Re: poly: democracy, etc.

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