Hardy-Weinberg law



F

Friend

Guest
Pardon my ignorance, but I have only just discovered this
law.

Applying it to evolution looks a little to me like applying
a rate of interest to your bank balance - is there an
equivalent to compound interest, without getting too much
into specifics.

It's fairly evident I think that it is unlike extending
Newton's laws to - say - rigid bodies (where a summation is
sufficient) and more like at minimum a noisy system with
many degrees of freedom.

The problem I was having with genetic drift was the
description of it as 'random' when random changes are
intermixed with less than random changes and selection
applying to the overall (but not just summed) genome - every
generation.

Maybe there is some magical method by which the random part
can be extracted after the fact, but that seems unlikely -
only a part of the result that meets tests for randomness
which is likely to be a different matter altogether.

Beginner
 
[email protected] (friend) wrote in message news:<[email protected]>...
> Pardon my ignorance, but I have only just discovered
> this law.
>
> Applying it to evolution looks a little to me like
> applying a rate of interest to your bank balance - is
> there an equivalent to compound interest,

(BTW, fitness is only calculable through compound interest,
which continues long after an organism is deceased.)

> without getting too much into specifics.
>
> It's fairly evident I think that it is unlike extending
> Newton's laws to - say - rigid bodies (where a summation
> is sufficient) and more like at minimum a noisy system
> with many degrees of freedom.
>
> The problem I was having with genetic drift was the
> description of it as 'random' when random changes are
> intermixed with less than random changes and selection
> applying to the overall (but not just summed) genome -
> every generation.
>
> Maybe there is some magical method by which the random
> part can be extracted after the fact, but that seems
> unlikely - only a part of the result that meets tests for
> randomness which is likely to be a different matter
> altogether.

Many of the more popular myths of the current paradigm of
evolutionary biology pivot off a kind of rhetorical trick.
Specifically the trick involves employing a word that has
more than one meaning in an argument (or special case) to
achieve the illusion of scientific validity. This is *all*
that's going on with the Hardy-Weinberg, socalled, Law. And
you hit the nail on the head with respect to which word is
the "pivot" with respect to how this rhetorical trick is
manifested in Hardy-Weinberg: randomness.

In common usage there are about three different meanings for
the word random. When one is careful to explicate which of
these meanings one actually intends (which can be done with
definitions and synonyms) the percieved validity of Hardy-
Weinberg evaporates.

Jim
 
friend wrote:
> Pardon my ignorance, but I have only just discovered
> this law.
>
> Applying it to evolution looks a little to me like
> applying a rate of interest to your bank balance - is
> there an equivalent to compound interest, without getting
> too much into specifics.
>
> It's fairly evident I think that it is unlike extending
> Newton's laws to - say - rigid bodies (where a summation
> is sufficient) and more like at minimum a noisy system
> with many degrees of freedom.
>
> The problem I was having with genetic drift was the
> description of it as 'random' when random changes are
> intermixed with less than random changes and selection
> applying to the overall (but not just summed) genome -
> every generation.
>
> Maybe there is some magical method by which the random
> part can be extracted after the fact, but that seems
> unlikely - only a part of the result that meets tests for
> randomness which is likely to be a different matter
> altogether.
>
One thing we can do with mathematical models is calculate
the amount of variation we would expect by chance. If you
look at something as simple as tossing a coin 100 times,
then not only do we know that, on average, it should come up
heads 50% of the time, but we also know that most of the
time the number of heads will be near 50% (e.g. there is
only a 1.8% chance that you will get less than 40 heads).
This comes from a simple model of the process that generates
the data - each coin toss is independent, and with the same
probabilty. The amount of variation depends on both the
probability of headds, and the total number of tosses.

For natural populations the situation is similar, although
the details are more complex. The amount of random variation
in an allele frequency will depend on it's expected
frequency (which is a function of the current frequency, and
the amount of selection - you can get this from
deterministic models of selection), and something called the
effective population size, which is like the total number of
coin tosses above. If we know the effective population size,
we can calculate how much variation we would expect, and
hence any excess variation is due to selection.

Measuring the effective population size can be difficult, as
you need to collect data from several years of changes in
genes where there is no selection. Or you have to use a
model of the factors which affect it, and these will depend
on the biology of the species.

