Date: Wed, 05 May 1999 09:50:54 +0200
From: "Gatherer, D. (Derek)" <D.Gatherer@organon.nhe.akzonobel.nl>
Subject: Homosexuality gene-culture coevolutionary model part 3
To: "'memetics@mmu.ac.uk'" <memetics@mmu.ac.uk>
Every male is related to his children by a factor of 0.5, since he gives one
haploid genome to each fertilised egg. Likewise for females.
However, molecular genetic studies have demonstrated that non-paternity
within nuclear families in Western Europe runs at 10%. This means that the
average relatedness of a male to his children under such cultural
circumstance is not 0.5 but 0.5 times 0.9 = 0.45. Note that this is not the
case for females, who are never non-maternal except if they lose the baby
and accidentally pick up the wrong one.
How does this relate to the homosexuality model debate? The basic maths
behind kin selection theory originates with Haldane in the late 1940s, and
was developed fully by Hamilton in the early 1960s.
Imagine a society where male philandering is rife. Under such cultural
circumstances non-paternity would not be a modest 10% but may rise to say
50%. Then the average relatedness of a man to the babies he fondly imagines
are his children is only 0.5 times 0.5 = 0.25.
Now, a man knows that his sister's children are definitely his nieces and
nephews. Regardless of who the father[s] of said nieces and nephews might
be, a man is definitely related at 0.25 to his nieces and nephews (provided
his sister is his full sister). If male philandering rises above 50%, then
genes for paternal investment in children will be at a selective
disadvantage - looking at the equations I presented yesterday and the day
before, s will start to rise above zero.
A better strategy under such circumstances would be to abandon reproduction
and invest all resouces in one's sister's offspring. Alleles which tend to
reduce reproductive behaviour would therefore be favoured over those that
stimulate herosexual behaviour.
This does provide a mathematically correct model for the selective advantage
of homosexuality alleles under cultural conditions of high male
philandering. Remember that the only other cogent model for the spread of
homosexuality alleles is heterozygote advantage. If you think that neither
model is empirically plausible, then I'd be inclined to agree with you.
However, importantly, these are the only two models which stand up to
mathematical scrutiny using the Hardy-Weinberg equations as modified by
Fisher and the extended version of Fisher's work by Hamilton, Trivers et al.
There is another possiblity, which is that founder effect, some time in the
past, caused a situation where the effective population size Ne was reduced
to such a degree that a homosexual allele found itself at a high frequency
in some isolated population, and that this isolated population then expanded
rapidly. Cavalli-Sforza has shown that the first principal component of
genetic variation in European populations consists of a gene frequency cline
running out from what is now Turkey, Syria and Jordan heading northwest.
This has been taken to represent a Neolithic founding population spreading
into Europe about 7000 years ago. If that group had a small Ne initially,
homosexuality may have been 'accidentally' high. As the generations pass,
and the allele is subject to selection as a recessive deleterious, the level
will have fallen. Taboos may have slowed this process, but they won't (very
importantly) have resulted in any 'proliferation' of the allele or any
'fluctuations' in its frequency, other than intermittently downwards.
All the maths I have presented in these last few posts is standard
evolutionary theory. These are not my 'freshly prepared' equations, but the
heritage of neo-Darwinism, built up by a long line heading out from Hardy
via Fisher to Feldman etc. It's very important that we memeticists are
aware of our evolutionary mathematical heritage and use it in our work.
That way we are less likely to make embarrassing mistakes like the taboo
theory.
I had hope that Aaron might tell us what the 'major fallacy' is that he
claims he has found in standard evolutionary theory, but he hasn't, so I can
only infer that he is still 'exercising restraint'. I also hope that I have
demonstrated that we MemeLabbers are neither 'intimidated' by maths nor are
we merely 'social scientists who although symptathetic to memetics fail to
understand its quantitative theory'.
Derek
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