Kin Selection contradiction?

Jim,

in article [email hidden], Perplexed in
Peoria at [email hidden] wrote on 6/23/04 9:06 AM:

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"Guy Hoelzer" <[email hidden]> wrote in message
"]news:[email hidden]...

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Jim,

in article [email hidden], Perplexed
in Peoria at [email hidden] wrote on 6/22/04
1:16 PM:

Quoted message said:

"Guy Hoelzer" <[email hidden]> wrote in message
"]news:[email hidden]...
> in article [email hidden], Perplexed
> in Peoria at [email hidden] wrote on 6/16/04
> 10:15 PM: Whatever method is used, the result has to be
> an "r" with the following property: Randomly choose one
> of the two genes at any locus in the donor. Suppose
> that the frequency of this allele in the general
> population is "p". Now, randomly choose one of the two
> genes at the same locus in the recipient. It must be
> the case that the probability that the two randomly
> selected genes are identical is (r + (1 - r)p). That
> is, there is a probability r that they are identical
> IBD, but if not, then there is still a probability p
> that they are identical for other reasons - because the
> allele is fairly common in the population.
>
> I think there is a big practical problem with applying
> any models relying on IBD calculations, because our
> data on genealogical history is virtually always very
> shallow and incomplete.

No doubt. I have no idea how field workers go about
applying the model. Though I would imagine that the
problems with estimating "b" and "c" are much larger
than the problems of estimating "r".

Well, "r" can never be known and can only be estimated
with an underestimation bias. The degree of the bias
depends on the amount of unknown inbreeding in the common
ancestry of two individuals. At least "b" and "c" might
be estimable without bias. Nevertheless, my biggest
problem with the kin selection literature has to do with
the uncritical (even unconscious) acceptance of kin
selection as THE explanation for altruism-like behaviors
observed in nature. I think the difficulty associated
with estimating these parameters has a lot to do with
giving in to this elegant model.

I disagree about the effect of unknown inbreeding below.

I fully agree that most altruism-like behaviors in nature
(excluding parental care, and perhaps the social insects)
are based on reciprocity rather than on the unilateral
altruism covered by the Rule.

It's good to know that our estimates of reality are close.

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But this conversation began because, IMO, you made some
false statements about the model - specifically that the
applicability of rb>c depends upon the frequency of the
altruistic allele. Or at least that is what you seemed to
say. I am trying to defend the model against distortion,
not to defend the importance or applicability of the
model. You would have to have that discussion with someone
who knows more "natural history". I am just an amateur OOL
person who happened to get interested in Hamilton's Rule
because it seemed to be controversial in this group. So,
ultimately, I suppose this conversation can be blamed on
Edser :-)

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> For example, all individual organisms (across all
> species) are probably genealogically related, but...
> There is also the problem of genealogical relatedness
> in the face of mutation (common decent without
> identity).

If you believe that these issues are "big practical
problems", then I suspect that you don't yet understand
the model. The effect on r of

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population.

The problem is not just about pushing the estimate of "r"
back additional generations. If that were the case, then
I would agree that say 3 generations would be sufficient
in most cases. Putting aside the fact that we rarely have
information going back more than one generation, the
greater issue has to do with inbreeding. The parameter
"r" can take on any value in the face of inbreeding. For
example, full sibs actually have 0.5 >= r <= 1. In fact,
it is very common to have levels of inbreeding that make
our naïve estimates of "r" significantly lower than they
actually are. Truth be told, r=1 for every pair of
individuals (even from different species) if you were to
consider all the data (and ignore mutation/divergence).
Do you have a justifiable rule for how ignorant we ought
to be when we try to estimate "r" in order to make the
false estimate useful in understanding kin selection in
nature?

It is clear that you still don't understand what "r" is.
The history of the population, and the fact that it may be
inbred in the recent or distant past is totally
irrelevant. The only way inbreeding could be relevant
would be if the population routinely breeds with close
relatives for reasons other than small population.

Forget IBD for a moment. Let p be the frequency of the
altruistic allele in the general population. Let P be the
frequency of the allele in the recipients. Define r to be
that value which satisfies the equation P = r + (1-r)p
That is, r represents, in a mathematically wierd way, the
degree to which P exceeds p.