Bob

--
Bob O'Hara

Dept. of Mathematics and Statistics
P.O. Box 4 (Yliopistonkatu 5) FIN-00014 University of
Helsinki Finland Telephone: +358-9-191 23743 Mobile:
+358 50 599 0540 Fax: +358-9-191 22 779 WWW:
http://www.RNI.Helsinki.FI/~boh/ Journal of Negative
Results - EEB: http://www.jnr-eeb.org
 
Jim McGinn wrote:
> [email protected] (friend) wrote in message
> news:<[email protected]>...
>
>>Pardon my ignorance, but I have only just discovered
>>this law.
>>
>>Applying it to evolution looks a little to me like
>>applying a rate of interest to your bank balance - is
>>there an equivalent to compound interest,
>
>
> (BTW, fitness is only calculable through compound
> interest, which continues long after an organism is
> deceased.)
>
>
>>without getting too much into specifics.
>>
>>It's fairly evident I think that it is unlike extending
>>Newton's laws to - say - rigid bodies (where a summation
>>is sufficient) and more like at minimum a noisy system
>>with many degrees of freedom.
>>
>>The problem I was having with genetic drift was the
>>description of it as 'random' when random changes are
>>intermixed with less than random changes and selection
>>applying to the overall (but not just summed) genome -
>>every generation.
>>
>>Maybe there is some magical method by which the random
>>part can be extracted after the fact, but that seems
>>unlikely - only a part of the result that meets tests for
>>randomness which is likely to be a different matter
>>altogether.
>
>
> Many of the more popular myths of the current paradigm of
> evolutionary biology pivot off a kind of rhetorical trick.
> Specifically the trick involves employing a word that has
> more than one meaning in an argument (or special case) to
> achieve the illusion of scientific validity. This is *all*
> that's going on with the Hardy-Weinberg, socalled, Law.
> And you hit the nail on the head with respect to which
> word is the "pivot" with respect to how this rhetorical
> trick is manifested in Hardy-Weinberg: randomness.
>
Wierd. The Hardy-Weinberg law is deterimistic: there is no
randomness in it.

Bob

--
Bob O'Hara

Dept. of Mathematics and Statistics
P.O. Box 4 (Yliopistonkatu 5) FIN-00014 University of
Helsinki Finland Telephone: +358-9-191 23743 Mobile:
+358 50 599 0540 Fax: +358-9-191 22 779 WWW:
http://www.RNI.Helsinki.FI/~boh/ Journal of Negative
Results - EEB: http://www.jnr-eeb.org
 
Anon. <[email protected]> wrote or quoted:
> Jim McGinn wrote:
> > [email protected] (friend) wrote in
> > message news:<[email protected]>...

> >>Pardon my ignorance, but I have only just discovered
> >>this law.

[...]

> > Many of the more popular myths of the current paradigm
> > of evolutionary biology pivot off a kind of rhetorical
> > trick. Specifically the trick involves employing a word
> > that has more than one meaning in an argument (or
> > special case) to achieve the illusion of scientific
> > validity. This is *all* that's going on with the Hardy-
> > Weinberg, socalled, Law. And you hit the nail on the
> > head with respect to which word is the "pivot" with
> > respect to how this rhetorical trick is manifested in
> > Hardy-Weinberg: randomness.
>
> Wierd. The Hardy-Weinberg law is deterimistic: there is no
> randomness in it.

The Hardy-Weinberg law is normally stated in a form that
refers to a large population where mating is random.

E.g. see:

http://library.thinkquest.org/19926/java/tour/06.htm-
?tqskip1=1

Alas, this page expresses the law in terms of an infinite
population :-(

A disasterous error - IMO - since talking about gene
frequencies in an infinite population is a sign of
mathematical ignorance.

Popularisers should make explicit the behaviour is what
happens as the population size tends towards infinity - and
not attempt to pass it off as an effect in an infinite
population.
--
__________
|im |yler http://timtyler.org/ [email protected] Remove
lock to reply.
 
