Testing random

[Laura Creighton]

Stick to dice.  Stay away from children.  One thing we know of, for sure,
is that certain breeding pairs are more likely to produce males, and
others are more likely to produce females.  We will ignore  those born who
are of indeterminate sex, for this discussion.

In human beings, as well as a whole lot of animal species, infant-and-
chidhood mortality is not sex neutral.  More baby boys die than baby
girls.  But when you look at breeding age men and women you will find
that the ratio is a lot closer to 50/50 than the birth age ratio.
Human beings, as a population currently produce more males than
females.

Now one way that could happen is if all human beings are predisposed to
have slightly more boy babies than girl babies when they breed.  But
this isn't what we think happens.  

Fisher's Principle says:

        Suppose sexually active males are less common than females in
	a population.

	A male then has better mating prospects than a female, and
  	can expect to have more offspring.  (Because some lucky males
	can expect to mate with more than 1 female).

	Therefore parents genetically disposed to produce males tend to
	have more than average numbers of grandchildren born to them.

        Thus genes for producing males will spread.

        But this means that more males will be produced.  Which means
	that at some point, the first priciple no longer holds --
	sexually active	males are no longer less common	than females
	in the population.  You	can reach a state where	females	are
	less common.

	But the	same thing kicks in, once more.	 And this time parents
	who produce daughters tend to get more offspring.  If you produce
	a son, who doesn't get to breed at all, from an evolutionary
	standpoint you have wasted your time in a bad investment.

	Thus the sex ratio will tend to 50/50.  It is self-adjusting
	that way.

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Now, human beings, despite being very interesting to us, are very bad to
study this way.  There are too many other complicating factors in human
reproduction, and human beings take too long to reach sexual maturity
anyway.  But you can study this in animals where you can artificially
bias the population any way you like, and who reach sexual maturity
quickly so you can watch and see if it plays out like Fisher says it
would.  And in lots of places that has been  studied, it does.

It is a little hard to see how you would get the proper correspondence
between infant mortality rates and sex ratio -- this species produces
precisely enough extra girl babies to offset the fact that more girls
die as infants -- unless something like this was going on.  And this
is measured to be so for some animals studied other than humans.

Bets are off in species where most of the males don't get to breed
anyway.  The logic doesn't work for them.

But what this shows is that the statement that a given birth is as likely
to be a son as a daughter (or 52% likely to be a son and 48% likely
to be a daughter) only works for large populations.  It's not going to
help you know if your next child is going to be a son or a daughter.
The parents of 4 boys who are trying, once again, thinking 'this time
it must be a girl!' may be up against something rather worse than
the gamblers fallacy. The odds that they have a girl may be substantially
lower than 50% -- it is quite possible that they are set up to only produce
boys, or to produce boys 80% of the time.  We have no way of knowing
this, because right now we don't know exactly how a bias in producing
one sex or another is expressed.  It is also quite possible that the
parents of 4 boys who want a girl have just been unlucky, because
they have no bias one way or another.  Or extremely unlucky because
their bias is for daughters, but they keep getting results against the
odds.

All we know is that notion that every human birth has a 50/50
chance of being male or female is wrong. 

Laura