of the sexes

January 10, 2020

Continuing the series of posts toward addressing the problem “Does the economy treat women fairly”

Evolution is damned clever, as I explained here and has repeatedly solved this problem: what’s the optimal sex ratio for a species. And what does evolution’s solution tell us about the relative values of the sexes?

For most mammals, the sex ratio is close to 1:1, which exceptions that illustrate how clever evolution can be in unusual circumstances, and what clever solutions it can create in odd ecological niches.

slightly biased towards the male sex, being estimated to be about 1.05 or 1.06 males/per female born

Why should the sex ratio at birth for most mammals at be close to 1:1, but significantly different from 1:1? Why not closer to 1:1 than it is? A good answer is given by Fisher’s principle, which has been described as “probably the most celebrated argument in evolutionary biology.”

The argument comes from Ronald Fisher

…a British statistician and geneticist. For his work in statistics, he has been described as “a genius who almost single-handedly created the foundations for modern statistical science” and “the single most important figure in 20th-century statistics”.

Haven’t heard of him? He’s another one of my unsung heroes, like Norman Borlaug and Vasily Arkhipov and Barry Marshall and Robin Warren.

Among his other accomplishments, Fisher is known for developing the notion of statistical testing against the Null hypothesis. The Fisherian approach still prevails today despite the increasing use of Bayesian statistics.

W.D. Hamilton gave the following basic explanation in his 1967 paper on “Extraordinary sex ratios,” [3] given the condition that males and females cost equal amounts to produce:

In modern language, the 1:1 ratio is the evolutionarily stable strategy (ESS).[4]

So that’s why it should be 1:1. But why not exactly?

Here’s Fisher’s argument:

In organisms of all kinds the young are launched upon their careers endowed with a certain amount of biological capital derived from their parents. This varies enormously in amount in different species, but, in all, there has been, before the offspring is able to lead an independent existence, a certain expenditure of nutriment in addition, almost universally, to some expenditure of time or activity, which the parents are induced by their instincts to make for the advantage of their young. Let us consider the reproductive value of these offspring at the moment when this parental expenditure on their behalf has just ceased. If we consider the aggregate of an entire generation of such offspring it is clear that the total reproductive value of the males in this group is exactly equal to the total value of all the females because each sex must supply half the ancestry of all future generations of the species. From this it follows that the sex ratio will so adjust itself, under the influence of Natural Selection, that the total parental expenditure incurred in respect of children of each sex, shall be equal; for if this was not so and the total expenditure incurred in producing males, for instance, were less than the total expenditure incurred in producing females, then since the total reproductive value of the males is equal to that of the females, it would follow that those parents, the innate tendencies of which caused them to produce males in excess, would, for the same expenditure, produce a greater amount of reproductive value; and in consequence would be the progenitors of a larger fraction of future generations than would parents having a congenital bias towards the production of females. Selection would thus raise the sex-ratio until the expenditure upon males became equal to that upon females.

Humans produce slightly more males than females at birth because what matters is average parental investment. Investment in a child stops if the child dies before it can reproduce. Males die at a higher rate. The differential mortality is the result of purely biological factors (lethal recessive genes on the X chromosome express themselves twice as often in males than in females) cultural factors (men fight in wars) and factors that are both biological and cultural—like risk raking.

Who’s more valuable, men or women?

Evolution figures all this stuff out, though it takes a long, long, long while for it to catch up to the latest changes in the environment, and right now, the answer is: they’re roughly equally valuable.

If we accept the meritocratic notion that economic reward should be closely correlated to value—then nature’s equal valuing of males and females could provide us with some guidance. Since clever evolution says that males and females are equally valuable then—across the economy (whatever that means)—they should be economically rewarded (whatever that means)—roughly equivalently (whatever that means.)

Humans can say screw nature

On the other hand, one could say: “Screw nature. We’re humans. We can do whatever the fuck we please” and apply a different set of criteria.

We humans could engineer a society with a sex ratio of 10:1 females to males. Just try that, muskrats!

In this engineered society, each male would reproduce with ten women, which might be fun for the males, and there are lots of females who might even prefer the arrangement.

Hell, with modern technology, we can reduce the amount the labor-intensive parts of impregnation and engineer a ratio of 100:1 or even 1000:1. It would probably not be fun, but it’s still possible. And so much more energy efficient!

But the sex ratio doesn’t change the economics. If there are 1,000 males for each female, then each male is 1,000 times as valuable as each female.

The argument remains: the aggregate economic reward for all males (or men) should be the same as the aggregate reward of females (or women)—although the individual rewards would be higher.

Apology

Yeah, I get that I switched from the man/woman binary to the male/female binary somewhere in the middle of this post. I tried to fix it, but no matter what I did, some part had problems, and I don’t want to take the additional time to figure out how to fix it—assuming there is away. Sorry. Please forgive me

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