As I said before, I like this way of thinking about the
model, at least in some ways. I think you have internalized
Maynard-Smith's version of Hamilton's model. Those two great
thinkers thought about things in very different ways, IMHO.
I am not sure that Hamilton ever verified that the Maynard-
Smith version was consistent with his thinking. IMHO
Hamilton thought of "r" primarily as a measure of
genealogical relationship, which is not what it means in
your equation above. My comment above about "0.5 >= r <= 1"
was specifically referring to the genealogical "r".
Nevertheless, I will go with the Maynard-Smith version of
things for our dialogue.

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This value r can be calculated (within sampling error) in
the field if you take DNA samples from a random sample of
the donor-recipient pairs. Of course, you have to
normalize against the results for random pairs that are
not donor-recipient. Or, if you have been observing the
population for a few generations and you know genealogies
of individuals, you can estimate r by truncated IBD. Or
use truncated IBD if you are not a fieldworker and you
just want to understand a reason why P>p might be
expected.

If you wish to understand why inbreeding is not important,
perform the following thought experiment. Imagine a
population derived from a single breeding pair which has
grown to a population of 64 with the population doubling
each generation. But, to make sure that we have variation
for altruism, make both of the original pair heterozygous.
Assume that mating is random and monogamous. "p" is 1/2.
Assume the altruism is directed to full sibs. I think that
you will find that r is not much larger than .5 and
certainly less than .6. Or, for variety, start with p =
3/4 or 1/4. "r" still will be less than .6 AFAICS

You assumed something like random mating in an exponentially
growing population, which basically the same as assuming
that inbreeding is not occurring. It is certainly not
surprising to conclude that inbreeding does not affect "r"
when you assume that inbreeding does not occur. To
illustrate why inbreeding IS important, consider a
hypothetical population in which sib-sib mating is the norm.
Such a population quickly loses its heterozygosity and
becomes constituted by families filled with altruists and
families lacking altruists. Now P>>p, and your "r" value is
correspondingly much higher. So "r" is sensitive to
inbreeding.

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And the chance that a mutation has destroyed an
altruistic allele within those few generations is also
small.

In most cases that is probably true. Of course, we
haven't even touched on the most common criticism of
Hamilton's kin selection model, which is that altruistic
behavior is probably not directly caused by a genetic
mutation most of the time.

I assume you mean that it is not caused by a single gene.
(If you meant something different by "mutation", you will
have to explain.)

I use the term "mutation" in a more general sense here. For
example, a chromosomal inversion might be involved, which
does not disrupt the function of any particular gene. I am
not trying to argue for the importance of non-genic
mutations. I am merely allowing for effects of a broader
class of mutations that would exhibit Mendelian segregation
as assumed under Hamilton's model.

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It is probably far more complicated than that, and it is
not clear to what extent the Hamilton's rule would work
outside of the genetic framework. Here again is where my
real problem lies. The vast majority of the empirical
literature claiming to support Hamilton's model never
addresses the issue of genetic control over altruism.

Well, it turns out that non-additive epistasis is not a
problem in this model, for the usual reasons. If you doubt
this, just make the penetrance factor "f" below depend on
both "p" and the frequency of some other gene(s). For a
derivation of the rule, I think we are justified in
treating each of these frequencies as a constant. Though
perhaps we are now adding a weak selection assumption.
However, pleiotropy turns out, surprisingly, to be more
problematic. My toy derivation of the Rule, sketched
below, doesn't handle it, for reasons sketched in my reply
to Bill Morse. I don't know whether Hamilton [1964]
handles it.

I don't think Hamilton ever challenged his model with such
mechanistic detail. I wasn't specifically implying anything
about non-additive epistasis in my comment. In fact, I was
thinking more about non-genetic effects altogether. Still,
it is nice to know that the model appears robust to non-
additive epistasis.

