Homosexuality gene-culture co-evolutionary model part 2

Gatherer, D. (D.Gatherer@organon.nhe.akzonobel.nl)
Tue, 04 May 1999 09:48:59 +0200

Date: Tue, 04 May 1999 09:48:59 +0200
From: "Gatherer, D. (Derek)" <D.Gatherer@organon.nhe.akzonobel.nl>
Subject: Homosexuality gene-culture co-evolutionary model part 2
To: "'memetics@mmu.ac.uk'" <memetics@mmu.ac.uk>

In yesterday's post I presented a derivation of the standard equation for
selection against a deleterious recessive allele:

delta q = -spqsquared / (1- sqsquared)

Remember that it is assumed that homosexuality is recessive (contentious but
not totally unlikely), and that under tabooless conditions, that homosexual
men will adopt a non-reproductive or poorly reproductive lifestyle (again
not an unreasonable postulate).

s is the selection co-efficient against homosexuality under these
circumstances. Yesterday I made it 0.9, since homosexual men may have some
children from time to time, but nowhere near as many as heterosexual men.
If I wanted homosexual men to be totally non-reproductive, I would have made
it s = 1.

Note that delta q is always negative. Where selection pressure is being
applied against a recessive allele, its trend will always be downwards.
This implies that homosexuality must be declining. However, there are a
couple of genetic mechanisms that might act to stabilise it under 'tabooless
society' conditions (as I'll mention in a minute)

What is clear however, is that as s tends to zero, delta q tends to zero.
delta q never becomes positive. In our present context, this is relevant to
cultural changes which impose taboos. Remember that taboo imposition forces
homosexual men to adopt heterosexual lifestyles. Their reproductive success
rate soars and s falls away rapidly. If homosexual men are 'totally
heterosexual' in their _reproductive_ life (regardless of their illicit
recreational life in a taboo society), then s = 0. delta q settles on zero
and the frequency of q stabilises.

But, importantly, it does not increase. Taboo imposition cannot cause an
increase in homosexual alleles, merely a halt in the rate at which they are
declining. This is where Aaron goes wrong, since his theory requires
homosexuality to somehow bounce back during periods of taboo:

As he says:

"As the taboo becomes extremely
widespread, most homosexuals live heterosexual lives, leading them to
reproduce any genes involved. As the genes gain prevalence, the rate of
taboo dropout increases."

"Take some genetic population segment that has a low
reproduction rate, give them a taboo that raises their reproduction rate to
perhaps mainstream levels, and their genes should start proliferating at a
rate much higher than that dictated by mutation alone."

"All of this [ie. the interaction of taboo and genes] leads
to potential fluctuations over long time spans."

Since delta p is zero, the genes are not 'proliferating' nor do they 'gain
prevalence' nor are there the 'potential fluctations'. The trend for
recessive gay genes (should there be such things) is remorselessly
downwards. Taboos only temporarily slow the process.

What are the current standard evolutionary theories for homosexuality? Why
are 1 in 10 men so reproductively disinclined? Remember this means a
recessive allele frequency q of neary one-third, q = 0.316

There are two usual explanations. The first is that carriers of
homosexuality somehow have a reproductive advantage over non-carriers. This
situation is hypothetically just like the known true situation for diseases
like sickle cell disease (carriers resistant to malaria), cystic fibrosis
(carriers resistant to cholera) and phenylketonuria (carriers resistant to
ergotamine poisoning)

In this case

HH non-carrier, fitness 1-t
Hh carrier, fitness 1
hh homosexual, fitness 1-s

Note that this is identical to yesterday's situation except that HH now has
a fitness differential t

[skipping the derivations]:


delta q = pq (tp - sq) / (1 - spsquared - tqsquared)

and skipping more maths:

(basically where sq = tp, there will be zero on the top line)

the equilibrium frequency of q is:

q = s / (s + t)

If you plot this, you can see that the stable state of q = 0.316, is only
achievable when t = 0.42

There is, of course, no empirical evidence for this. But unlike the taboo
theory it is mathematically coherent. In this model, homosexuality neither
declines nor increases, but sits at a stable level maintained by the
hypotheisied advantage that the carriers have. Sociobiologists have always
felt that t = 0.42 is far too high to be plausible (I agree, it's far too
high), so consequently modelling of homosexuality has shifted into the
domain of kin selection.

But that one will have to wait for tomorrow.................


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