> > Many of the more popular myths of the current paradigm
> > of evolutionary biology pivot off a kind of rhetorical
> > trick. Specifically the trick involves employing a
> > word that has more than one meaning in an argument (or
> > special case) to achieve the illusion of scientific
> > validity. This is *all* that's going on with the
> > Hardy-Weinberg, socalled, Law. And you hit the nail on
> > the head with respect to which word is the "pivot" with
> > respect to how this rhetorical trick is manifested in
> > Hardy-Weinberg: randomness.

> Wierd. The Hardy-Weinberg law is deterimistic: there is no
> randomness in it.

TT:- The Hardy-Weinberg law is normally stated in a form
that refers to a large population where mating is random.
E.g. see: http://library.thinkquest.org/19926/java/tour/06.-
htm?tqskip1=1 Alas, this page expresses the law in
terms of an infinite population :-( A disasterous error
- IMO - since talking about gene frequencies in an
infinite population is a sign of mathematical
ignorance. Popularisers should make explicit the
behaviour is what happens as the population size tends
towards infinity - and not attempt to pass it off as an
effect in an infinite population.

JE:- All HW represents is a defined random distribution,
E.h. a random pattern. Such random patterns only represent a
defined zero state, i.e. a state in which nothing of
_significance_ has been observed. Like an artists blank
sheet of paper, without a defined zero state, nothing
exists to draw on. Thus any non random distribution
will _not_ be a HW distribution and would represent a
_non_ random pattern ( a drawing on the blank sheet)
which, consequently, has to be explained using
_contesting_ theories of nature.

Misused over simplified models, such as genetic drift,
attempt to employ random patterns (which are incorrectly
assumed to be caused by only a random process) as
significant, when they are always, non significant. Even
using a null hypothesis much more is required than just
the observation of a random pattern to produce a
significant result.

Best Wishes,

John Edser Independent Researcher

PO Box 266 Church Pt NSW 2105 Australia

[email protected]
 
>>Maybe there is some magical method by which the random
>>part can be extracted after the fact, but that seems
>>unlikely - only a part of the result that meets tests for
>>randomness which is likely to be a different matter
>>altogether.

> Many of the more popular myths of the current paradigm of
> evolutionary biology pivot off a kind of rhetorical trick.
> Specifically the trick involves employing a word that has
> more than one meaning in an argument (or special case) to
> achieve the illusion of scientific validity. This is *all*
> that's going on with the Hardy-Weinberg, socalled, Law.
> And you hit the nail on the head with respect to which
> word is the "pivot" with respect to how this rhetorical
> trick is manifested in Hardy-Weinberg: randomness.

BOH:- Wierd. The Hardy-Weinberg law is deterimistic: there
is no randomness in it.

JE:- "Wierd"? Dr O'Hara is not correct. The HW distribution
is just a binomial distribution derived from Pascale's
Triangle. This represents a triangle formed when a number of
objects are dropped one by one from a single point, e.g. a
cross section through one conical pile of sand grains that
can easily be formed this way. Such a distribution only
represents a random causative pattern, i.e. the objects (in
this case the sand grains) can only settle in a binomial
distribution forming Pascale's Triangle because nothing
stopped them from doing so! HW represents the distribution
of genes on which _only_ random processes are operating and
can only suppose an infinite population as a _heuristic_
assumption, simply because nobody can observe an infinite
population within nature.

Best Wishes,

John Edser Independent Researcher

PO Box 266 Church Pt NSW 2105 Australia

[email protected]
 
JM:- That is what happens when you are an armchair theorist.
You forget whether it is the model or the reality that is
the real truth.

JE:- Exactly. So, how do you tell a model from the reality
it was supposed to model? I have to ask this rather obvious
question because nobody here has differentiated between a
model and a theory despite many protests from myself.

Regards,

John Edser Independent Researcher

PO Box 266 Church Pt NSW 2105 Australia

[email protected]
 
>>BOH:- But, as we know know, in a finite population, there
>>will be an excess of homozygotes (because of inbreeding),
>>so H-W isn't correct (but a reasonable approximation if
>>the population is large).

GH:-
> I am not sure how extensive you intended this claim to be,
> but I think it
is
> generally false. The finiteness of populations does not
> cause an excess
of
> homozygosity relative to HWC expectations. Similarly,
> there is no reason
to
> expect the excess of homozygosity to grow with decreasing
> population size, nor is there a reason to expect the
> degree of inbreeding to increase relative to that which
> would occur in random mating as population size decreases.