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>> Or, if like McGinn, you have an intuition that
>> geneological history cannot be causal in this
>> situation, ignore the IBD above. "r" is simply a
>> measure of how much more likely than "p" it is that
>> the two genes are identical for whatever reason. The
>> key thing is that the formula (r + (1-r)p) gives the
>> probability that the alleles are "shared".
>>
> Hmm. There are some things about this formulation that
> I like, and some problems I see. Can you please save me
> a little research time and tell us where you come by
> the formula (r + (1-r)p)? Is this your interpretation
> of Hamilton, or has it been published?

It is a straightforward interpretation of the verbal
explanation given in Maynard Smith's "Evolutionary
Genetics" (2nd ed. p169)

Now we can picture the genome of the recipient as
consisting of two parts:
1. a fraction r containing genes IBD to genes in the
actor; and
2. a fraction (1-r) consisting of genes that are a
random sample of genes in the population.

This is a very familiar modeling trick. The same thing is
done when modeling inbreeding for other purposes. It is,
however, just a trick that makes the math work out
easily. The flaw becomes clear when you recognize that
any random sample of the gene pool will potentially
contain gene copies that are IBD with the target, so the
fractions are not mutually exclusive. Given your
definition of "r", "(1-r)" must be the fraction of the
recipient's genome containing genes that are NOT IBD,
which is different from "a random sample of genes in the
population."

I think that my argument above including the phrase
"forget about IBD for a moment" addresses this concern.

I agree that this second way in which you defined your
parameters is more logical. However, that does not validate
the way you defined them at first, which I still argue had a
logical flaw. In fact, I think these two definition sets are
inconsistent with one another, so you should decide which
one you want to use and stick with it.

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As a "proof" that this is the correct interpretation,
you can derive "rb>c" from this formula.
1. Assume b and c are the benefits and costs of a single
altruistic action.
2. Assume a "penetrance factor" f (which may depend on
r!) gives the number of times an allele causes
altruism during its organism's lifetime. Assume that
homozygous altruists share the cost between alleles.
The factor f allows us to ignore whether the allele
is dominant or recessive. For example, if the allele
is recessive, then f will be small when p is small.
But if the allele is dominant, then f will start
large and then fall to half the original value, due
to "sharing the credit" between homozygous gene
instances.
3. Calculate the total benefit received by recipients.
Divide this up between carriers and non-carriers,
with the benefit split in heterozygotes. Now
calculate the "per capita" benefit to each haploid
genome of the two types.
4. Calculate the total and per capita costs of altruism.
5. Compare the per capita benefit for non-carriers to
the per capita (benefit - cost) for carriers. You
will notice that the variable factor f cancels out,
as does the allele frequency
p. You are left with the fact that carriers receive
enough extra altruism to compensate for the costs
of acting altruistically when rb>c. Try it. As I
wrote:

This is very clever. Given my logical analysis above,
your "proof" would seem to reveal cryptic ambiguities in
Hamilton's original thesis. BTW, have you agreed in the
past that all of this goes out the window for
deterministic reasons when there is only one copy of the
allele around, because then altruism only costs the
allele fitness points?

I understand what you are saying. Clearly, the only
altruist in the population cannot also be a recipient,
and hence can't be more fit than the rest of the
population. (I could point out that you are assuming that
the allele is dominant, but that is not my real objection
to your point.)

Frankly, I consider this a minor quibble - not much more
forceful than if you had pointed out that a rabbit's speed
is simply a drain on its metabolism if it never encounters
a fox. But, I admit that what you say is true. I'm not
going to try to convince you of the validity of my earlier
response to your point.

So I guess that you concede that the validity of Hamilton's
rule depends "p", at least at this singular point. I suspect
you would even concede that the effect of "p" would be
observed at very low values of "p" when there is more than
one copy of the altruism allele around. So, we only disagree
about how far this effect will reach as you increase the
value of "p", which I have been arguing depends strongly on
population structure (and I would add population size).

