Price's equations, Hamiton's rule, Fisher's fundamental theorem, ESS

The purpose of this note is to share links to some papers on
Population Genetics that I have read recently.

-------------
1. "George Price's Contributions to Evolutionary Genetics",
Steve Frank. http://stevefrank.org/reprints-pdf/95JTB-
Price.pdf

Wow! I had never even heard of Price until recently. His
biography is as bizarre as that of Turing or Godel, and his
impact may turn out to be comparable. A must read.
--------------
2. "A geometric view of relatedness", Alan Grafen, 1985
http://users.ox.ac.uk/~grafen/cv/oseb.pdf

A very long (62pp) paper that does an outstanding job of
explaining
rB>C, Price's equations, IBD, and several other topics
rB>of recent
interest, including the "paradoxes" of "Perplexed in
Peoria". Mathematical maturity not required.
--------------
3. "Fisher's fundamental theorem of natural selection",
Steve Frank and
M. Slatkin, 1992 http://stevefrank.org/reprints-choice/92TREE-
R.html

Fisher "proved" that fitness is continually increasing, but
he also pointed out that the environment is continually
deteriorating. Huh? This has been going on for 3 billion
years? A clear exposition of what it means, using a model of
clutch-size evolution. It certainly cleared up my thinking
about fitness and NS.
--------------
4. "The Price Equation, Fisher's fundamental theorem,
kin selection, and causal analysis", Steve Frank,
1997 http://stevefrank.org/reprints-choice/97Evol-
Causal-R.html

Some additional applications of Price's formulation of
Natural Selection. More mathematical than the previous
papers.
--------------
5. "Developments of the Price equation and natural selection
under uncertainty", Alan Grafen, 2000
http://users.ox.ac.uk/~grafen/cv/PriceUnc.pdf

Yet more applications and extensions of the Price equations.
--------------

More papers by Frank: http://stevefrank.org/pub-date.html

More papers by Grafen http://users.ox.ac.uk/~grafen/cv/

--------------
My take on Price: The equation is very pretty. But it has
the deficiency of "dynamic insufficiency" (as described in
the papers). One of the earliest applications of the
equation was to group selection, and the book "Unto Others"
by Elliot Sober and D. S. Wilson sketches some credible
biological models in which "group selection" ala Price
obviously can work. The trick is that the group lifetime is
comparable to the individual lifetime.

However, the book then tries to apply group selection to
human evolution of altruism, and I don't think it applies.
My reason has to do with the dynamic insufficiency. There
needs to be some kind of mechanism to continually refresh
the variance between groups in the frequency of altruists -
otherwise within-group selection will overwhelm between-
group selection. Humans don't live in haystacks.

My current thinking is that reciprocity is the key. (In a
sense, a reciprocal relationship is a group, a small short-
lived one.) Since it is unlikely that I will be able to get
Edser to clarify what he means by OFM, it looks like I will
have to read up on Trivers/reciprocity and game theory
models. :-(

jimmenegay@sbcglobal.net (Jim Menegay) wrote

> My take on Price: The equation is very pretty. But it has
> the deficiency of "dynamic insufficiency" (as described in
> the papers). One of the earliest applications of the
> equation was to group selection, and the book "Unto
> Others" by Elliot Sober and D. S. Wilson sketches some
> credible biological models in which "group selection" ala
> Price obviously can work. The trick is that the group
> lifetime is comparable to the individual lifetime.

Even this trick is unneccessary if you don't start from the
assumption that individual organisms represent "the"
parameter of evolutionary truth.

> However, the book then tries to apply group selection to
> human evolution of altruism, and I don't think it applies.
> My reason has to do with the dynamic insufficiency. There
> needs to be some kind of mechanism to continually refresh
> the variance between groups in the frequency of altruists
> - otherwise within-group selection will overwhelm between-
> group selection.

The notion that selection at one level/unit of biological
phenomena can or will overwhelm selection at another
"competing" level/unit of biological phenomena is a common
fallacy. It suggests this existence of logical
relationships that have no empirical existence. Levels (of
biological phenomena) don't compete, so there is no such
thing as selection at one level overwhelming selection at
another level.

> Humans don't live in haystacks.

Humans live in communities. The fate of humans is often
largely determined by the fate of their community and the
fate of their community is largely determined by the actions
of the members that comprise the community.

> My current thinking is that reciprocity is the key.

If the situational factors dictate group selection then
reciprocity is a given.

I think your whole approach is, in part, indicative of a
common fallacy. The fallacy pivots off the common
misconception that individual selection is provable and
proven and/or that individual selection is a distinct
process or even a distinct force. The reality is that
individual selection is no more provable or proven (and no
less provable or proven) than is selection at any other
level and it is not a distinct process or force.