BOH:- OK, at the very least I should have specified random
mating (which is specified under H-W as well). Under these
conditions, a smaller population size means a greater chance
of mating with a close relative
(i.e. inbreeding), which leads to the increase in inbreeding
over time (at least in the simple models). On the
point that the expected excess of homozygosity growing
with decreasing population size, I agree. What will
happen, under random mating (in a closed population
etc. etc.), is that the rate of increase in
homozygosity over time will increase. How all this
relates to the real world is another matter - this all
started off with a discussion about the H-W model,
rather than about reality.

JE:- We know nothing of "reality" except via the theories
that we have invented to suggest (guess) what it may be.
Thus your last sentence should read:

How all this relates to the real world is another matter -
this all started off with a discussion about the H-W model,
rather than about testable theories of reality.

Please note I included "testable" because this is a
science list.

Note also, that the "H-W model" is actually referred to in
the literature as the "HW law", but I suggest that it is, in
reality, just a HW distribution used to _define_ a _zero_
state, i.e. an allelic distribution within a heuristic
population in which nothing of significance can happen. The
fact that nobody except myself refers to the "HW law" as the
"HW distribution" does not mean that my a reference is
invalid. Rather, it highlights a consistent misuse of HW
reasoning.

So, what was the theory of reality you were referring to and
what was the model? Are they independent or is one derived
from the other? If they are derived from one another which
one is only derived and which process is used to make such a
derivation?

Yours,

John Edser Independent Researcher

PO Box 266 Church Pt NSW 2105 Australia

[email protected]
 
"Anon." <[email protected]> wrote

<snip>

> Wierd. The Hardy-Weinberg law is deterimistic:

Your ability to demonstrate its determinism is precluded by
your inability to demonstrate its existence.

Jim
 
Tim Tyler wrote:
> Anon. <[email protected]> wrote
> or quoted:
>
>>Jim McGinn wrote:
>>
>>>[email protected] (friend) wrote in message
>>>news:<[email protected]>...
>>
>
>>>>Pardon my ignorance, but I have only just discovered
>>>>this law.
>>>
>
> [...]
>
>
>>>Many of the more popular myths of the current paradigm of
>>>evolutionary biology pivot off a kind of rhetorical
>>>trick. Specifically the trick involves employing a word
>>>that has more than one meaning in an argument (or special
>>>case) to achieve the illusion of scientific validity.
>>>This is *all* that's going on with the Hardy-Weinberg,
>>>socalled, Law. And you hit the nail on the head with
>>>respect to which word is the "pivot" with respect to how
>>>this rhetorical trick is manifested in Hardy-Weinberg:
>>>randomness.
>>
>>Wierd. The Hardy-Weinberg law is deterimistic: there is no
>>randomness in it.
>
>
> The Hardy-Weinberg law is normally stated in a form that
> refers to a large population where mating is random.
>
The theorem was derived for an infinite population.

> E.g. see:
>
> http://library.thinkquest.org/19926/java/tour/06.htm?tq-
> skip1=1
>
> Alas, this page expresses the law in terms of an infinite
> population :-(
>
> A disasterous error - IMO - since talking about gene
> frequencies in an infinite population is a sign of
> mathematical ignorance.
>
No, it's a simplifying assumption. I think to accuse Hardy
in particular of mathematical ignorance deserves, well, a
non-mathematician's apology.

> Popularisers should make explicit the behaviour is what
> happens as the population size tends towards infinity -
> and not attempt to pass it off as an effect in an infinite
> population.

But it is - in finite populations, you get an excess of
homozygotes, as any student of population genetics
should know.

Bob

--
Bob O'Hara

Dept. of Mathematics and Statistics
P.O. Box 4 (Yliopistonkatu 5) FIN-00014 University of
Helsinki Finland Telephone: +358-9-191 23743 Mobile:
+358 50 599 0540 Fax: +358-9-191 22 779 WWW:
http://www.RNI.Helsinki.FI/~boh/ Journal of Negative
Results - EEB: http://www.jnr-eeb.org
 
Jim McGinn wrote:
> "Anon." <[email protected]> wrote
>
> <snip>
>
>>Wierd. The Hardy-Weinberg law is deterimistic:
>
>
> Your ability to demonstrate its determinism is precluded
> by your inability to demonstrate its existence.
>
Existence proof: HARDY, G. H., 1908 Mendelian proportions in
a mixed population. Science
28:49-50. WEINBERG, W., 1908 Über den Nachweis der Vererbung
beim Menschen. Jahresh. Wuertt. Ver. vaterl. Natkd. 64:369-
382. [for an English translation, see BOYER 1963]..
BOYER, S. H., IV, 1963 Papers on Human Genetics.