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>> Why is that particular formula so important? Well,
>> when you do the math, you will see that the average
>> fitness of allele carriers will be greater than non-
>> carriers, as long as the carriers direct their
>> altruism to recipients of relatedness "r". That is,
>> average fitness of carriers will be higher as long as
>> rb>c. And the parameter "p" nicely cancels out of the
>> equations. Hamilton's rule is independent of p. As
>> long as "r" has the meaning above.
>>
> My criticism here is the same as one that I have been
> posting earlier in this thread. Your conclusion is
> sensitive to the implicit assumption that the
> population is large (effectively infinite) and well
> mixed. This combination does not generally exist in
> nature, because the larger a system is the harder it is
> to mix up.

Not my conclusion. Hamilton's. But I think you exagerate
the sensitivity.

Like you, I would say "just try it." If you do a simple-
minded model of agents interacting in space I think you
will quickly see the sensitivity.

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I think that all that is required is that the "well-
mixed" or effectively random mating breeding population
is larger than the local socially-interacting clique of
each individual.

Interesting. I would like to see the argument to this
conclusion; or is this your "gut feeling" at this point.
[BTW, I do not intent to impune "gut feelings." I admire
people that are in touch with their guts.]

Assume that the population is divided into "states",
within which mating is random (well mixed). Assume that
states are subdivided into "zip-codes", within which
organisms interact. A state can have one zip-code, or
several. Let "p" vary between states, but be constant
within a state. Perform the derivation of the Rule
separately for each state. Since p is constant within a
state, the derivation still works in each case. Note that
this would no longer be valid if a single zip-code covered
two different states with different "p" values.

I'm beginning to lose the thread of our argument, but I
think the assumption of constant "p" values within
subpopulations subverts the problem I was pointing to.
Indeed, that assumption is inconsistent with Hamilton's
model, which is about predicting changes in "p". If you
loosen up your model a little to allow for dynamic "p"
values, then each of your subpopulations can evolve
deterministically in different directions under their own
versions of Hamilton's rule. What would this mean for the
evolution of the whole system? I don't think that Hamilton's
rule would be a very precise guide at the global scale.

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And that "r" is pretty much the same everywhere.

As I have indicated before, I think this is a very
unrealistic assumption if you mean that "r" is the same
everywhere for any particular individual. If you mean
that the distribution of "r" is the same in the
neighborhood of every individual, then this may be a
reasonable approximation for some systems.

The altruistic gene "directs the altruism" toward kin or
neighbors. I am assuming that the gene produces the same
biased effects everywhere, and, as you say, that
neighborhoods are similar in their kinship structure
everywhere.

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It is not important whether "p" is pretty much the same
everywhere.

What if I moved the pieces on the board of life so that
each copy of the altruism allele is surrounded by a sea
of purely selfish individuals? Note that this can only be
done when "p" is small.

But this means you have just set "r" to zero (or
actually, to a small negative number)! Everywhere. So the
Rule still works.

Sorry. I forgot about your definition of "r". I was still
using it in the genealogical sense of KIN selection.

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If "p" is large, then I could still change the balance of
Hamilton's rule when "rb" is only slightly larger than
"c" by isolating many copies of the altruism allele in
local seas of selfishness.

Your thought experiments strike me as artificial, and
hence not particularly relevant. Maybe you are trying to
tease out hidden assumptions. I think that the assumption
that you are attacking here is an explicit one - that "r"
is constant. In this case, you are still changing "r".

So your "r" is critically dependent upon population
structure. Right? Didn't you once argue that Hamilton's rule
did not depend upon population structure?

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> It also gets harder and harder to effectively mix the
> finite population when "p" is either very small or very
> large, because in either case there are very few quanta
> of the rare allele.

True enough, but now you are criticizing how
deterministic Hamilton's rule is, rather than claiming
that it is incorrect (biased) at extreme frequencies.

Note my arguments above about bias when "p" is small
and/or unevenly distributed.

Noted. I am discounting your small p argument, and
accepting your uneven distribution argument only if you
have interactors that, for some reason, don't interbreed.
Perhaps modern human India, Bosnia, or Northern Ireland
fit your requirements. Hmmm. Now that I think about it,
perhaps my zip-code analysis is extraneous.

What do you think of my "flipside" argument above regarding
systems constrained to sib-sib mating?

