Re: Hamilton's rule


"Guy Hoelzer" <hoelzer@xxxxxxx> wrote in message news:dlvnf1$mea$1@xxxxxxxxxxxxxxxxxxxxxx
> in article dlotn2$gvg$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$1@xxxxxxxxxxxxxxxxxxxxxx
> >> in article dliqtb$ohd$1@xxxxxxxxxxxxxxxxxxx, Perplexed in Peoria at
> >> jimmenegay@xxxxxxxxxxxxx wrote on 11/17/05 12:58 PM:
> >>
> >>> "Guy Hoelzer" <hoelzer@xxxxxxx> wrote in message
> >>> news:dlh6sj$274$1@xxxxxxxxxxxxxxxxxxxxxx
> > [snip]
> >>>> Under your graphical model, which I accept as a representation of
> >>>> Hamilton's model, the strength of kin selection diminishes monotonically
> >>>> with the frequency of the allele.
> >>>
> >>> Well, if you mean that the difference between the inclusive fitness of an
> >>> altruist and the inclusive fitness of a member of the general population
> >>> decreases monotonically, then yes.
> >>
> >> That's right. Selection is generated by fitness differences, and the
> >> strength (effectiveness) of selection is determined by the extent of fitness
> >> differences.
> >>
> >>>> I guess you have swayed me to the position that
> >>>> under Hamilton's model, as opposed to a more realistic version of the same
> >>>> model, there is not a frequency threshold where kin selection becomes
> >>>> irrelevant. Instead, it becomes irrelevant monotonically.
> >>>
> >>> In the same way that any beneficial trait becomes irrelevant as more and
> >>> more of the population has that trait.
> >>
> >> Well, you have been arguing that it happens in a different 'way' because the
> >> strength of selection changes in a sigmoid fashion relative to frequency for
> >> 'ordinary' beneficial traits. A simple way to see this is to use Joe's
> >> freeware program called PopG, which simulates changes in allele frequencies
> >> under specified models of evolution. If you start a simulation with a
> >> beneficial allele in low frequency, you will see the sigmoid trajectory of
> >> its frequency by tracing the 'infinite population size' line that eliminates
> >> the noise of drift. While some aspects of the trajectory's shape will
> >> depend on dominance/recessiveness of the allele, it is always sigmoidal.
> >
> > I claim that the trajectory of the altruism trait is sigmoid in almost exactly
> > the same way that the trajectory of any other trait is sigmoid. Felsenstein
> > recently delivered himself of the same opinion.
>
> OK. Well, the effectiveness of selection is directly revealed by the slope
> of the line relating allele frequency to time. If the expected shape of
> this relationship is sigmoid, then one expects that selection is relatively
> ineffective at causing allele frequency change when the allele is very
> common.
>
> >>> But perhaps a better way to look at it is to compare the possessor of the
> >>> trait to (not the population average, rather to) an individual without the
> >>> trait. If you compare in this way, then I don't agree that the 'strength of
> >>> kin selection' decreases monotonically. Once the allele becomes fixed in
> >>> the population, there is still strong selection AGAINST mutations that
> >>> change the altruism allele to selfishness (i.e. ineffectiveness).
> >>
> >> Here I think you have contradicted yourself.
> >
> > I don't think so, though apparently I have contradicted your understanding
> > of what I said.
>
> You just said "I claim that the trajectory of the altruism trait is
> sigmoid", which is a claim that kin selection becomes ineffective when the
> altruism allele is very common. The effectiveness of drift does not
> diminish when the allele is very common, so the system is easily invaded by
> selfish alleles at low frequency. This idea is analogous to a genetic load,
> although it is specifically about selfishness as an alternative to altruism.
>
> >> While you have been convincing
> >> me of the validity of your argument along the way, that same argument
> >> persuades me that your last point is false. A largely altruistic population
> >> would be quite vulnerable to invasion and persistence of low frequencies of
> >> alleles for selfish behavior. If what you meant was that the largely
> >> altruistic population is unlikely to be replaced by a regime of selfishness,
> >> then I would agree.
> >
> > The easiest way to refute your latest claim is to note that Hamilton's
> > rule also applies to selfishness. Selfishness genes are contra-selected
> > if rb < c with b and c negative.
> >
> > If rb>c for altruism, then rb<c for selfishness. A selfish population is
> > subject to invasion by altruism, but an altruistic population is not
> > subject to invasion by selfishness.
> >
> > To repeat for the last time, Hamilton's rule, as an arbiter of what traits
> > are favored by selection, IS NOT FREQUENCY DEPENDENT.
>
> But, as you argued yourself by agreeing that you expect the trajectory of
> frequency increase by an altruism allele to be sigmoid, kin selection
> becomes ineffective when the allele becomes very common. My comments were
> meant to apply to real (finite) population, rather than hypothetically
> infinite populations. I have never argued that the direction of kin
> selection reverses when the allele becomes very common.

