From: david friedman <ddfr@best.com>

Date: Thu Feb 12 1998 - 00:20:42 PST

Date: Thu Feb 12 1998 - 00:20:42 PST

At 12:39 AM -0800 2/11/98, d.brin wrote:>Did you know that there's a

correlation, in mammals,

*>betweem male-female size ratio and 'natural harem size'? Truly monogamous
*

*>species like gibbons are same-size. Male elephant seals, which have harems
*

*>of 40 or more are gigantic, not in order to dominate females, but in order
*

*>to drive off the other 39 males who want in.
*

This particular result follows from Fisher's explanation of sex ratios,

without requiring any male/male combat at all. The causation goes from

large males to unequal sex ratio to harem.

We start with a puzzle: why are roughly equal numbers of male and female

humans born, despite the fact that, for reproductive purposes, a fifth of

the males would be adequate?

Suppose that, on average, there were twice as many female children as male

children. Each child has one mother and one father, so it follows that the

average male is having twice as many children as the average female. It

follows from that that someone who has a son has, on average, twice as many

grandchildren as someone who has a daughter. It follows that genes for

having sons increase in the population--and continue to do so until the sex

ratio is equal.

So far I have been assuming a species (ours) with relatively little sexual

dimorphism, so that the biological cost of producing male and female

offspring is about the same. Now consider a species where the male

offspring weigh twice as much at birth and consume twice the resources in

being brought to maturity. The same argument implies that there will be

twice as many female offspring as male. Each male costs his parents twice

as much and produces twice as many grandchildren for them. Go up to

elephant seals, and you get a high female to male ratio, hence harems.

I apologise if everyone already knows this--it is, among other places, in

the first chapter of my _Price Theory_, which is webbed on my site.

Note, by the way, that if Fisher's argument is correct, there are not 39

other males who want in.

It isn't clear to me that Brin's argument works. It apparently assumes that

fighting is more productive, reproductively speaking, the larger the harem

size. I don't think that is correct if harem size is simply coming out of

sex ratio--after all, the cost of fighting--injury-- scales up with sex

ratio as well, since high f/m ratio implies that a male who survives has

lots of offspring.

You might be able to get the argument out of ratio of harem size to sex

ratio, since if it is large there are lots of celibate males willing to

take even a high risk fight in order to get someone else's harem. You then

have two equations: m/f body weight ratio (proxy for biological cost)=f/m

birth ratio, and an equation showing that an increase in male size costs

just as much in food etc. as it gains in extra reproduction through

successful combat.

David Friedman

Received on Thu Feb 12 08:19:55 1998

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