Re: Haldane's Hangover
From: Guy Hoelzer (hoelzer_at_unr.edu)
Date: 01/26/05
- Next message: Jason: "Molecular Evolution"
- Previous message: Tim Tyler: "Re: Can viruses transfer genetic material between individuals ?"
- In reply to: Perplexed in Peoria: "Re: Haldane's Hangover"
- Next in thread: Perplexed in Peoria: "Re: Haldane's Hangover"
- Reply: Perplexed in Peoria: "Re: Haldane's Hangover"
- Messages sorted by: [ date ] [ thread ]
Date: Wed, 26 Jan 2005 11:41:10 -0500 (EST)
in article ct61nn$1v5n$1@darwin.ediacara.org, Perplexed in Peoria at
jimmenegay@sbcglobal.net wrote on 1/25/05 10:04 AM:
> "Guy Hoelzer" <hoelzer@unr.edu> wrote in message
> news:ct4l3j$1g93$1@darwin.ediacara.org...
>> in article csu4eg$2a8m$1@darwin.ediacara.org, Joe Felsenstein at
>> joe@removethispart.gs.washington.edu wrote on 1/22/05 10:01 AM:
>>
>>> In article <csorml$g5r$1@darwin.ediacara.org>,
>>> Jim McGinn <jimmcginn@yahoo.com> wrote:
>>>> Perplexed stated:
>>>>
>>>>> . . . my children have half copies of my genome
>>>>> (r = 0.5) so a certain amount of parental care
>>>>> looks like it would be in my interests. But my
>>>>> nephews also have partial copies of my genome
>>>>> (r = 0.25) so, . . .
>>>>
>>>> Did anybody else notice that Perplexed fell back
>>>> into Haldane's fallacy? It's subtle, I know, but
>>>> that's why it's so difficult to overcome.
>>>>
>>>> Perplexed, both your children and your nephews
>>>> have copies of over 99.9% of your genome.
>>>
>>> There is no fallacy but some slightly misleading terminology.
>>> When someone says that my genome is 50% similar to my
>>> brother's they are thinking not of DNA-level similarity
>>> (which is 99.9%) but of Identity by Descent. This isn't
>>> always made clear...
>>
>> Thanks for saying this so clearly and directly, Joe. I would only specify
>> it a bit further to say that the IBD calculations you refer to are limited
>> to looking back in time only a single generation. IBD calculations are
>> ambiguous unless such a limitation is obeyed. Indeed, in finite populations
>> the value of IBD goes up as one includes more ancient generations due to the
>> presence of cycles in pedigrees (inbreeding).
>
> Yes, it goes up as you increase the number of generations. But it
> doesn't go up by much. (And it definitely does not approach 1 as
> the number of generations-back goes to infinity.)
You really can't make any such blanket statement, because the way that IBD
changes with depth of the pedigree depends strongly on both population size
and mating system.
> However, the consequences of inbreeding may be different than you
> think. Suppose that we are investigating altruistic behavior
> between full sibs in a species with complete monogamy. The
> behavior only is expressed between sibs - it is something that
> happens in the nest, for example. We might use r=0.5 for this
> situation. But suppose we now discover that this population
> is very inbred. That still doesn't mean that we need to increase
> r. If the population bottleneck is recent, the extent of altruism
> that we find in the population may be an adaptation to a less
> inbred past, so using r = 0.5 may still be right.
OK. I don't think this is inconsistent with anything I have posted.
> But suppose we know that this species has always been small, and
> we calculate that the average IBD relatedness of sibs would be
> r = 0.55 if the geneologies were pushed back "all the way".
I'm sure that you are assuming random mating here, which is fine as long as
we recognize it. Even so, the mean IBD value among sibs could be much
higher than this. It depends on how small your small is. I haven't done
the calculation under the random mating assumption. If you have, can you
tell us the size of the population that yields an average IBD of 0.55, and
how many generations you are reaching back?
Just to be a pain about it, I will also point out that the use of average
IBD values between siblings can obfuscate a huge variance within the
population regarding those values. Using such a mean field approximation
represents an assumption that the extent and possible structure of all that
variation has no important effects. I don't know whether it does, and I
doubt anybody has considered this in publication, so it might.
> Does
> this species have a greater tendency for full-sib altruism than
> does one with r = 0.5? I'm not convinced that it does.
I agree, because in your model inbreeding is raising the mean field
expectation of relatedness among all individuals in a way that is
monotonically related to IBD relatedness. If you introduce inbreeding
structure to the mating system, instead of more diffuse inbreeding by making
the population small, you can probably see that you would get a different
outcome. If mates tend to be close relatives, then full siblings have
higher IBD values (on average), but the mean relatedness among random pairs
in the population does not change. Under this scheme, the species probably
would have a greater tendency for full-sib altruism than does one with r =
0.5. Do you agree?
> The logic
> behind the rule is that you should be particularly nice to those
> who are more related to you than is the general population. But
> in the case of an inbred population, EVERYONE, all your competitors,
> have some small relatedness to you.
Yup. I'm not sure why you thought these points would surprise me.
> In the 1963 and 1970 papers, Hamilton said that r is a regression
> coefficient. In the 1964 paper he said that it is Wright's
> correlation coefficient (which is not quite true) and also that
> r is well approximated by IBD as long as the population is not
> very inbred (which is true). I suspect that it is the case, in
> the situation described above, that we have two errors that
> approximately cancel out. It is "wrong" to truncate the IBD
> calculation, and it is also "wrong" to use IBD for r in an inbred
> population. But my intuition is that if you make both mistakes,
> you still come out pretty close to the truth.
I agree that you are left with a rough approximation that is reasonable
enough for the model. I would also point out here that ALL populations are
inbred to some degree in the sense that there are always cycles in pedigrees
if you had all the data.
> Of course, if we have a collection of inbred populations that
> comprise a species, and there is competition between populations
> for resources, then that is another matter. My intuition is that
> r = 0.55 is the right number to use for that case.
Yup. That is basically what I argued above.
> But now we
> are talking about a combination of kin selection and classical
> group selection, so, even in this case, r=0.5 may be a better
> choice if you want to isolate the kin selection component.
I don't think so, but I could be wrong about this. As I argued above, there
is no need to bring the idea of group selection into it just because you
have a family structured society (mating system). Hamilton's theory already
allows for the level of selection to be interpreted as coming from multiple
levels. The more explicit model of kin selection theory is, as I see it,
specifically a model of selection at the gene level. Rick Michod convinced
me of this many, many years ago.
> Or,
> to say the same thing in different words, use r=0.55 if you
> want to know if the behavior spreads in the species, but use
> r = 0.5 if you want to know if the behavior spreads in the
> local population.
OK, I guess. This all depends on the sizes of the family units involved,
though.
Regards,
Guy
- Next message: Jason: "Molecular Evolution"
- Previous message: Tim Tyler: "Re: Can viruses transfer genetic material between individuals ?"
- In reply to: Perplexed in Peoria: "Re: Haldane's Hangover"
- Next in thread: Perplexed in Peoria: "Re: Haldane's Hangover"
- Reply: Perplexed in Peoria: "Re: Haldane's Hangover"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