We appear to have three points of disagreement:

1. You seem to use 'intensity of selection' to describe the rate of allele
count increase (or decrease) as a fraction of the total number of alleles
(of all varieties) at that locus in the population. As such, you insist
that the derivative of the sigmoid curve gives 'intensity'. I am holding
out for a metric that measures 'intensity' by taking the ratio of allele
count change to the number of alleles of that type, or else to the number
of individuals expressing that phenotype.

I am too lazy to attempt to impose my language usage on you. However, if
you are more industrious and can cite authorities correcting my use of
language, it would be appreciated.

2. I use the term 'subject to invasion' to describe situations in which
there is no effective selective pressure to counter the invasion. You
apparently use the term more broadly to describe situations in which
countervailing selective pressure may exist, but it is insufficient to
counteract drift. Since the amount of selection pressure (the size of the
selection coefficient) needed to counteract drift is dependent on the
population size, you point out (correctly) that in small populations,
weakly counterselected alleles may drift to appreciable levels.

Again, I am too lazy to attempt to impose my own language, but would not
scorn authoratative correction.

3. Perhaps I am reading too much into your words, but you seem to be
arguing that there is something special about the social behaviors
covered by Hamilton's rule that make them behave differently at low
frequencies than traits that are more individualistic and self-directed.
I disagree. Social traits follow much the same logic as any other
trait. There is a p(1-p) factor which makes the intensity of selection
low (by your usage) at both extremes of allele frequency. There is also
a dominance/recessiveness effect that makes one tail or the other of
the sigmoid particularly flat. But there is nothing special about kin-selected
behaviors that provides additional flattening of the sigmoids.

Well, let me qualify that. Selection for social traits does involve the
presence of alleles in more than one individual. You need the allele in
the donor to express the trait, and you need at least an expectation of the
allele in the recipient for selection to favor the trait. So, there is a
kind of time delay in the effectiveness of selection. A new mutation does
not get into the dynamic flow of selection until several generations have
passed. In addition, there may be a factor significant in small populations
in which the 'effective' allele count in the population is (Np-1) or
(Np-2) rather than simply Np.


.

Relevant Pages

  • Re: Hamiltons rule
    ... >>> frequency of the allele. ... Selection is generated by fitness differences, ... I claim that the trajectory of the altruism trait is sigmoid in almost exactly ... >> altruism allele to selfishness. ...
    (sci.bio.evolution)
  • Re: Hamiltons rule
    ... Selection is generated by fitness differences, ... which simulates changes in allele frequencies ... >>> change the altruism allele to selfishness. ... although it is specifically about selfishness as an alternative to altruism. ...
    (sci.bio.evolution)
  • Re: Cost of sex - a bargain!
    ... Don't-Be-Asexual is not an 'allele' of Be-Asexual at all. ... If asexuals were ... The selection in this case is in the population as a whole, ... variant portion of the population (the sexuals) will undergo selective ...
    (talk.origins)
  • Re: Cost of sex - a bargain!
    ... Don't-Be-Asexual is not an 'allele' of Be-Asexual at all. ... in a functional sexual female. ... Selection is blind to the distinction between sexuals and asexuals. ...
    (talk.origins)
  • Re: Hamiltons rule
    ... >> selection pressure at all, leaving alternative alleles free to drift. ... >> selection) becomes very weak as the altruism allele becomes common. ... My skeptical view of the role of kin selection ...
    (sci.bio.evolution)