Regards,

Guy

"Guy Hoelzer" <[email hidden]> wrote in message
"]news:[email hidden]...

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in article [email hidden], Perplexed
in Peoria at [email hidden] wrote on 6/23/04
9:06 AM:

Quoted message said:

"Guy Hoelzer" <[email hidden]> wrote in message
"]news:[email hidden]...

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in article [email hidden], Perplexed
in Peoria at [email hidden] wrote on 6/22/04
1:16 PM:
> "Guy Hoelzer" <[email hidden]> wrote in message
> "]news:[email hidden]...
>> in article [email hidden],
>> Perplexed in Peoria at [email hidden] wrote
>> on 6/16/04 10:15 PM: Whatever method is used, the
>> result has to be an "r" with the following property:

Randomly

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>> choose one of the two genes at any locus in the
>> donor. Suppose that

the

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>> frequency of this allele in the general population is
>> "p". Now,

randomly

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>> choose one of the two genes at the same locus in the
>> recipient. It

must be

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>> the case that the probability that the two randomly
>> selected genes

are

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>> identical is (r + (1 - r)p). That is, there is a
>> probability r that

they

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>> are identical IBD, but if not, then there is still a
>> probability p

that

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>> they are identical for other reasons - because the
>> allele is fairly

common

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>> in the population. [snip]
Well, "r" can never be known and can only be estimated
with an underestimation bias. The degree of the bias
depends on the amount of unknown inbreeding in the
common ancestry of two individuals.

[snip]

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Putting aside the fact that we rarely have information
going back more than one generation, the

greater

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issue has to do with inbreeding. The parameter "r" can
take on any

value in

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the face of inbreeding. For example, full sibs actually
have 0.5 >= r

<= 1.

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In fact, it is very common to have levels of inbreeding
that make our

naïve

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estimates of "r" significantly lower than they actually
are. Truth be

told,

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r=1 for every pair of individuals (even from different
species) if you

were

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to consider all the data (and ignore
mutation/divergence). Do you have

a

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justifiable rule for how ignorant we ought to be when
we try to

estimate "r"

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in order to make the false estimate useful in
understanding kin

selection in

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nature?

It is clear that you still don't understand what "r" is.
The history of

the

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population, and the fact that it may be inbred in the
recent or distant past is totally irrelevant. The only
way inbreeding could be relevant

would

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be if the population routinely breeds with close
relatives for reasons

other

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than small population.

Forget IBD for a moment. Let p be the frequency of the
altruistic

allele

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in the general population. Let P be the frequency of the
allele in the recipients. Define r to be that value
which satisfies the equation P = r + (1-r)p That is, r
represents, in a mathematically wierd way, the degree to

which

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P exceeds p.

As I said before, I like this way of thinking about the
model, at least in some ways. I think you have
internalized Maynard-Smith's version of Hamilton's model.
Those two great thinkers thought about things in very
different ways, IMHO. I am not sure that Hamilton ever
verified that the Maynard-Smith version was consistent
with his thinking. IMHO Hamilton thought of "r" primarily
as a measure of genealogical relationship, which

is

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not what it means in your equation above.

I'm not sure how Hamilton thought of "r". But someone else
on this thread seemed pretty convinced that WDH thought it
was a regression coefficient. If I understand things
correctly, that is exactly what the "r" in my formula
is.

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If you wish to understand why inbreeding is not
important, perform the following thought experiment.
Imagine a population derived from a single breeding pair
which has grown to a population of 64 with the
population doubling each generation. But, to make sure
that we have variation for altruism, make both of the
original pair heterozygous. Assume that mating is random
and monogamous. "p" is 1/2. Assume the altruism is
directed to full sibs. I think that you will find that r
is not much larger than .5 and certainly less than .6.
Or, for variety, start with p = 3/4 or 1/4. "r" still
will be less than .6 AFAICS

You assumed something like random mating in an
exponentially growing population, which basically the same
as assuming that inbreeding is not occurring.

Inbreeding is not occurring now, though it did in the F1 and
F2 generations.

