Re: Hamilton's rule

in article dlotn0$gsg$1@xxxxxxxxxxxxxxxxxxx, Perplexed in Peoria at
jimmenegay@xxxxxxxxxxxxx wrote on 11/19/05 8:22 PM:

> "Guy Hoelzer" <hoelzer@xxxxxxx> wrote in message
> news:dll6au$1qor$1@xxxxxxxxxxxxxxxxxxxxxx
>
>> OK. I think I see your logic on this point now. Let me try another taste
>> test, assuming that you agreed with my claim that the position of the R line
>> can vary and its mean position is a function of the distribution of 'r'
>> values from realized altruistic interactions in the population.
>
> The R line IS a mean. If you wish to call a simple mean 'a function of the
> distribution', I guess that is true.

OK. What would a mean be if not a function of a distribution? I was trying
to emphasize the idea that your R line can actually exist in any location in
your graphical space depending on who interacts with whom.

>> To tie this
>> discussion more closely to HR, I am also going to invoke 'b' and 'c'. I
>> think you are saying that if 'b' is marginally larger than 'c', then 'r'
>> must only be marginally greater than the average relatedness among
>> individuals in the population for kin selection to favor an increase in
>> frequency of the altruism allele.
>
> Aaaaaarrrrgh! I think that I AM talking to McGinn.
>
> If 'b' is only marginally larger than 'c', then 'r' must be near 1.0 in
> order to favor an increase in the frequency of the allele.

Right. Sorry for my ill-conceived statement. What I should have said was,
if c=0 and 'b' is marginally greater than 0, "then 'r' must only be
marginally greater than the average relatedness among individuals in the
population for kin selection to favor an increase in frequency of the
altruism allele." Of course, the allele shouldn't be called an altruism
allele when c=0, but I hope you get my point.

> The average relatedness among individuals in the population is close to
> zero.
>
> I occurs to me that 'r' has two meanings, and they may be becoming confused
> here. On the one hand 'r' is a measure of relatedness between two
> individuals. Any two individuals. On the other hand 'r' can also be taken as
> and average (over all acts of altruism) of the first kind of 'r', where the
> two individuals for each 'r' in the sample are the donor and the recipient.
>
> If you read Hamilton's rule as "If rb>c then the altruism allele will increase
> in frequency in the population", then you are obviously using the second kind
> of 'r'. But if you take the rule as "If rb>c, then the donor is advancing
> his genetic interests", then you are obviously using the first kind of 'r'.
> I wouldn't think there should be any confusion between these two meanings,
> but you seem to be confused by this. Or, you are convinced that I am
> confused, so you are just not understanding what I am saying. Or perhaps
> I am confused, but I don't think so.

I agree that the mean field 'r', versus the specific event 'r', can be a
source of confusion. Maybe it is part of our difficulty, but I'm not sure.
I think there are other problems, too, that are interfering with our
communication about your graphical approach. I confess that I still don't
see how it fully integrates with Hamilton's model, or how it helps us to
understand kin selection. I'd be happy to drop the discussion of it here
unless you want to explore my confusion further. :-)

Guy


.

Relevant Pages

  • Re: Hamiltons rule
    ... The average relatedness among individuals in the population is close to ... If you read Hamilton's rule as "If rb>c then the altruism allele will increase ... then you are obviously using the first kind of 'r'. ... I wouldn't think there should be any confusion between these two meanings, ...
    (sci.bio.evolution)
  • Re: Perpetually Perplexed
    ... There seems to be confusion over the point of Hamilton's rule. ... selection tends to decrease the frequency of the altruism allele ... the tipping point at which kin selection would ... > There were other, smaller, logical lapses in Dr. Hoelzer's remarks, ...
    (sci.bio.evolution)