Re: Hamilton's rule


"Joe Felsenstein" <joe@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message news:dk0krn$2mla$1@xxxxxxxxxxxxxxxxxxxxxx
> In article <djr59g$9ns$1@xxxxxxxxxxxxxxxxxxx>,
> Perplexed in Peoria <jimmenegay@xxxxxxxxxxxxx> wrote:
> >
> >"Joe Felsenstein" <joe@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in
> >message news:djoo5q$2a2j$1@xxxxxxxxxxxxxxxxxxxxxx
> >> In article <djkei9$gs6$1@xxxxxxxxxxxxxxxxxxx>,
> >> Jim McGinn <jimmcginn@xxxxxxxxx> wrote:
> >> >
> >> >Perplexed in Peoria wrote:
> >> >> "Tim Tyler" <tim@xxxxxxxxxxx> wrote
> >> >
> >> >> But lets define a new number M (for McGinn) which is the % similarity
> >> >> between donor and recipient measured at the base pair level. And
> >> >> let us also define a number T (for Tyler) which is the average
> >> >> % similarity between the donor and a random member of the population.
> >> >>
> >> >> Then, it is the case that (M-T)/(1-T) is pretty much the same thing
> >> >> as Hamilton's 'r'.
> >> >
> >> >Let's see if this checks out:
> >> >
> >> >M = 99.9%
> >> >T = 99.5%
> >> >
> >> >(99.9% - 99.5%) / (1-99.5%) = 0.4% / 0.5% = 0.8
> >> >
> >> >I can't make any sense of this. 0.8 = 50%?
> >>
> >> If r = 0.5, one is talking about full sibs. And for that case the
> >> number T that McGinn chooses is wrong. If a random pair of genes
> >> from the population has M = 0.995, then what is the value of T?
> >>
> >> Well, in a pair of full-sibs, the probability that a particular
> >> gene in the recipient is a copy of the same parental gene as one randomly
> >> chosen from the donor is 0.25. So 25% of the time, a random copy in the
> >> recipient is 100% identical to the copy in the donor, and the other
> >> 75% of the time it is a copy of a different parental gene, one that
> >> is expected to be 99.5% similar. So
> >>
> >> T = 0.25 (1.0) + 0.75 (0.995) = 0.99625
> >>
> >> Actually Tyler's formula then does not work out, because the r Hamilton
> >> uses is not the probability that a random gene from the recipient is
> >> IBD to the gene in the donor. It is the expected number of copies
> >> IBD, which because there are two copies of the gene in the recipient
> >> is twice the 0.25. Tyler's formula gets the 0.25 (not 0.5):
> >>
> >> (0.99625 - 0.995) / (1 - 0.995) = 0.00125 / 0.005 = 0.25
> >>
> >> which once one makes the factor of two adjustment is fine.
> >
> >Well, let me start by clearing up a misunderstanding. The formula
> > r = (M - T) / (1 - T)
> >is my formula, not Tyler's.
> >
> >I admit that I have thought carefully about this formula only in the
> >haploid case. Your arithmetic casts considerable doubt upon the
> >validity of the formula in the diploid case. Exactly where in this
> >formula am I supposed to stick that 'factor of two adjustment'?
>
> I found the formula was fine if you end up by multiplying it by
> two. That two is the ploidy (diploid in this case). Your formula,
> for haploids, computed the expected number of copies in the recipient
> identical to the one in the altruist. With diploidy you have this
> for both genes so there is another factor of two.

I get it. So the correct formulas are r = (M-T)/(1/T) for haploids
and r = 2(M-T)/(1-T) for diploids.
Furthermore, M is the probability that a specific segment (a base pair
or larger) in one chromosome of the donor is identical to a randomly
chosen (two choices) homologous segment in the recipient. T is the
corresponding probability when the role of 'recipient' is taken by
a randomly selected member of the general population.



.

Relevant Pages

  • Re: Hamiltons rule
    ... >>> between donor and recipient measured at the base pair level. ... >>> % similarity between the donor and a random member of the population. ... > gene in the recipient is a copy of the same parental gene as one randomly ...
    (sci.bio.evolution)
  • Re: Hamiltons rule
    ... >> between donor and recipient measured at the base pair level. ... >> % similarity between the donor and a random member of the population. ... gene in the recipient is a copy of the same parental gene as one randomly ...
    (sci.bio.evolution)
  • Re: Hamiltons rule
    ... >> gene in the recipient is a copy of the same parental gene as one randomly ... >> chosen from the donor is 0.25. ... >what is meant by '% similarity'. ...
    (sci.bio.evolution)
  • Re: Hamiltons Nonsense
    ... [snip another insult] ... >> behavior caused by possession of this gene. ... "recipient" he meant the recipient of the behavior. ... to state clearly that "the probability that the gene was IBD" ...
    (sci.bio.evolution)