Re: Hamilton's rule
- From: Guy Hoelzer <hoelzer@xxxxxxx>
- Date: Sat, 22 Oct 2005 13:02:00 -0400 (EDT)
in article dj91v5$1t5o$1@xxxxxxxxxxxxxxxxxxx, Catherine Woodgold at
an588@xxxxxxxxxxxxxxxxxxx wrote on 10/20/05 2:24 PM:
> Guy Hoelzer (hoelzer@xxxxxxx) writes:
>> 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
>
> It will always have some influence. I like to look
> at things just at the fuzzy edge where they begin to
> disappear, so I might consider something important
> when someone else considers it "virtually" nonexistent.
In this case I meant something precisely measurable by "virtually no
influence", so Ohta's (and my) claim is not a matter of perspective. The
claim is that a neutral theory model, which assumes no influence of
selection, will effectively describe evolution when the equation above is
satisfied. This is an empirically testable claim.
> Prediction 1: If you look at a set of genes each of which
> is the same in almost all members of a species, you will
> find a fair number of places where changing one base pair would
> lead to an organism which is viable but with just slightly
> lower fitness, but it will be rare to find places where
> changing one base pair would lead to an organism with
> slightly higher fitness (unless maybe the environment is different
> from the one in which the organism evolved. Maybe rare
> even then.)
I expect these predictions are true.
> If Otah's claim as stated by you above and as understood
> by me is correct, then it would lead to a further prediction,
> something like the following:
>
> Statement 2, but which I'm not necessarily convinced is true:
> If an organism has had an effective number of organisms N
> each generation for a very long time, then when you take
> the set of genes each of which is the same in almost all
> individuals, you will find approximately the same number
> of loci where changing one base pair will increase the
> fitness by an amount less than 1/(2N), as loci where changing one
> base pair will decrease the fitness by an amount less
> than 1/(2N).
I'm not sure how my statements about Nearly Neutral theory would have given
you the impression that this prediction would follow. It does not, as I
understand the theory. The equation presented above only suggests that
evolutionary changes in frequency of mutations generating sufficiently small
fitness effects will not be influenced by selection, only drift. It makes
no claim about the relative number of mutations improving vs. diminishing
fitness.
> In other words, species which have had a small population
> size for a long time will tend to have room for improvement
> in many places in their genome.
Ah. This is a prediction I agree with, but it does not come from Nearly
Neutral Theory. It is, however, related to Carson's ideas on the evolution
of coadapted gene complexes.
> These statements are not quite well-defined because you
> need to fill in the other genes to get a whole organism.
> You could choose genes at random from the population a
> number of times and average over the result.
Agreed.
>> 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.
>
> When one forgoes social amenities, one tends to get
> punished and it affects one's fitness. That is not
> the kind of situation I'm talking about at all.
> For purposes of this discussion I would classify that
> along with having a mutation that makes you blind
> or something: it just decreases your fitness, that's
> all.
Thanks for keeping the discussion focused. :-)
>> This is not the situation addressed by Hamilton's model,
>> however. He asked how altruistic behavior could get started in an
>> essentially asocial system.
>
> There are lots of ways. For example, fetuses in the womb
> might happen to secrete substances that are beneficial
> to themselves. It might happen that these same substances are
> also beneficial to their littermates in the same womb.
> A mutation that causes them to secrete a larger amount of
> the substances would be an easy next step and could be
> an example of altruism which would follow a Hamilton-type
> rule (though I think the rule needs to be modified for
> the diploid case, as I think you already understand).
I like this hypothetical mechanism as a way to anchor the discussion. The
question Hamilton addresses in this context is whether the cost to the
individual of producing and secreting more of this substance than is optimal
for the individual considered in isolation will be favored by (kin)
selection given the social context in which the individual is embedded. He
concludes with Hamilton's Rule that (kin) selection will favor the spread of
the mutation if the average relatedness of individuals benefiting from the
excess secretions to the secretor is great enough, and the extent of the
benefit is great enough, to overcome the fitness cost to the secretor. How
much is "enough" is defined by the rule.
> Similarly, algae that grows in rows might secrete
> substances that benefit the algae next to it, which
> would usually be related to it. Again, it might
> start by just secreting substances that are useful
> to itself. It's not that hard to come up with
> examples of how altruism could begin, starting with
> a non-social species.
Right. When I said "how it could get started", I really meant how selection
could favor its increase in frequency. Sorry for my ambiguity.
>> IMHO the fitness effects of receiving altruism
>> would typically be quite modest in this situation.
>
> I think they could be quite important.
>
>> Similarly, failing to
>> receive altruism in a nearly asocial system would not effect fitness much
>> either.
>
> Yes, it would, if you're competing with organisms that
> have a slight advantage over you because they do
> carry out altruism with each other.
> Or: it could, if the substance being secreted
> is quite important to life, for example.
I think this could not be true in an asocial system (one in which the
secretion was previously unavailable). If it was important to life, then
how could the population have been successful in the past without it.
>> 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.
>
> No, I think it was you who mentioned the case where the
> altruism allele was common. You claimed that in that
> case the selection pressure would be small; I disagree.
>
>> 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.
>
> For now, I'm looking at a simplified model where
> there is no opportunity to play the tit-for-tat game.
> You just choose to be altruistic or not, and that's it:
> no one has the opportunity to use the information about
> whether you did or not. The tit-for-tat stuff is
> very interesting too but that's not what I'm
> talking about right now.
>
> Besides that, though, I see that you've already
> worked out some of the results I hope to present
> in algebraic form as soon as I have time.
>
>> 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.
>
> I definitely disagree. Non-altruistic mutations will tend to
> die out, just as other non-adaptive mutations will tend to die out.
How Panglossian of you. :-)
Guy
.
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