Individual organisms do exist. Natural selection is the
cause of individual origanisms. Social groups of organisms
do exist. Natural selection is the cause of social groups of
organisms. Species, ecosystems, biotas, cells, genes, do
exist. NS is the cause of all of these also. There is no
contradiction in any of this.

Jim

"Jim McGinn" <jimmcginn@yahoo.com> wrote in message
news:c2t9dr$1lr7$1@darwin.ediacara.org...
> jimmenegay@sbcglobal.net (Jim Menegay) wrote

> Individual organisms do exist. Natural selection is the
> cause of individual origanisms. Social groups of organisms
> do exist. Natural selection is the cause of social groups
> of organisms. Species, ecosystems, biotas, cells, genes,
> do exist. NS is the cause of all of these also. There is
> no contradiction in any of this.

This smacks of someone trying to cause a topic of delicious
analysis to be philosophically settled! ;-)

This cannot be tolerated since the freedom from pain (even
pleasure!) that can be derived from this intellectual form
of 'AEVASIVE drive' is far to precious to most people.

In fact, a positive self-worth, social worth, and financial
worth can be (and often is) strongly dependent on the
capacity to carry out and carry on (maintain) such, and such-
like, AEVASIVE (type) preoccupations.

P

On Thu, 11 Mar 2004 16:31:00 +0000 (UTC), jimmenegay@sbcglobal.net
(Jim Menegay) wrote:

>The purpose of this note is to share links to some papers
>on Population Genetics that I have read recently.
>
>-------------
>1. "George Price's Contributions to Evolutionary Genetics",
> Steve Frank. http://stevefrank.org/reprints-pdf/95JTB-
> Price.pdf
>
>Wow! I had never even heard of Price until recently. His
>biography is as bizarre as that of Turing or Godel, and his
>impact may turn out to be comparable. A must read.

In "Narrow Roads of Gene Land" Hamilton discusses his
contacts with Price. When they first had contact Price was
thinking his equation was so simple it could not be
original with him and was really surprised to find it was.
By the time of his death, when his life had taken a very
religious turn, he had formed the view that he could not
have derived this equation if men of greater ability had
not already done so and concluded he must have been chosen
as a conduit of some divine source and had truly been
divinely inspired. All quite strange. I do think the 'Price
equation' is not as fully appreciated as it may one day be.
William L Hunt

... [snip] ...

jimmcginn@yahoo.com (Jim McGinn) wrote in message news:<c2t9dr$1lr7$1@darwin.ediacara.org>...
> jimmenegay@sbcglobal.net (Jim Menegay) wrote
>
> > My take on Price: The equation is very pretty. But it
> > has the deficiency of "dynamic insufficiency" (as
> > described in the papers). One of the earliest
> > applications of the equation was to group selection, and
> > the book "Unto Others" by Elliot Sober and D. S. Wilson
> > sketches some credible biological models in which "group
> > selection" ala Price obviously can work. The trick is
> > that the group lifetime is comparable to the individual
> > lifetime.
>
> Even this trick is unneccessary if you don't start from
> the assumption that individual organisms represent "the"
> parameter of evolutionary truth.
>
> > However, the book then tries to apply group selection to
> > human evolution of altruism, and I don't think it
> > applies. My reason has to do with the dynamic
> > insufficiency. There needs to be some kind of mechanism
> > to continually refresh the variance between groups in
> > the frequency of altruists - otherwise within-group
> > selection will overwhelm between-group selection.
>
> The notion that selection at one level/unit of biological
> phenomena can or will overwhelm selection at another
> "competing" level/unit of biological phenomena is a common
> fallacy. It suggests this existence of logical
> relationships that have no empirical existence. Levels (of
> biological phenomena) don't compete, so there is no such
> thing as selection at one level overwhelming selection at
> another level.
>
> > Humans don't live in haystacks.
>
> Humans live in communities. The fate of humans is often
> largely determined by the fate of their community and the
> fate of their community is largely determined by the
> actions of the members that comprise the community.
>
> > My current thinking is that reciprocity is the key.
>
> If the situational factors dictate group selection then
> reciprocity is a given.
>
>
>
> I think your whole approach is, in part, indicative of a
> common fallacy. The fallacy pivots off the common
> misconception that individual selection is provable and
> proven and/or that individual selection is a distinct
> process or even a distinct force. The reality is that
> individual selection is no more provable or proven (and no
> less provable or proven) than is selection at any other
> level and it is not a distinct process or force.
>
> Individual organisms do exist. Natural selection is the
> cause of individual origanisms. Social groups of organisms
> do exist. Natural selection is the cause of social groups
> of organisms. Species, ecosystems, biotas, cells, genes,
> do exist. NS is the cause of all of these also. There is
> no contradiction in any of this.
>
> Jim