(copied and pasted from
<http://www.genetics.org/cgi/content/full/152/3/821>)

Bob

--
Bob O'Hara Department of Mathematics and Statistics
P.O. Box 4 (Yliopistonkatu 5) FIN-00014 University of
Helsinki Finland Telephone: +358-9-191 23743 Mobile:
+358 50 599 0540 Fax: +358-9-191 22 779 WWW:
http://www.RNI.Helsinki.FI/~boh/ Journal of Negative
Results - EEB: www.jnr-eeb.org
 
in article [email protected], Tim Tyler at [email protected]
wrote on 6/18/04 3:26 PM:

> Anon. <[email protected]> wrote
> or quoted:
>> Jim McGinn wrote:
>>> [email protected] (friend) wrote in
>>> message news:<[email protected]>...
>
>>>> Pardon my ignorance, but I have only just discovered
>>>> this law.
>
> [...]
>
>>> Many of the more popular myths of the current paradigm
>>> of evolutionary biology pivot off a kind of rhetorical
>>> trick. Specifically the trick involves employing a word
>>> that has more than one meaning in an argument (or
>>> special case) to achieve the illusion of scientific
>>> validity. This is *all* that's going on with the Hardy-
>>> Weinberg, socalled, Law. And you hit the nail on the
>>> head with respect to which word is the "pivot" with
>>> respect to how this rhetorical trick is manifested in
>>> Hardy-Weinberg: randomness.
>>
>> Wierd. The Hardy-Weinberg law is deterimistic: there is
>> no randomness in it.
>
> The Hardy-Weinberg law is normally stated in a form that
> refers to a large population where mating is random.
>
> E.g. see:
>
> http://library.thinkquest.org/19926/java/tour/06.htm?tq-
> skip1=1

First, the Hardy-Weinberg-Castle "Law" is as far from a law
as one could possibly get. In fact, it's assumptions are
universally false, and any resemblance or dissimilarity
between the predictions of the HWC model and reality are
impossible to interpret with confidence. The HWC model is
just a simple expression of combinatorics.

Second, expressing an assumption of the HWC model as "random
mating" is not accurate, although I think it has been a
useful guide for a plethora of population genetics students.
By assuming an infinite population size the HWC model
obliterates the existences of individuals (quanta)
altogether. The "random mating" assumption is really an
assumption of perfect mixing in the sense of the physicist.
Thus, the HWC model is indeed deterministic, despite the
misleading impression that the "random mating" assumption
gives a stochastic influence.

[snip]

Regards,

Guy
 
"Anon." <[email protected]> wrote in message
news:[email protected]...
> Tim Tyler wrote:
> > Anon. <[email protected]> wrote or
> > quoted:
> The theorem was derived for an infinite population.
>
> > E.g. see:
> >
> > http://library.thinkquest.org/19926/java/tour/06.htm?-
> > tqskip1=1
> >
> > Alas, this page expresses the law in terms of an
> > infinite population :-(
> >
> > A disasterous error - IMO - since talking about gene
> > frequencies in an infinite population is a sign of
> > mathematical ignorance.
> >
> No, it's a simplifying assumption. I think to accuse Hardy
> in particular of mathematical ignorance deserves, well, a
> non-mathematician's apology.

Huzzah!

> > Popularisers should make explicit the behaviour is what
> > happens as the population size tends towards infinity -
> > and not attempt to pass it off as an effect in an
> > infinite population.
>
> But it is - in finite populations, you get an excess of
> homozygotes, as any student of population genetics
> should know.