Yes, I am trying to show that in an inbred population, which
is now mating randomly, the fact of the past inbreeding
makes little difference in whether "r" calculated by IBD
matches "r" calculated by my formula. I thought that I was
responding to what you wrote above. Apparently, I
misinterpreted what (still) seems to be a clear claim that
the degree to which the population is inbred must be taken
into account before assuming that a truncated IBD
calculation is a good estimator of "r".

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It is certainly not surprising to conclude that inbreeding
does not affect "r" when you assume that inbreeding does
not occur. To illustrate why inbreeding IS important,
consider a hypothetical population in which sib-sib mating
is the norm. Such a population quickly loses its
heterozygosity and becomes constituted by families filled
with altruists

and

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families lacking altruists. Now P>>p, and your "r"
value is

correspondingly

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much higher. So "r" is sensitive to inbreeding.

I never said it wasn't. To quote myself a few lines above:
"The only way inbreeding could be relevant would be if the
population routinely breeds with close relatives for reasons
other than small population."

I'm still not sure I understand the differences between
Malecot's IBD and Wright's coefficient of relationship in
populations with recent inbreeding. I also don't know
which is the best estimator of "r". However, I am not yet
convinced that one of these genealogical parameters, even
if truncated after N generations, say, doesn't still give
an estimate of "r" that is valid to within 1 / 2^N. You
are welcome to try to convince me. Obviously, the true IBD
"r" for full sibs will be greater than 1/2 in your
incestuous population, as will the truncated IBD "r" and
the real (my formula) "r". But I don't quite know how to
calculate any of them.

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>>> [snip] Or, if like McGinn, you have an intuition
>>> that geneological history

cannot

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>>> be causal in this situation, ignore the IBD above.
>>> "r" is simply a measure of how much more likely than
>>> "p" it is that the two genes

are

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>>> identical for whatever reason. The key thing is that
>>> the formula (r

+

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>>> (1-r)p) gives the probability that the alleles are
>>> "shared".
>>>
>> Hmm. There are some things about this formulation
>> that I like, and

some

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>> problems I see. Can you please save me a little
>> research time and

tell us

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>> where you come by the formula (r + (1-r)p)? Is this
>> your

interpretation of

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>> Hamilton, or has it been published?
>
> It is a straightforward interpretation of the verbal
> explanation given

in

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> Maynard Smith's "Evolutionary Genetics" (2nd ed. p169)
>
> Now we can picture the genome of the recipient as
> consisting of two parts:
> 1. a fraction r containing genes IBD to genes in the
> actor; and
> 2. a fraction (1-r) consisting of genes that are a
> random sample of genes in the population.

This is a very familiar modeling trick. The same thing
is done when

modeling

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inbreeding for other purposes. It is, however, just a
trick that makes

the

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Quoted message said:

math work out easily. The flaw becomes clear when you
recognize that

any

Quoted message said:

Quoted message said:

Quoted message said:

random sample of the gene pool will potentially contain
gene copies

that are

Quoted message said:

Quoted message said:

Quoted message said:

IBD with the target, so the fractions are not mutually
exclusive. Given

your

Quoted message said:

Quoted message said:

Quoted message said:

definition of "r", "(1-r)" must be the fraction of the
recipient's

genome

Quoted message said:

Quoted message said:

Quoted message said:

containing genes that are NOT IBD, which is different
from "a random

sample

Quoted message said:

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of genes in the population."

I think that my argument above including the phrase
"forget about IBD for a moment" addresses this concern.

I agree that this second way in which you defined your
parameters is more logical. However, that does not
validate the way you defined them at

first,

Quoted message said:

which I still argue had a logical flaw. In fact, I think
these two definition sets are inconsistent with one
another, so you should decide which one you want to use
and stick with it.

I wish you had given that advise to Hamilton. ;-)

Even in Maynard Smith's formulation, there is not the
logical flaw that you claim. The fraction "r" does not
contain ALL of the IBD genes. Only enough of them that the
"1-r" fraction looks like the general population in ITS
content of IBD genes.

Another way of looking at this is that the fraction "r"
contains approximately all of the genes that are recently
IBD, and those genes that are IBD due to events in the
distant past (a history you share with the general
population) are in the (1-r) fraction. Of course, this fuzzy
language cannot be part of the definition, it is part of a
fuzzy "empirical" observation.