I'm not sure that we are in disagreement. I am a believer
(though a recent convert) in multi-level selection. However,
I remain enough of a reductionist to believe that insight
can be gained by looking at a phenomenon at low levels. For
example, I am skeptical that deme-level or society-level
selection can cause evolution of the underlying species of
individuals, UNLESS the deme or society somehow enforces its
norms upon its members. That is, cheaters must get punished.

In order to understand just how much enforcement and what
kind of enforcement is necessary, I want to look at the
dynamics as it affects the individual.

Reductionism isn't always bad. When used moderately (as
all ideological stances should be used) it can
illuminate things.

does anybody of you by coincidence know something more about
george price than is available from the publications of
steven frank etc. frank's paper does not even mention the
birth date. didn't any historian of science by now hit upon
the idea to write a biography of this most interesting
figure in evolutionary biology?

cheers, joe

Joachim Dagg <jdagg@gwdg.de> wrote:

> does anybody of you by coincidence know something more
> about george price than is available from the publications
> of steven frank etc. frank's paper does not even mention
> the birth date. didn't any historian of science by now hit
> upon the idea to write a biography of this most
> interesting figure in evolutionary biology?
>
> cheers, joe

IIRC Hamilton wrote an obit somewhere.
--
John Wilkins john_SPAM@wilkins.id.au
http://www.wilkins.id.au "Men mark it when they hit, but do
not mark it when they miss"
- Francis
Bacon

In article <c34m71$1304$1@darwin.ediacara.org>,
Joachim Dagg <jdagg@gwdg.de> wrote:
>does anybody of you by coincidence know something more
>about george price than is available from the publications
>of steven frank etc. frank's paper does not even mention
>the birth date. didn't any historian of science by now hit
>upon the idea to write a biography of this most interesting
>figure in evolutionary biology?

There is more biographical material on the web:
www.darwinwars.com/wdhessay.html
www.kuleuven.ac.be/bio/ento/schwartz2000.pdf (the latter
also as HTML:
http://www.gametheory.net/News/Items/009.html )

I never ran into George Price. It sounds like he was a very
troubled individual. As interesting as the Price covariance
formulae are, I think Hamilton and Maynard Smith still stand
as making the greatest contributions to evolution of
reproductive strategies and behavior. And both interesting
and fun people to talk to.

--
Joe Felsenstein joe@removethispart.gs.washington.edu
Department of Genome Sciences and Department of
Biology, University of Washington, Box 357730, Seattle,
WA 98195-7730 USA

wlhunt@earthlink.net (William L Hunt) wrote in message news:<c34m6s$12oq$1@darwin.ediacara.org>...

> I do think the 'Price equation' is not as fully
> appreciated as it may one day be. William L Hunt

Wouldn't you thinlk, William, that a biography of Price
would do a lot towards this end. If I remember right,
Hamilton's book is as poor as Steven Frank's on this. All we
get is a legend (see also The Darwin Wars).

Shall I take the silence on my previous question as meaning
that nothing is available?

On Tue, 16 Mar 2004 16:17:31 +0000 (UTC), jdagg@gwdg.de (Joachim Dagg)
wrote:

>wlhunt@earthlink.net (William L Hunt) wrote in message
>news:<c34m6s$12oq$1@darwin.ediacara.org>...
>
>> I do think the 'Price equation' is not as fully
>> appreciated as it may one day be. William L Hunt
>
>Wouldn't you think, William, that a biography of Price
>would do a lot towards this end. If I remember right,
>Hamilton's book is as poor as Steven Frank's on this. All
>we get is a legend (see also The Darwin Wars).
>
I would also like to see a full biography of Price but I
think an appreciation of the worth or usefulness the
covariance equation will be independent of a connection
with the man who derived it. It might work the other way
though, if the equation was deemed more important, it would
create more interest to know the background of the man who
derived it. William L Hunt

[snip]

Joachim Dagg wrote:
> does anybody of you by coincidence know something more
> about george price than is available from the publications
> of steven frank etc. frank's paper does not even mention
> the birth date. didn't any historian of science by now hit
> upon the idea to write a biography of this most
> interesting figure in evolutionary biology?
>
There's some information in Segerstr†le's book "Defneders of
the Faith", which is a fascinating sociological history of
the debates over sociobiology and surrounding issues.