I am a student of population genetics who is foolishly
attempting to proceed without purchasing a good textbook.
Your claim surprised me, so I tried to check it. I used a
population of 4 consisting of two heterozygotes and both
kinds of homozygotes. Hermaphrodites. I performed all
crosses except the selfings with four offspring per cross.
(I am assuming that the finite population effect arises from
the prohibited selfings.) The problem is that I ended up
with an excess of heterozygotes. What am I doing wrong?
 
"Anon." <[email protected]> wrote in message
news:[email protected]...
> But it is - in finite populations, you get an excess of
> homozygotes, as any student of population genetics
> should know.

Dooohh! Ignore my other post. Reality gives an excess of
heterozygotes. The Hardy-Weinberg "law" gives an excess of
homozygotes.

That is what happens when you are an armchair theorist. You
forget whether it is the model or the reality that is the
real truth.
 
Anon. <[email protected]> wrote or quoted:
> Tim Tyler wrote:
> > Anon. <[email protected]> wrote or
> > quoted:
> >>Jim McGinn wrote:
> >>>[email protected] (friend) wrote in
> >>>message news:<[email protected]>...

> >>>>Pardon my ignorance, but I have only just discovered
> >>>>this law.
> >
> > [...]
> >
> >>>Many of the more popular myths of the current paradigm
> >>>of evolutionary biology pivot off a kind of rhetorical
> >>>trick. Specifically the trick involves employing a word
> >>>that has more than one meaning in an argument (or
> >>>special case) to achieve the illusion of scientific
> >>>validity. This is *all* that's going on with the Hardy-
> >>>Weinberg, socalled, Law. And you hit the nail on the
> >>>head with respect to which word is the "pivot" with
> >>>respect to how this rhetorical trick is manifested in
> >>>Hardy-Weinberg: randomness.
> >>
> >>Wierd. The Hardy-Weinberg law is deterimistic: there is
> >>no randomness in it.
> >
> > The Hardy-Weinberg law is normally stated in a form that
> > refers to a large population where mating is random.
>
> The theorem was derived for an infinite population.
>
> > E.g. see:
> >
> > http://library.thinkquest.org/19926/java/tour/06.htm?-
> > tqskip1=1
> >
> > Alas, this page expresses the law in terms of an
> > infinite population :-(
> >
> > A disasterous error - IMO - since talking about gene
> > frequencies in an infinite population is a sign of
> > mathematical ignorance.
>
> No, it's a simplifying assumption. I think to accuse Hardy
> in particular of mathematical ignorance deserves, well, a
> non-mathematician's apology.

I never said the problem was at Hardy's end.

> > Popularisers should make explicit the behaviour is what
> > happens as the population size tends towards infinity -
> > and not attempt to pass it off as an effect in an
> > infinite population.
>
> But it is - in finite populations, you get an excess of
> homozygotes, as any student of population genetics
> should know.

Any mention of gene frequencies in an infinite population is
nonsense - as I stated originally.

You can't talk about a fraction of an infinite population
having a trait. You would get different results for that
fraction depending on how you enumerated through the
population.

It's like claiming that half the integers are even.

Such statements are total mathematical gibberish.

What *can* be said is that the fraction of the set of
integers from to N that are even tends to 0.5 - as N => oo.

No serious mathematician can talk about fractions of
infinite sets and expect to be taken seriously.
--
__________
|im |yler http://timtyler.org/ [email protected] Remove
lock to reply.
 
On Sat, 19 Jun 2004 22:40:58 +0000 (UTC), "Anon."
<[email protected]> wrote:

>Tim Tyler wrote:
>> Anon. <[email protected]> wrote or
>> quoted:
>>
>>>Jim McGinn wrote:
>>>
>>>>[email protected] (friend) wrote in
>>>>message news:<[email protected]>...
>>>
>>
>>>>>Pardon my ignorance, but I have only just discovered
>>>>>this law.
>>>>
>>
>> [...]
>>
>>
>>>>Many of the more popular myths of the current paradigm
>>>>of evolutionary biology pivot off a kind of rhetorical
>>>>trick. Specifically the trick involves employing a word
>>>>that has more than one meaning in an argument (or
>>>>special case) to achieve the illusion of scientific
>>>>validity. This is *all* that's going on with the Hardy-
>>>>Weinberg, socalled, Law. And you hit the nail on the
>>>>head with respect to which word is the "pivot" with
>>>>respect to how this rhetorical trick is manifested in
>>>>Hardy-Weinberg: randomness.
>>>
>>>Wierd. The Hardy-Weinberg law is deterimistic: there is
>>>no randomness in it.
>>
>>
>> The Hardy-Weinberg law is normally stated in a form that
>> refers to a large population where mating is random.
>>
>The theorem was derived for an infinite population.
>
>> E.g. see:
>>
>> http://library.thinkquest.org/19926/java/tour/06.htm?t-
>> qskip1=1
>>
>> Alas, this page expresses the law in terms of an infinite
>> population :-(
>>
>> A disasterous error - IMO - since talking about gene
>> frequencies in an infinite population is a sign of
>> mathematical ignorance.
>>
>No, it's a simplifying assumption. I think to accuse Hardy
>in particular of mathematical ignorance deserves, well, a
>non-mathematician's apology.
>
>> Popularisers should make explicit the behaviour is what
>> happens as the population size tends towards infinity -
>> and not attempt to pass it off as an effect in an
>> infinite population.
>
>But it is - in finite populations, you get an excess of
>homozygotes, as any student of population genetics
>should know.

This above statement doesn't sound right to me? It is
known that if the matings are other than random there
will be an excess of homozygotes (over a Hardy-Weinberg
equilibrium prediction with random matings) but this is
even usually best to see when the populations are large.
Small populations (with random matings) are expected to
diverge from a precise Hardy-Weinberg equilibrium simply
from the sampling effects of the small size but I don't
recall any bias to this divergence (more or fewer
homozygotes than a Hardy-Weinberg prediction). If the
sampling (mating) is truly random, I don't see how you
could predict a direction (excess of homozygotes)?
William L Hunt

>
>Bob
>
>--
>Bob O'Hara
>
>Dept. of Mathematics and Statistics
>P.O. Box 4 (Yliopistonkatu 5) FIN-00014 University of
> Helsinki Finland Telephone: +358-9-191 23743 Mobile:
> +358 50 599 0540 Fax: +358-9-191 22 779 WWW:
> http://www.RNI.Helsinki.FI/~boh/ Journal of Negative
> Results - EEB: http://www.jnr-eeb.org
 
Perplexed in Peoria wrote:
> "Anon." <[email protected]> wrote in
> message news:[email protected]...
>
>>Tim Tyler wrote:
>>
>>>Anon. <[email protected]> wrote or
>>>quoted:
>>
>>The theorem was derived for an infinite population.
>>
>>
>>>E.g. see:
>>>
>>> http://library.thinkquest.org/19926/java/tour/06.htm?t-
>>> qskip1=1
>>>
>>>Alas, this page expresses the law in terms of an infinite
>>>population :-(
>>>
>>>A disasterous error - IMO - since talking about gene
>>>frequencies in an infinite population is a sign of
>>>mathematical ignorance.
>>>
>>
>>No, it's a simplifying assumption. I think to accuse Hardy
>>in particular of mathematical ignorance deserves, well, a
>>non-mathematician's apology.
>
>
> Huzzah!
>
>
>>>Popularisers should make explicit the behaviour is what
>>>happens as the population size tends towards infinity -
>>>and not attempt to pass it off as an effect in an
>>>infinite population.
>>
>>But it is - in finite populations, you get an excess of
>>homozygotes, as any student of population genetics
>>should know.
>
>
> I am a student of population genetics who is foolishly
> attempting to proceed without purchasing a good textbook.
> Your claim surprised me, so I tried to check it. I used a
> population of 4 consisting of two heterozygotes and both
> kinds of homozygotes. Hermaphrodites. I performed all
> crosses except the selfings with four offspring per cross.
> (I am assuming that the finite population effect arises
> from the prohibited selfings.) The problem is that I ended
> up with an excess of heterozygotes. What am I doing wrong?
>
You're not using a good textbook. :)

You need to include the selfings, otherwise you skew the
genotype freqencies.