Quoted message said:

Quoted message said:

Quoted message said:

[snip] BTW, have you agreed in the past that all of
this goes out the window for

deterministic

Quoted message said:

Quoted message said:

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reasons when there is only one copy of the allele
around, because then altruism only costs the allele
fitness points?

I understand what you are saying. Clearly, the only
altruist in the population cannot also be a recipient,
and hence can't be more fit than

the

Quoted message said:

Quoted message said:

rest of the population. [snip]

Quoted message said:

So I guess that you concede that the validity of
Hamilton's rule depends "p", at least at this singular
point. I suspect you would even concede

that

Quoted message said:

the effect of "p" would be observed at very low values of
"p" when there

is

Quoted message said:

more than one copy of the altruism allele around. [snip]

Actually, if "r" is calculated by my formula, I don't need
to concede anything. My formula gives the value of "r" as
zero (or actually -1/N) when there is only one carrier of
the allele. So Hamilton's rule still works.

What you are actually proving is that the assumption that
r is independent of p is an impossible assumption to
actually carry out when Dr Hoelzer is busy constructing
counter-examples.

Quoted message said:

[snip] I think the assumption of constant "p" values
within subpopulations subverts the problem I was pointing
to. Indeed, that assumption is inconsistent with
Hamilton's

model,

Quoted message said:

which is about predicting changes in "p".

My understanding of the jargon of pop gen is that an
assumption that "p" is constant in a model which attempts to
predict changes in "p" is known as a "weak selection
assumption". It is, IIUIC, pretty standard.

Quoted message said:

[snip] So your "r" is critically dependent upon population
structure. Right?

Of course. It is very dependent on it if the altruism is
dispersed indiscriminately to neighbors. It is less
dependent if the altruism is based on kin recognition, but
even here, it is hard to be nice to your kin if an ecologist
hostile to Hamilton has rearranged the population so that
you can't find your kin. :-)

Quoted message said:

Didn't you once argue that Hamilton's rule did not depend
upon population structure?

I don't recall doing so. I would be extremely reluctant to
do so now, given your creativity in postulating structures.
However, I will note that having "r" dependent on the
population structure is a different matter than having the
Rule dependent.

Quoted message said:

[snip] What do you think of my "flipside" argument above
regarding systems constrained to sib-sib mating?

You want to know what I *honestly* think of it? ;-)

I can't offer an opinion until someone clears up the
Wright/Malecot confusion for me. But I strongly suspect
that it makes absolutely no difference to the
applicability of the Rule when "r" is calculated using my
formula. It may make a difference as to whether IBD is a
good estimator of "r".

"John Edser" <[email hidden]> wrote in message
"]news:[email hidden]...

Quoted message said:

JM:- I fully agree that most altruism-like behaviors in
nature (excluding parental care, and perhaps the social
insects) are based on reciprocity rather than on the
unilateral altruism covered by the Rule.

JE:- Proposition: Reciprocity is only stable if Darwinian
fitness gains are mutualised.

JM:- I have no problem agreeing with this statement. In
fact, as I have said, I believe that even Hamilton's
unilateral altruism without hope of reciprocation is favored
by natural selection and by Hamilton's Rule, only if the
Darwinian fitness gains are mutualized on average.

I think that Hamilton realized this. I think that many,
though perhaps not all, of the defenders of Hamilton in this
newsgroup realize it.

However, Hamilton's rule is not dispensible. It is the
simple way to determine whether or not unilateral altruism
directed toward kin does turn out to be effectively
mutualized. It will be mutualized if and only if the
recipients of your genetically directed altruism are enough
like you genetically that they are genetically directed to
be altruistic to you. If rb>c, then the fitness gains are
mutualized. If rb<c, then an altruist is a net loser (as
compared to non-altruists).

