Date: Fri, 30 Apr 1999 09:57:07 +0200
From: "Gatherer, D. (Derek)" <D.Gatherer@organon.nhe.akzonobel.nl>
Subject: RE: JASSS Critical Review of Thought Contagion
To: "'memetics@mmu.ac.uk'" <memetics@mmu.ac.uk>
Aaron:
Anyone who knows enough about mathematics in the sciences
Derek:
Well actually I have 4 published papers in mathematical genetics and 1 in
press, but I'll let that typically Lynchian comment pass..........
Aaron:
Anyone who knows enough about mathematics in the sciences knows that
equations do not need to be based on prior work in a different field. The
equations were freshly developed, and were not adaptations of
epidemiological equations.
Derek:
That's a very strange comment Aaron, you make it sound like you are working
in an intellectual vacuum. When Cavalli-Sforza and Feldman presented their
treatment of horizontal transmission back in 1981, they were quite happy to
acknowledge their debt to mathematical epidemiology going back several
decades. You, as a mathematician, must know what are the intellectual
sources of your work. If your equations look like those previously
developed by epidemiologists, then they are epidemiological equations or
derivatives thereof.
For instance in what follows I am quite happy to admit that I draw on
Fisher's work from the 1930s, and all the textbnook versions since then. I
would not be so presumptuous, or divorced from reality, as to claim that it
is 'freshly developed'.
You claim that:
"As the taboo [ie. against homosexuality] 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."
This won't happen. Even if there is no selection pressure against a 'gene
for homosexuality' (let's make the standard sociobiological assumption that
there is such a thing), then it will not 'gain prevalence'. In fact it is
perfectly possible that it might go extinct.
Imagine a population in which there is a gene for homosexuality S1 with
frequency p. The corresponding gene for heterosexuality S2 therefore has
frequency 1-p.
Let's assume that there is a net mutation rate, u, to homosexuality
[mutation rates occur in both directions, but net mutation rates, for
obvious reasons are always towards the least prevalent allele], then the
rate of increase of S1 in time, t, is:
dp/dt = up
and therefore:
dp/p = u dt
thus:
ln p = ut + ln c
where c is a constant, so:
p = ce[to the power ut]
At time t=0 (whenever we choose that to be), the frequency of p can be said
to be p0
So at t=0 we calculate p0:
p0 = ce[to the power u0]
ie:
p0 = c
thus, for all t after t=0:
p = p0e[to the power ut]
But what is u under normal circumstances? The empirically determined answer
is about 10[to the power -5]
So if we want significant change to occur in the value of p, we will have to
wait a while. How long?
Let's imagine that homosexuality is recessive (a la Dean Hamer) and that 1
in 100 men are initially gay. That means that p0-squared = 0.01, so p0 =
0.1
then:
p = 0.1 e[to the power 10e-5 t]
so for p to climb to its estimated present level (i in 10 men gay, p = 0.32)
0.32 = 0.1 e[to the power 10e-5 t]
3.2 = e[to the power 10e-5 t]
ln 3.2 = 10e-5 t
which makes t about 116315 generations or approximately 3 million years
So your statement:
"As the taboo [ie. against homosexuality] 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."
is superficially plausible, but even the most perfunctory mathematical
treatment (eg. above)shows it to be false. You have committed what
geneticists call the 'eugenicist's fallacy' [of course you are not a
eugenicist, that's just the name of the fallacy] which is the assumption
that if selection _against_ a trait is removed that trait will increase to
an appreciable frequency. The fact that homosexual men reproduce at the
same rate as heterosexual men (because for instance there is a taboo and
they are socially obliged to father kiddies) will not cause any increase in
homosexuality alleles within historically appreciable time. It will only
work if you assume that the taboo against homosexuality originated about 3
million years ago.
In order for homosexuality to increase, it must be positively advantageous.
There is plenty of work on this in the context of kin selection, the classic
review being, of course:
Ruse M (1981) Are there gay genes? Sociobiology and
homosexuality. J Homosex 1981 Summer;6(4):5-34
and much has been done since
This is what Paul means when he says you ignore the literature. He isn't
just sating that you ignore what we might call the grand synthetic works of
cultural evolution, but that you ignore the literature even in those narrow
areas where you present your speculations.
That's the difference between a hypothesis and mere speculation. A real
hypothesis is couched in terms of the intellectual landscape, the work that
people have done before. It isn't 'freshly developed'.
Incidentally, Fisher's treatment above assumes that the effective population
size Ne is infinite. Alleles may experience sudden increases or decreases
in frequency with a probability 1/2Ne, as Motoo Kimura demonstrated back in
the 60s. However, in historical time, Ne for human populations is probably
quite large, unless you assume that homosexuality originated in a
reproductive isolate etc., but I see no reference to any of those standard
evolutionary possibilities in your work.
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