Re: Hamilton's rule
- From: "Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx>
- Date: Sat, 15 Oct 2005 01:22:44 -0400 (EDT)
<name_and_address_supplied@xxxxxxxxxxx> wrote in message news:dioln6$uug$1@xxxxxxxxxxxxxxxxxxxxxx
> The sequence similarity / proportion of identical genes
> distinction is a red herring. Hamilton was fundamentally after an
> explanation for why certain unselfish *phenotype* abound in the natural
> world -- e.g. altruism. He started by constructing the usual one locus,
> two allele models that are standard as a first grasp at population
> genetical problems, and derived the results presented in 1963 and 1964.
> But there was a more general principle at work, which he elucidated in
> his 1970 paper. Say we have a three allele model, where two alleles are
> different in sequence and yet code for exactly the same altruistic
> phenotype, and the third allele codes for selfishness. In terms of
> molecular evolution it may be interesting to follow the dynamics of
> these three alleles. But in terms of the evolution of altruism -- which
> is what Hamilton was, and I am, interested in -- we might as well count
> the first two alleles as a single altruistic variant.
>
> Hopefully this will help to illustrate why sequence similarity and
> proportion of identical genes are besides the point. What is crucial is
> that relatedness measures a statistical association between social
> partners. If the only cause of this statistical association is
> coancestry, and in the majority of cases assuming this is so will lead
> us to a very good approximation, then we may phrase relatedness in
> terms of probabilities of identity *by descent*. However, other causes
> of statistical associations are possible, for example due to
> environmental sorting of individuals with similar (or dissimilar)
> phenotypes. Say there is a genetic basis to prefering red wine rather
> than white wine. Then statistical associations at the wine-preference
> loci will tend to emerge between individuals standing close together at
> wine stores, because their environment has sorted them according to
> their genetics. Hamilton was quite aware of this, but he realised that
> this genetic association (relatedness) would not select for altruism in
> the wine-store model, because it is the relatedness at the altruism
> loci and not at the wine-preference loci that is of interest. Hamilton
> did suggest the greenbeard example -- essentially, where the
> wine-preference and the altruism are pleiotropic effects of the same
> gene -- to illustrate selection for altruism not based on coancestry.
Thanks for you posting agreeing with me. However, ...
At the risk of sounding like Edser here, I must offer my opinion that
the 1970 version of the rule may be good mathematics, but it is bad
biology. In fact, it is not biology at all. It is a mathematical
tautology based on Price's theorem, which, as Price himself points
out, makes no assumptions about mechanisms of heredity or anything of
that sort.
If no biological information goes into the derivation of the rule,
how can we extract biological conclusions from the rule?
What you (and Hamilton) have done to arrive at your "green beard"
conclusion is to insert some hidden biological assumptions into
your application of the rule. And those assumptions seem pretty
dubious to me, biologically speaking. You are implicitly assuming
that a statistical relationship (covariance) between wine preference
(or beard color) and altruism will be stable from one generation
to the next. That might be possible if both genes are closely linked
on the same chromosome. But then what about all of the other genes
which have a small epistatic effect on altruism or on wine preference.
Unless they are also linked, their frequency is going to change over
time in a way that decreases the statistical correlation between
altruism and wine preference.
As Steve Frank and others have pointed out, Price's equation is
'dynamically insufficient' to supply a model of natural selection
over several generations. Feed into it a set of starting gene
frequencies and the relevant variances and covariances, and out
pops a set of gene frequencies for the next generation. But you
don't get a new set of variances and covariances. If you insert
the hidden assumption that they don't change, then you are inserting
a hidden biological assumption - an assumption that is almost
certainly false in the real biological world.
I much prefer the 1964 version of the rule which is based upon
an explicit biological assumption - independent Mendelian segregation.
An organism that practices kin-selected altruism with rb>c is
increasing the frequency of ALL of its genes in the population -
not just the few that predominantly affect wine preference, beard
color, or altruism.
.
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- Hamilton's rule
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