Re: Hamilton's rule
- From: Guy Hoelzer <hoelzer@xxxxxxx>
- Date: Wed, 19 Oct 2005 19:14:06 -0400 (EDT)
in article dj603t$kb4$1@xxxxxxxxxxxxxxxxxxx, Catherine Woodgold at
an588@xxxxxxxxxxxxxxxxxxx wrote on 10/19/05 10:34 AM:
> Guy Hoelzer (hoelzer@xxxxxxx) writes:
>> in article dj1v9g$1p6k$1@xxxxxxxxxxxxxxxxxxx, Perplexed in Peoria at
>> jimmenegay@xxxxxxxxxxxxx wrote on 10/17/05 9:56 PM:
>> As we know from Ohta's Nearly
>> Neutral Theory, very weak selection pressure is virtually the same as no
>> selection pressure at all, leaving alternative alleles free to drift.
>
> (A)
> Only if it's really extremely weak. Suppose it's so weak that
> in the time it would normally take for genetic drift to wipe out
> a gene that started as being in half of a large population, the
> weak selection pressure only increases the number of individuals
> with the gene by 1. Well! The gene has just greatly increased
> its chance of survival, then, hasn't it? Instead of being
> completely wiped out, there's still this one individual with
> it. It would then have something like a 50% chance of
> soon getting completely lost, and a 50% chance of continuing,
> with perhaps about as much chance of taking over the whole
> population by genetic drift as of being wiped out later.
>
> I consider weak selection pressure to be a very important
> factor in evolution. To put it another way: you can neglect
> it if you choose to, but I find it quite interesting.
You might find Otah's work on Nearly Neutral Theory interesting reading.
Her theory predicts that selection will have virtually no influence when:
s <= 1/2Ne
for diploid populations (s = selection coefficient; Ne = effective
population size). You may consider this degree of selection to be large or
small, but the question is really how often does selection reach this degree
of intensity for traits with a reasonable amount of heritable variation. In
any case, this equation captures the point I was making.
>> My
>> contention is that the extent of kin selection pressure (the strength of kin
>> selection) becomes very weak as the altruism allele becomes common.
>
> (B)
> I disagree. Even if 99.99% of the population has the altruism
> gene, the individuals who do not have it face a quite significant
> probability that their siblings and close relatives don't have
> it either: something on the order of 0.5, 0.25 etc., not 0.0001.
> This lack of the gene in their siblings can then provide quite a
> considerable impact on the fitness of those individuals
> without the gene, causing considerable selection pressure against
> individuals without the gene.
I think we have pretty different expectations of the strength of selection
generated by altruism. In a mature social system, cooperation and altruism
may have become critical for successful participation in the society. At
this stage it could indeed be very damaging to one's fitness if they forego
social amenities. This is not the situation addressed by Hamilton's model,
however. He asked how altruistic behavior could get started in an
essentially asocial system. IMHO the fitness effects of receiving altruism
would typically be quite modest in this situation. Similarly, failing to
receive altruism in a nearly asocial system would not effect fitness much
either. We often imagine large effects to help us understand the model, and
I think this is very useful. My skeptical view of the role of kin selection
in nature, on the other hand, comes from the next phase of model processing
where you narrow the realm of the model to realistic parameter values. We
may disagree on that range, but that is a purely empirical question.
It is interesting that you flip the coin this way to consider the
disadvantage of being in a family without the altruism allele, rather than
focusing on the advantage of being in a family with the altruism allele. It
is a good way to make your point. On the other hand, relatedness (r)
becomes a poor criterion for discriminating those likely to carry the allele
from those unlikely to carry the allele once the allele reaches intermediate
frequencies. At that point, an altruist would do just about as well by the
altruism allele to distribute its generous behaviors randomly, and that
might avoid costs of kin discrimination. At that point the altruist would
do even better by the altruism allele to play the tit-for-tat game, than it
would through kin discrimination. Another factor that diminishes the
strength of kin selection at intermediate frequencies of the altruism allele
in my view is that the effectiveness of kin selection would be optimized by
being twice as altruistic toward homozygotes compared with heterozygotes.
To the extent that heterozygotes benefit by receiving altruism, they
increase the frequency of the less common allele. When the altruism allele
exceeds a frequency of 50%, altruism toward heterozygotes has the net effect
of favoring the non-altruistic allele. Of course, altruism toward
heterozygotes is a key to the effectiveness of kin selection when the
altruism allele is very rare.
>> In
>> fact, I think it would typically become negligible even at intermediate
>> frequencies of the altruism allele (say above 20 or 30%).
>
> I completely disagree (see two arguments above).
Consider my counter arguments.
>> To be clear, the validity of the kin selection model is NOT dependent on
>> allele frequencies, however the influence of kin selection over the
>> evolutionary process IS dependent on allele frequencies. I am not arguing
>> that kin selection is an example of a frequency dependent selection model.
>
> To be honest, I don't understand the above paragraph at all.
I'm not sure how to say it more clearly, or rather how to say it in a way
that would work for you. Try this. The distinction I am making is
analogous to the distinction between statistical significance and biological
significance. The former is utterly unimportant in the absence of the
latter. Regarding kin selection, I am arguing that the logic of the model
is equally valid for all frequencies of the allele, hence the validity of
your coin flipping perspective above, but that the evolutionary force
generated by kin selection becomes so weak when the altruism allele is no
longer rare that it loses its relevance to the evolutionary process.
>>> Or are you saying that 'rb>c' remains valid in determining the direction
>>> of the evolutionary force, regardless of frequency, but that the
>>> magnitude of the force depends upon frequency? If that is your position
>>> then I apologize unconditionally.
>>
>> Oops. I should have read this first. This is indeed my position.
>>
>> Guy Hoelzer
>
> I would need a quantifiable definition of "evolutionary force"
> before I could decide whether I agree with the above.
> I suspect I disagree with it (see my argument labelled "(B)" above).
I am tempted to bring up the issue of response to selection, but that is
called "R", which has been co-opted in this discussion for a different
meaning. This wouldn't be directly responsive to your request anyway.
One standard way to quantify the force of selection is with the selection
coefficient. [Jim McGinn - Please don't jump all over me for using the term
"force" improperly. I am admittedly using it in a metaphorical sense as
applies universally in discussions of evolutionary "forces."] The selection
coefficient is he difference in relative fitness between the best-adapted
phenotype (or genotype in Pop Gen models) and that of some other, less
well-adapted phenotype (or genotype). Selection is generated by fitness
differences and the selection coefficient aims to measure the extent of
those differences. Under standard population genetic models of natural
selection (assuming infinite population size to eliminate drift), the
strength of selection can be measured directly as the rate of change in
allele frequencies in a population, and it can be nicely estimated by
considering the fitness difference between pairs of individuals selected at
random in the population.
Guy
.
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