Re: Underestimating 'r'
- From: "Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx>
- Date: Tue, 4 Oct 2005 21:18:11 -0400 (EDT)
"Tim Tyler" <tim@xxxxxxxxxxx> wrote in message news:dhml43$1f57$1@xxxxxxxxxxxxxxxxxxxxxx
> Criticisms of Hamilton's thinking in this group are common - and
> rarely seem to be received very well, so it's with some hesitation
> that I post on a related subject.
Actually, criticisms of Hamilton's thinking are very rare. What is
common is criticism of strawmen - criticisms of false notions as to
what Hamilton's thinking was.
> One of the fairer criticisms of Hamilton's thinking I've seen here
> is the idea that "r" is being consistently under estimated.
And I think we are about to see another attack against a strawman.
> It's common to calculate "r" by using a truncated family tree - and
> ignore relationships between great grandparents as being of low
> relevance.
>
> Such truncated trees tend to give lower values for relatedness
> than using a full tree would give.
True. But do they give a worse value? Do they give a value which
is less usefully employed in Hamilton's rule?
If we are looking at, for example, social behaviors which take place
between siblings - two cheetah cubs from the same litter, say, there is
no point in not truncating the tree. The right r to use is 1/2, even
if the population is somewhat inbred. The cub is competing within that
inbred population. It will have no particular good will toward a
third cousin if every other cheetah is a third cousin. And its good
will toward its sibling is not increased because its sibling is also
another third cousin.
> How much lower is a question difficult question. If calculating
> relatedness using hamming distnaces, the figure depends to some extent on
> the size of the units being compared - and how close a match is needed
> before two units are described as being related.
>
> Also, the figures may be significantly different for groups of organisms
> like cheetahs (an inbred group) and mice (an outbred one).
>
> If "r" between organisms in a group or species is *actually* higher
> than is commonly belived, that might contribute to group/species-level
> selection - the extent of the power of which is still the subject
> of some controversy and debate.
You seem to be agreeing with McGinn here that the absolute degree of
similarity between donor and recipient is important in the justification
for altruism. It is not. What is important is the degree to which
the recipient is more closely related to the donor than is a member
of the general breeding and competing population.
> Hamilton's rule talks about the circumstances under which a trait
> will spread through a population - but it doesn't itself consider
> the possibility of populations competing with one another - and the
> possibilty of high level selection trumping the effects of low-level
> selection.
>
> So - is "r" higher than convention would dictate; and if so - how
> much higher? Evidence I've previously posted relating to the
> frequency of SNPs (and other polymorphisms) suggests to me that
> it is higher - and significantly so - perhaps enough to make me
> 70% related to my mother - rather than the 50% convention
> dictates - and enough to make individuals quite a bit more
> than 0% related to other "unrelated" members of the population.
Well, if you use the 1970, regression, version of r, your relatedness
to a randomly selected member of the population is zero BY DEFINITION.
The fact that the untruncated IBD calculation of r gives a value
slightly greater than zero indicates a deficiency in the IBD
definition of r. It does not indicate that altruism should be
more common than we might think. There can not be any kin-selection
justification for even the slightest amount of altruism to randomly
selected conspecifics, regardless of how inbred the species is.
> If so, what's the practical effect of this? As far as I can
> tell, the effect would be pretty limited. It ought to make
> individuals behave somewhat altruistically to other members
> of their species. However there are a raft of other theories
> that predict this sort of thing (e.g. reciprocal altruism) -
> so the effect may be hard to tease out. It wouldn't make
> *much* difference to how relatives are treated - since
> their relative relatednesses would remain pretty much
> the same.
>
> Any comments about all this?
Google in this group for r_ibd_hat to see some of my previous postings
on this subject.
Also see discussion of this topic between Guy and myself on the thread
"Kin Selection Contradiction" around June 24, 2004.
> What's your personal estimate
> of "r" between, say, randomly-selected humans?
Regression (1970) r = 0.0000000...
IBD (1964) r = approximately 2 /6,446,131,399 as of July 2005
http://www.cia.gov/cia/publications/factbook/rankorder/2119rank.html
Hmmm. Actually these figures are for random selection 'with replacement'.
You probably intended 'without replacement'. So decrease both estimates
by 1/6,446,131,400 or so
.
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