Bob
 
Tim Tyler wrote:
> Anon. <[email protected]> wrote
> or quoted:
>
>>Tim Tyler wrote:
>>
>>>Anon. <[email protected]> wrote or
>>>quoted:
>>>
>>>>Jim McGinn wrote:
>>>>
>>>>>[email protected] (friend) wrote in
>>>>>message news:<[email protected]>...
>
>
>>>>>>Pardon my ignorance, but I have only just discovered
>>>>>>this law.
>>>
>>>[...]
>>>
>>>
>>>>>Many of the more popular myths of the current paradigm
>>>>>of evolutionary biology pivot off a kind of rhetorical
>>>>>trick. Specifically the trick involves employing a word
>>>>>that has more than one meaning in an argument (or
>>>>>special case) to achieve the illusion of scientific
>>>>>validity. This is *all* that's going on with the Hardy-
>>>>>Weinberg, socalled, Law. And you hit the nail on the
>>>>>head with respect to which word is the "pivot" with
>>>>>respect to how this rhetorical trick is manifested in
>>>>>Hardy-Weinberg: randomness.
>>>>
>>>>Wierd. The Hardy-Weinberg law is deterimistic: there is
>>>>no randomness in it.
>>>
>>>The Hardy-Weinberg law is normally stated in a form that
>>>refers to a large population where mating is random.
>>
>>The theorem was derived for an infinite population.
>>
>>
>>>E.g. see:
>>>
>>> http://library.thinkquest.org/19926/java/tour/06.htm?t-
>>> qskip1=1
>>>
>>>Alas, this page expresses the law in terms of an infinite
>>>population :-(
>>>
>>>A disasterous error - IMO - since talking about gene
>>>frequencies in an infinite population is a sign of
>>>mathematical ignorance.
>>
>>No, it's a simplifying assumption. I think to accuse Hardy
>>in particular of mathematical ignorance deserves, well, a
>>non-mathematician's apology.
>
>
> I never said the problem was at Hardy's end.
>
In fairness, Hardy does suppose "that the numbers are fairly
large". But, as we know know, in a finite population, there
will be an excess of homozygotes (because of inbreeding), so
H-W isn't correct (but a reasonable approximation if the
population is large).

>
>>>Popularisers should make explicit the behaviour is what
>>>happens as the population size tends towards infinity -
>>>and not attempt to pass it off as an effect in an
>>>infinite population.
>>
>>But it is - in finite populations, you get an excess of
>>homozygotes, as any student of population genetics
>>should know.
>
>
> Any mention of gene frequencies in an infinite population
> is nonsense - as I stated originally.
>
> You can't talk about a fraction of an infinite population
> having a trait. You would get different results for that
> fraction depending on how you enumerated through the
> population.
>
I don't understand what you mean, but by that argument, you
can't even define a fraction or a probability.

> It's like claiming that half the integers are even.
>
Err, they are. There are just rather a lot of them.

> Such statements are total mathematical gibberish.
>
> What *can* be said is that the fraction of the set
> of integers from to N that are even tends to 0.5 -
> as N => oo.
>
So what happens when N is infinity?

> No serious mathematician can talk about fractions of
> infinite sets and expect to be taken seriously.

But they do. It's how probability is defined as a concept. I
have a colleague who even wrote mathematical papers about
fractions of uncountable sets.

Infinity is a difficult concept (I know - there are lots of
it I don't understand), so I think one should be cautious
about making any pronouncements on it unless one is sure
about what mathematics does and does not say on the subject.

Bob

--
Bob O'Hara Department of Mathematics and Statistics
P.O. Box 4 (Yliopistonkatu 5) FIN-00014 University of
Helsinki Finland Telephone: +358-9-191 23743 Mobile:
+358 50 599 0540 Fax: +358-9-191 22 779 WWW:
http://www.RNI.Helsinki.FI/~boh/ Journal of Negative
Results - EEB: www.jnr-eeb.org
 
"Perplexed in Peoria" <[email protected]> wrote in message news:<[email protected]>...
> "Anon." <[email protected]> wrote in
> message news:[email protected]...
> > But it is - in finite populations, you get an excess of
> > homozygotes, as any student of population genetics
> > should know.
>
> Dooohh! Ignore my other post. Reality gives an excess of
> heterozygotes. The Hardy-Weinberg "law" gives an excess of
> homozygotes.
>

To clarify, are we assuming no selfing here? If not, I'm
struggling to see why you get the result that you do.
 
You must log in or register to reply here.
Top Bottom Back