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

> JF:- joe@removethispart.gs.washington.edu wrote in message
news:<c363a5$1i8i$1@darwin.ediacara.org>...
> There is more biographical material on the web:
> www.darwinwars.com/wdhessay.html
> www.kuleuven.ac.be/bio/ento/schwartz2000.pdf (the latter
> also as HTML:
http://www.gametheory.net/News/Items/009.html )
>
> I never ran into George Price. It sounds like he was a
> very troubled individual. As interesting as the Price
> covariance formulae are, I think Hamilton and Maynard
> Smith still stand as making the greatest contributions to
> evolution of reproductive strategies and behavior. And
> both interesting and fun people to talk to.

JE:- Price appears hopelessly emotionally involved in
proving organism fitness altruism (OFA) existed within
nature because of a religious belief. In the end his
inability to separate testable theory from non testable
belief send him insane.

I think that this quote from the above sources: "When Price
first read Hamilton's equations he recognised that they
raised a terrible problem. He saw that altruism in this
biological and equation- bound sense is limited. It cannot
supply the absolute and universal commandment of
Christianity or the other global ethical systems."

Hamilton's inequality only measured a _relative_ difference
in fitness between rb and c for the donor altruist. No
absolute measure of the fitness of the donor was ever
included. If it had been, it would have had the value of
cmax. Because of the absence of any total fitness of the
donor, "altruism in this biological and equation-bound sense
is limited". Nobody then, or today, wished to discuss the
exact extent of these limitations! This has led to
Hamilton's model being misused to support organism fitness
altruism in nature when classical group selection failed to
be able to do so over half a century ago. The proof of this
misuse is the fact that the sign of c always remains
arbitrary within the rule, yet OFA is only possible when the
sign of c is negative. When the sign of c is positive
organism fitness mutualism (OFM) is said to be operating.
Thus at all times, EITHER OFM or OFA can be said to be
operating within Hamilton's rule. OFM is _not_ fitness
altruistic it is fitness mutualistic. Here the cost c
reflects an investment cost and not just an altruistic give
away. Such a mutual but not necessary equal gain does _not_
involve any independent selfish geneism or OFA. Thus, it
remains totally consistent with Darwinian selection
operating at just the level of the fertile organism.

The fact that the sign of c remains arbitrary within
Hamilton's rule will always be so until a general term for
donor total fitness is included within Hamilton's rule. Thus
I have included it:

rb>K-c

Here K has the value of cmax (the maximal cost possible) but
represents the total fitness of the donor altruist. In this
case, the sign of c becomes non arbitrary and _only_ OFM can
be said to be operating within this corrected form of
Hamilton's rule. What does it all mean? It means that
Hamilton's rule never ever allowed OFA within nature and was
utterly misused to support OFA when classical group
selection failed to do so. Neo Darwinians have made a basic
error in this _application_ of Hamilton's but they
steadfastly refuse to admit it. Like Price they are
hopelessly emotionally involved in what they are doing. They
wish nature to allow OFA so they are going to do anything to
attempt to prove this is the case. When challenged they just
wheel in Post Modern epistemology (everything is relative)
to protect their view.

People needlessly shy away from absolute assumptions because
they have been wrongly taught. There is a world of
difference between "an absolute assumption" and "an
absolute". Absolutes are just biased dictates of nature
favoured by dictators who wish to evade any test of their
dictates. On the other hand, absolute assumptions from the
basis of all contestable theories of nature. Post modern
epistemology attempts to delete absolute assumptions because
it has utterly failed to discriminate between "absolutes"
and "absolute assumptions". Once absolute assumptions are
deleted just about "anything goes".

It was J.B.S. Haldane who first mooted relative altruistic
gains in his now famous pub discussion. Like Hamilton he did
not include any total donor fitness within his calculations.
Haldane did not set himself any limit to the number of
offspring he could have had if he had not altruistically
donated all his efforts to just offspring reproduction by a
relative. Thus he, like Hamilton, was only calculating a
relative fitness gain. Such a view is hopelessly incomplete.
It allows the altruistic gene to relatively spread compared
to the wildtype while at the same time both can reduce their
absolute fitness count. This being the case, both genes can
be selected to move towards extinction! Note that within OFM
this is never the case because the cost c as an investment
cost, pays more than it cost. The failure to include a
general term for constant or maximal values within gene
centric Neo Darwinistic models of fitness was endemic at it
conception and remains so, today. Allowing such hopelessly
limited model to contest and win against the theory they
were simplified from is an epistemological error of the 1st
order, i.e. it is just, absurd. No will exists to even
examine the possibility that Neo Darwinistic models are
being misused so this misuse continues at taxpayer's
expense. The real horrific cost has been the failure of gene
centric Neo Darwinists to appreciate the massive extent and
importance of OFM within nature.

