jamenegay{at}ra.rockwell.com (Jim Menegay) wrote in
news:bsfmkr$1kur$1{at}darwin.ediacara.org: 

> William Morse  wrote in message
> news:... 
>> Dear Perplexed
>> 
>> jamenegay{at}ra.rockwell.com (Jim Menegay) wrote in
>> news:brm67b$4l5$1{at}darwin.ediacara.org: 
>> 
>> > I am sure that the root of my problem lies in the kinds of
>> > phenomena you suggest, but I remain perplexed.  For example, I have
>> > a fourth cousin who is my fourth cousin by two different lines.  He
>> > has twice as many of my genes as my other fourth cousins, and I
>> > fully intend to give his daughters twice as much money as the other
>> > children of fourth cousins.  I don't yet see what has been gained
>> > when a single person assumes two roles in my tree.  
>> 
>> Unfortunately I deleted your original post, so I am now trying to 
>> reconstruct your three problems (cf. other follow in the ng). You
>> would seem to be correct when going forward in time, that having one
>> person assume two roles doesn't help. It does help when going
>> backward in time, as the two roles represent one instance of the gene
>> (and I got it backward in my follow). But on further reflection I
>> don't see your problem with the forward going application. If I am
>> recreating this correctly, you are saying that you have one copy of
>> the gene, your sibling has (on average) 1/2 copy of the gene, your
>> four cousins have a total of 1/2 copy of the gene, your 16 second
>> cousins have a total of 1/2 copy of the gene, etc. But  you have two
>> total genes at this locus, as does your sibling, as does _each one_
>> of your four cousins ( a total of eight genes, of which only on
>> average 1/2 is IBD to yours), as does _each one_ of your 16 second
>> cousins. So in each iteration out your IBD gene becomes a
>> successively smaller proportion of the total genes available at this
>> locus. Where did I go wrong in this logic? 

> Dear Mr. Morse,
> For your convenience, I include here a copy of my original letter:

(snipped to keep our moderator happy)
 
> I do believe that you have solved the first of my problems.  To add
> additional detail to your solution, let me point out that one of my
> great^5 grandfathers was the brother of one of my great^5
> grandmothers. Their parents count as great^6 grandparents on two
> different lines and thus have twice as many of my genes as my other
> great^6 grandparents. So far in this reasoning, nothing has been
> gained toward resolving the paradox. 
> 
> But now note that this pair of great^6 grandparents only had those two
> children - my two great^5 grandparents.  Unlike my other great^6
> grandparents, they were not the source of any great^5 uncles and 
> aunts.  So, my naive assumption - that the increment (of 1/2 of 
> my genome found in the present for each generation analyzed in the 
> past) would remain constant at each stage - is wrong.


(snip)

As you noted in a second follow, my explanation on the joint grandparents 
doesn't solve your first problem. My explanation only tells you why you 
do not have several trillion great-great-great-.....-great-great-great 
grandparents. However my second attempt does I think solve your problem. 
Since you are undoubtedly, while perplexed, a handsome and witty 
individual, we will call the gene that produces these traits (and which 
you are attempting to reward with your largesse) the HWP gene.We will 
further assume that such handsomeness, wittiness, and perplexity could 
not be produced by only a single copy of the gene, and that you in fact 
bear two copies of the gene. You note that, for instance, you have 
sixteen second cousins with an average total relatedness of 1/2, so that 
they have an average of 1 HWP gene. However they have a total of 32 
alleles at this loci, and the HWP gene represents only about 3% of the 
total variability in the second cousin population.  So even though, as 
you go farther out in the population there are more and more copies of 
the HWP gene, they represent a smaller and smaller fraction of the total 
alleles at that locus. 

Now as you also have realized, the only way that as you go farther out in 
the population there will be more and more copies of the HWP gene is if 
the HWP gene was present not just in your grandparents but in your great-
great-great etc grandparents. But even though the total number of HWP 
genes in your great-great-etc. grandparents stays at two as you go back N 
generations, it is not as though each of them has 1/N copies of the gene. 
In fact you only actually got the gene from two forebears (or is it four 
toobears? - sorry) in each generation, no matter how far back you go. But 
what if one of the actual forebears from whom you inherited the gene, 
instead of being handsome, witty, and perplexed , was in fact dumb and 
ugly and perplexed. What happened is that the gene received from this 
forebear mutated from DUP to HWP. Going further back in time from this 
forebear (and then forward to your umpty-umpth cousins) will no longer 
yield an additional copy of the HWP gene  - and will therefore save you 
500 grand plus postage and handling :-)   


 
> Regarding my second point of perplexity, allow me to restate the
> problem.  As I have said, I believe that my luck derives from my
> genetics.  I had always thought, though, that luck was a phenotypic
> or organism-level phenomenon.  My perplexity is that my geneological
> researches have provided evidence that it is the genes themselves that
> are lucky!
 
> Observe.  My paternal grandfather carried only 1/4 of my genes.  One
> would expect that if a person has two children, then that person would
> on average pass 1/2 copy of his genome to each child - that is, his 
> genes would not proliferate.  And, indeed, my paternal grandfather's
> genes did not proliferate.  But the 1/4 portion of his genes that he
> shares with me DID proliferate.  His children had 3/8 copy of my genes
> from him (and another 3/8 copy of my genes from his wife).  My genes,
> and apparently only my genes, are lucky enough to increase their
> population, even though the total number of genes of all kinds is not
> increasing.
> 
> If anyone can point out the error in my thinking here, I will buy them
> a free order of fries.  If they can provide a better name for this
> statistical phenomenon than my wife's suggestion of "The Anthropic
> Principle", then they will also receive 1/2 off on a soft-drink or
> dessert.


You will have to be more explicit on how you got to the 3/8 number for me 
to have a chance at increasing my glucoconsumptive success.

 
> My third implicit paradox is more technical, and I am probably not
> yet educationally equipped to judge the responses and feed the winner.
> I am simply curious why, in Hamilton's "rb>c", I should not use
> "r=0.95" in deciding whether I should also feed the chimpanzee at 
> the zoo - the one that my wife uses as an example when she gives me
> math lessons. 

This last has been the subject of much debate on the newsgroup, and you 
would be better off getting an answer from Dr. Felsenstein, but to do my 
best the answer is that Hamilton is talking about genes that are 
identical by descent (IBD), one of the key points being that the gene is 
in fact  _completely identical_. The reason is that (as I understand it) 
Hamilton was simply trying to explain how kin selection could work, and 
was pointing out that a gene for helping kin could increase in the 
population based on rb being greater than c, with r in this case being 
essentially the odds of a relative having the exact gene (i.e. the gene 
being IBD).  The 95% figure(there are more accurate estimates that I have 
seen recently in another thread on the newsgroup) refers to the 
percentage of genes that have the same function (e.g. hemoglobin) that we 
share with chimps (actually not even that, it is how much of the DNA is 
complementary). The details of the gene may well differ (e.g. the sickle 
cell trait that affects some human hemoglobin).


Yours with best regards for the season,

Bill Morse
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