Re: Units of IBD
- From: "Jim McGinn" <jimmcginn@xxxxxxxxx>
- Date: Wed, 5 Oct 2005 11:50:40 -0400 (EDT)
Perplexed in Peoria wrote:
> "Jim McGinn" <jimmcginn@xxxxxxxxx> wrote in message news:dhv9kr$1m6k$1@xxxxxxxxxxxxxxxxxxxxxx
> >
> > Perplexed in Peoria wrote:
> > > Jim McGinn wrote:
> > >
> > > > IBD does have units. Use them.
> >
> > <snip>
> >
> > > I'm going to venture a guess. Let me know if I guess correctly.
> > > The "units" that you have in mind are "IBD-alleles-at-the-locus
> > > over all-alleles-at-the-locus".
> >
> > Good. So you are cognizant of the units/dimensions.
> > And all that subterfuge you presented earlier is, well,
> > subterfuge.
> >
> > [innocuous rearrangement here]
> > > That is the only sense I can
> > > make out of your claim that all probabilities have units.
> >
> > Gee, this time it only took you about a week and a
> > half to answer the question honestly.
>
> As I am sure others will also point out, there are some severe
> technical problems with your position that probabilities have
> units.
Severe technical problems? Please, spare us the drama and get to the
point.
> For example, recall my question as to what are the "units"
> of the probability (1/6) of throwing a seven with two dice.
You're so full of it.
>
> You would presumably say that the units are "sevens per throw".
> Similarly, you would calculate the probability of throwing an eleven
> as "1/18 elevens per throw. Lets add these two probabilities to get
> the probability of 'craps'. The answer is 2/9 and the units are
> presumably "sevens or elevens per throw".
Gee, you figured this one out on your own.
>
> Hmmm. Is that the rule for adding dimensional quantities? Lets try
> it with velocities. Suppose we have a fish swimming downstream at
> a velocity of 3 (units of feet per second) and the stream is moving
> with a velocity of 12 (units of centimeters/second). So if we use
> the same rule that was used for probabilities, we would calculate the
> total velocity of the fish as 15 (units of 'feet or centimeters per
> second').
>
> As most people understand dimensional analysis,
dimensional analysis? You're just putting big words together and
pretending it means something important.
> you simply are not
> allowed to add or subtract two quantities unless their dimensions
> match EXACTLY. McGinn style 'extended dimensional analysis' (in
> which probabilities have dimensions) follows no such rules.
I don't know how you expect anybody to take anything you're saying here
seriously.
> You are imagining a 'proof' that Hamilton must have made a mistake
> that runs something like this. Hamilton started with a model
> of population genetics in which "alleles IBD at the locus" just
> doesn't show up as a factor. After some algebra, he ends up with
> a formula "rb>c" in which "alleles IBD at the locus" does appear
> in the units of r. How can that be?
After some algebra? Where is this mysterious algebra that nobody is
able to find? I suspect you also have a formula for turning lead into
gold.
>
> Well, I suspect that the loophole in your sketch proof is the fact
> that probabilities don't add by the same rules as velocities do.
ludicrous.
> In fact, "alleles IBD" + "alleles identical but not by descent" +
> "alleles not identical" add together in a way such that the units
> all cancel out and you are left with simply "alleles". But in
> order to see that this is actually the way Hamilton avoids your
> 'proof', you are going to have to sit down and work through the
> algebra. USING A TEXTBOOK!
The ol' textbook ploy. All of your arguments always
end up the same way. You are just trying to avoid
admitting the obvious fact that you can't figure out
Hamilton's rationale for R = Genes IBD. Give up the
subterfuge. You aren't fooling anybody.
> > [end innocuous rearrangement]
> > IBD (identical by descent) indicates the
> > number of genes (in this instance I'm using the term
> > gene to indicate alleles at locuses [which is really
> > the only rationally consistent usage of gene]) that
> > have been copied through osmosis
>
> "Osmosis"? No comment. I think I will just skip this diversion.
>
> > from a specific
> > individual *and* that are identical (not either
> > variations or mutations). It does *not* indicate the
> > number of genes that are identical.
> >
> > Now see if you can do one of the following:
> >
> > 1) Explain why Hamilton assumed genes IBD of two
> > individuals represents the relatedness (R) of these
> > two individuals.
>
> He didn't, if you continue to think that "relatedness" means
> degree of genetic similarity.
How does what I think determine what Hamilton assumed? This makes no
sense at all. Make more of an effort to follow the logic of the
discussion.
> But if "relatedness" is taken
> to mean something like 'degree of closeness in a genealogical
> tree' then it is fairly obvious that the probability of IBD
> is a natural measure of 'relatedness'. Hamilton chose
Hamilton never chose. He left it ambiguous. As I explained to you
previously. Remember?
> this
> metric of relatedness rather than some other natural metric
> because this metric results in a simple formula "rb>c".
Very poor answer. You are basically saying here--and accurately
IMO--that Hamilton assumed genes IBD = R because it looked good on
paper. You seem to be completely abstracted from the realization that
what Hamilton should have been striving to achieve is causal efficacy.
As I explained to you previously. Hamilton's thinking only appears to
work if you are not conscious of the fact that Hamilton left
relatedness ambiguous.
>
> It is important to keep that word 'probability'. The probability
> that any particular gene of mine is shared IBD by my brother
> is 0.5. However, it is possible, due to the random nature of
> meiosis, that the fraction of our genes shared IBD is anywhere
> between 0.0 and 1.0. When you add in the fraction of genes that
> we shar identical but not by descent, you get up near 99%. But
> this is simply irrelevant.
irrelevant to what?
>
> > 2) Explain Hamilton's rule using only the term "genes
> > IBD" in place of R (relatedness).
> >
> > If you can do either of these I will send you a check
> > for $10,000.
>
> Buy a textbook. The author has already received royalties
> exceeding $10,000 and you only lose $50-100. Use the money
> that you saved to buy some more textbooks. Who knows, you
> might actually learn something.
If you are any indication textbooks are a waste of money. It seems you
employ textbooks as an excuse for not thinking.
Jim
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