Re: Hamilton's rule


"Guy Hoelzer" <hoelzer@xxxxxxx> wrote in message news:dldgfc$1drk$1@xxxxxxxxxxxxxxxxxxxxxx
> in article dl58qa$p8l$1@xxxxxxxxxxxxxxxxxxx, Catherine Woodgold at
> an588@xxxxxxxxxxxxxxxxxxx wrote on 11/12/05 9:29 AM:
>
> > Guy Hoelzer (hoelzer@xxxxxxx) writes:
> >> My confusion is rearing its ugly head again. If the axes of the graph are
> >> "frequency in focal individual (Y axis) vs frequency in population (X
> >> axis)", then I don't see how dominance/recessiveness can influence the lines
> >> at all. What am I missing?
> >
> > One of the lines is labelled "donor". The only individuals
> > who act out the "donor" phenotype are the ones which have
> > the set of genes that code for altruism. If altruism is
> > a recessive trait, then all of the "donors" must have
> > two copies of the altruism gene. Therefore the frequency
> > in the "donor" focal individual is always 1 if altruism
> > is a recessive trait.
> >
> > But if the altruism gene
> > is dominant, then the set of "donors" includes some
> > individuals with one copy of the gene and some individuals
> > with two copies of the gene. If an individual is
> > observed to carry out an altruistic act, or if it
> > finds itself experiencing an overwhelming urge to
> > carry out an altruistic act, then an observer
> > (or the organism itself) can conclude that the
> > individual has one or two copies of the altruism gene.
> > The expected frequency in this individual can thus be
> > predicted to lie between 0.5 and 1 (closer to 1 if
> > the altruism gene is very common in the population).
>
> Maybe I should have said more. All of this was apparent to me. In the
> artificially restricted world of modeling perfect dominance/recessiveness
> the starting point of the donor line would be 0.5 (pure recessiveness) or
> 1.0 (pure dominance). In either case, however, there is a simple linear
> relationship on the frequency/frequency graph that converges on the point
> (1,1). The comment you quoted above came from a discussion where I thought
> it was implied that the shape of the relationship (e.g., linearity) was said
> to depend on dominance/recessiveness. I may have been reading too much into
> Jim's comments, which I still think reached way outside the scope of the
> simple frequency/frequency graph.

Reached way outside how? My claims are fairly simple:
- If the (single) altruism locus is purely recessive, the graph of allele
frequency in donors is a constant 1.0. (Obviously).
- If the altruism locus is purely dominant, the graph of allele frequency
in donors rises linearly from 0.5 to 1.0 as the allele frequency in the
population rises from 0.0 to 1.0. I am uninterested in a 'glitch' in
this curve at allele frequency exactly 0.0 - there technically are no
donors at exactly this frequency.
- Given other assumptions about gene expression besides pure dominance or
recessiveness, it is possible that the donor line may be something other
than linear. That doesn't matter as long as the donor D line never drops
below the 45 degree population P line. Regardless of how the line runs,
or of how many loci are involved, it remains the case that the recipient
R line lies a fraction 'r' of the way up from the P line to the D line.
This fact is a consequence of the definition of IBD 'r' and the assumption
of random mating. This fact is all that is needed to establish
Hamilton's rule. The rule does not depend on linearity. The frequency
independence of the rule does not depend upon frequency.
- What MAY depend on frequency is how fast the altruism allele spreads.
That will depend upon just how separated the lines are, and the count
of altruists (or of acts of altruism, depending on what b and c measure).
It will also depend on the size of b and c. I offered my straight lines
as an argument against YOUR claim that the impetus toward the spread of
the altruism alleles pretty much peters out at gene frequencies of 30-40%.

So, I have to ask, what exactly are your claims? Do you still believe that
the spread of kin-selected altruism peters out at this level, and that only
reciprocity can take things further? If so, what kind of D and R curves
are you postulating? And why do you think the curves have that shape?


.

Relevant Pages

  • Re: Hollowness of Hamiltons Rule
    ... > carries the gene for altruism, ... > to its fitness, which means that it will pass on fewer copies of the ... selection event has ever been documented ...
    (sci.bio.evolution)
  • Re: Holowness of SBE
    ... > can be characterized as a kind of altruism to individuals with an ... only additive gene by gene information is heritable, ... of selection, as Hamilton was. ... gene level of selection forcing organism fitness ...
    (sci.bio.evolution)
  • Re: Perpetually Perplexed
    ... Hamilton's incomplete fitness total rb it ... Once again no Darwinian altruism ... gene level of selection within the bodies ...
    (sci.bio.evolution)
  • Re: Hamiltons Nonsense
    ... What are the preadaptations for altruism? ... is parental nurturing. ... nurturing behaviors/morphologies. ... "What we are interested in is under what circumstances a "gene for" ...
    (sci.bio.evolution)
  • ISRAELI RESEARCHERS FIND ALTRUISM GENE
    ... Israeli researchers find 'altruism gene' ... The first gene linked to altruistic behavior has been ... Ebstein, a psychologist, and colleagues at the Hebrew ...
    (sci.med)