Yours,

John Edser Independent Researcher

PO Box 266 Church Pt NSW 2105 Australia

edser@tpg.com.au

Bob, this sounds really dubious to me. Couldn't find the
book at amazon (not by that author), but it sounds like a
creationist's pamphlet. I wasn't interested in creationists
taking Price fot whatever they will, if you understand. Or
is it not that kind of book?

[moderator's helpful info: Bob got the title slightly wrong;
it's "Defenders of the Truth: The Battle for Science in the
Sociobiology Debate and Beyond", Oxford Univ. Press, 2000.
493 pp. Author is, approximately, Ullica Christina
Olofsdotter Segerstrale, but there's a little circle over
the final "a" in Segerstrale; if you search Amazon by title,
it turns up. - JAH]

"Anon." <bob.ohara@SOD.OFF.Spammers.helsinki.fi> wrote in
message news:<c379as$1sta$1@darwin.ediacara.org>...
> There's some information in Segerstr?le's book "Defneders
> of the Faith", which is a fascinating sociological history
> of the debates over sociobiology and surrounding issues.
>
> Bob

*shakinwithmyhead* not even the exact birthdate
*shakinwithmyhead*

thanks, john and joe, for your answers. i daresay, haven't
you been around here ever since 1997? *gosh*, what patience
and perserverence.

joe@removethispart.gs.washington.edu wrote in message
news:<c363a5$1i8i$1@darwin.ediacara.org>...
> There is more biographical material on the web:
> www.darwinwars.com/wdhessay.html
> www.kuleuven.ac.be/bio/ento/schwartz2000.pdf (the latter
> also as HTML:
> http://www.gametheory.net/News/Items/009.html )
>
> I never ran into George Price. It sounds like he was a
> very troubled individual. As interesting as the Price
> covariance formulae are, I think Hamilton and Maynard
> Smith still stand as making the greatest contributions to
> evolution of reproductive strategies and behavior. And
> both interesting and fun people to talk to.

Sure, but i thought the usual cv (nice chap graduates from
harvard or oxbridge, gets postdoc or tenure somewhere
abroad, finally returns back home and establishes himself,
and that was that) wasn't as interesting as price's. the
movie "a beautiful mind" also showed that the vicinity
between ingenuity and madness is highly popular. but maybe
it's too embarrassing for the darwinian establishment, to
have one of their heros turn fanatically christian?

nevertheless, there are many interesting questions related
to this turn. would price have become a devout christian, if
his formula had not worked for group selectionn and
altruism? was his earlier frire-spitting atheism a rebellion
against his environment? was his work in evolutionary
biology a last battle against a religious streak that was
always in him?

or, very interesting to the usa, as there seems to be a
strong polarisation between darwinians and creationists:
how did price manage to do revolutionary research in
evolutionary biology and be a devout christian at the
same time?

Joachim Dagg <jdagg@gwdg.de> wrote:

> Bob, this sounds really dubious to me. Couldn't find the
> book at amazon (not by that author), but it sounds like a
> creationist's pamphlet. I wasn't interested in
> creationists taking Price fot whatever they will, if you
> understand. Or is it not that kind of book?
>
> [moderator's helpful info: Bob got the title slightly
> wrong; it's "Defenders of the Truth: The Battle for
> Science in the Sociobiology Debate and Beyond", Oxford
> Univ. Press, 2000. 493 pp. Author is, approximately,
> Ullica Christina Olofsdotter Segerstrale, but there's a
> little circle over the final "a" in Segerstrale; if you
> search Amazon by title, it turns up. - JAH]
>
>
> "Anon." <bob.ohara@SOD.OFF.Spammers.helsinki.fi> wrote:
> > There's some information in Segerstr?le's book
> > "Defneders of the Faith", which is a fascinating
> > sociological history of the debates over sociobiology
> > and surrounding issues.
> >
> > Bob

Segerstråle covers Price's ideas and provides a few pages
of his personal life in pages 64-69. Price committed
suicide by refusing to take his medication for
hypoglyceamia. She cites Hamilton's Narrow Roads, so it is
no more information than before.

I would *love* to see his life made into a film,
embarrassing to "Darwinians" or not.
--
John Wilkins john_SPAM@wilkins.id.au
http://www.wilkins.id.au "Men mark it when they hit, but do
not mark it when they miss"
- Francis
Bacon