Re: Hamilton's rule

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.

Guy


.

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: Challenges for Evolutionary Ethics
    ... Altruism and selfishness are crossed-purposes, so-to-speak, nested ... biological altruism is based on kin selection/group selection. ... Apparently the two forms of selection aren't the same but in kin ...
    (sci.bio.evolution)
  • Re: Hamiltons rule
    ... Selection is generated by fitness differences, ... >>> strength of selection changes in a sigmoid fashion relative to frequency for ... which simulates changes in allele frequencies ... >> I claim that the trajectory of the altruism trait is sigmoid in almost exactly ...
    (sci.bio.evolution)
  • 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)
  • Re: Kin Selection contradiction?
    ... > allele within those few generations is also small. ... never addresses the issue of genetic control over altruism. ... a fraction r containing genes IBD to genes in the actor; ... Calculate the total and per capita costs of altruism. ...
    (sci.bio.evolution)
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