Re: Perpetually Perplexed

From: William Morse (wdmorse_at_twcny.rr.com)
Date: 01/23/05 

Date: Sun, 23 Jan 2005 15:18:43 -0500 (EST)

Guy Hoelzer <hoelzer@unr.edu> wrote in
news:csormi$g19$1@darwin.ediacara.org:

> in article csjdvd$1p8i$1@darwin.ediacara.org, Joe Felsenstein at
> joe@removethispart.gs.washington.edu wrote on 1/18/05 8:37 AM:

>> There is no assumption in Hamilton's work that the altruist
>> recognizes kin. This is a common misconception about the kin
>> selection argument. One does not need to adjust Hamilton's condition
>> for altruism "not being graded" (in Guy's terminology). The
>> calculation of the quantity r takes care of it.
 
> I don't know whether you had a chance to read the entirety of my post
> from which the quote above was taken, but I would very much like to
> get your response to my argument (as opposed to my naked conclusion).
> I appreciate the argument you provide above as a mean-field
> approximation to the problem. If the organism's altruism is expressed
> to a particular degree in all social interactions (b and c are
> invariant for all social interactions), then Hamilton's Rule would
> hold if r is calculated as the average of all social interaction
> weighted by the frequencies of interactions with individuals of
> differing relatedness to the actor. However, the restriction on
> holding b and c constant was certainly not part of many kin selection
> arguments made by Hamilton (and consider Haldane's famous presaging
> statement), and it is not the assumption in most of the empirical kin
> selection literature. For example, kin selection is most often said
> to be supported by evidence that altruism is preferentially aimed
> toward close kin, and Hamilton agreed with this perception. He (and
> I) agreed with your position that kin recognition and perfectly graded
> altruism were not necessary for kin selection to favor the spread of
> altruism, but that is a different issue from the precise tipping point
> prediction embodied by Hamilton's Rule.

> In sum, I agree that a mean field approximate model can be constructed
> that works, and which does not require perfectly graded (by
> relatedness) altruism. However, I would disagree if you are arguing
> that this is the only, or even the primary, model described by
> Hamilton. He, and the army of empiricists who followed him, was
> largely interested in kin-targeted altruism, whether or not kin
> recognition was involved. Under these conditions, the strength of the
> correlation between relatedness and expressed altruism affects the
> tipping point, which is what Hamilton's Rule aims to pinpoint. Where
> is the problem with this reasoning?
>
> Cheers,
>
> Guy
 

I would assume that the rb is generally calculated as the sum of the
individual interactions rsubi x bsubi for i = 1 to N, where N is the
population of interactors. .(I am not at all familiar enough with the
literature to know what Hamilton thought). But I fail to see why this
requires b to be graded, perfectly or otherwise, with respect to r. One
could assume that many "altruistic" interactions will not in fact be
graded, but because interactions tend to occur in a small population of
closely related individuals, the r will be significant even if the b is
indiscriminate.

If you are assuming that c is directly proportional to b (I am giving
money to my relatives, so the money I have is decreased by the total of
the money I give out), then there is an obvious advantage to graded
altruism - for a given c, I maximize the ratio of rb to c by grading b
based on r.

But in many cases there will be no such relation between b and c. I may
give an alarm call that has a fixed cost no matter how many relatives are
within earshot. Or my cost (getting eaten by a bird because I am
brightly colored) may only benefit those who actually carry the allele,
regardless of their calculated relatedness. Hamilton's rule still works
quite well in these cases - the behavior will spread as long as the net
change in inclusive fitness is positive.

And I think that evidence that altruism is preferentially aimed towards
kin is taken as supporting a kin selection mechanism is that otherwise
there are competing hypotheses, such as reciprocal altruism or selection
for groups that contain altruists, that can also explain the apparent
altruism.

Yours,

Bill Morse

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