JE:-

Quoted message said:

The most basic absolute assumption of evolutionary theory
is Darwinian fitness which is a finite total.
______________________________________________________-
________
Darwinian fitness is EXACTLY: The _total_ number of
_fertile_ forms reproduced by _one_ parent within _one_
population.
______________________________________________________-
________

JM:- I am still unclear about what an "absolute assumption"
is, but I would definitely agree that Darwinian fitness, as
you have defined it, is central to evolutionary theory. As
you will recall, Hamilton said so too, in 1964.

JE:-

Quoted message said:

When an altruistic gene only relatively increases in freq
at just one point in time because it increased more than
the wildtype gene did, but the _total_ number of both
genes _decreases_, then Hamilton et al cannot validly
claim that the altruistic gene has spread because both
genes are now heading for extinction.

JM:- Here, you are arguing against the habit within
population genetics of working with relative fitnesses
rather than absolute fitnesses. But this habit is
independent of Hamilton's kin selection theory - you can
derive Hamilton's rule, AFAICS, regardless of whether "b"
and "c" are taken to be increments to an absolute fitness or
increments to a relative fitness. (Or, for that matter,
increments to a selection coefficient).

In any case, Hamilton's rule simply cannot favor spiteful
behaviors that tend to drive the population to extinction
unless r < 0. Hamilton did indeed consider this possibility
in 1970, but it has not been encountered in the real world,
AFAIK. Altruism could drive the population to extinction
only if r>1, and that is impossible. Of course, selfishness
can drive a population toward extinction under either
Hamilton's rule or "Darwin's rule" - "0 > c". The reason is
that NS is not Kantian - it never asks the question: "What
if everyone did this?"

JE:-

Quoted message said:

Likewise, if the total number of wildtype genes increases
more than the total number of altruistic genes does
because both totals have increased, then no altruism is
evident even as the "altruistic gene" decreases relatively
to the wildtype.

JM:- I'm not sure I understand what you are saying here with
"no altruism is evident".

JE:-

Quoted message said:

Hamilton's relative measure of gene freq. change was never
enough to substantiate his argument, which entirely
dominates evolutionary theory even today, that a TESTABLE
altruistic in fitness gene can spread.

Without a fully testable definition of Darwinian
fitness ...

JM:- John, I'm not going to respond to this part about
"testable". However, you will be happy to hear that
Amazon has just today delivered to me a copy of "The
Logic of Scientific Discovery", along with Miller's
"Critical Rationalism". So, I may be re-engaging with you
regarding epistemology in a few weeks when I have had
time to read them.

Quoted message said:

JM:- [snip] I am just an amateur OOL person who happened
to get interested in Hamilton's Rule because it seemed to
be controversial in this group. So, ultimately, I suppose
this conversation can be blamed on Edser :-)

JE:- Don't shoot me I'm just a messenger who plays
trombone for a living, shoot Hamilton et al who are paid
to do this stuff...

JM:- I hope to have my intellectual guns loaded in the near
future. Only then will I begin the search for targets. ;-)

Until then, have a nice day.

William Morse said:

Quoted message said:

JM:- I fully agree that most altruism-like behaviors in
nature (excluding parental care, and perhaps the social
insects) are based on reciprocity rather than on the
unilateral altruism covered by the Rule.

Quoted message said:

GH:- It's good to know that our estimates of reality
are close.

WM:- I disagree with both of your estimates of reality. I
thought Hamilton originally suggested his rule to answer the
question of how a feature like the toxicity of monarch
butterflies could evolve. This feature has nothing to do
with reciprocity. It might not be considered altruism by
most, but in fact is, since being toxic doesn't help an
individual at first - the individual will still be killed by
the predator.

JE:- If the sacrificed individual was just an infertile form
then it only had zero Darwinian fitness so no Darwinian
fitness altruism re: that individual, results from its
death. The genes within infertile forms can only be selected
within their _fertile_ parents, i.e. from whence they came
because all genes within infertile forms cannot be passed
on. Thus it is logically possible to argue that the parents
of a predated species that had some of their infertile forms
taken by predators, allowing the predator species to learn
the prey type it was eating was toxic raised more and not
less infertile forms to fertile adulthood. Note that if the
toxicity to the predator species also reduced that predators
Darwinian fitness then selection was reciprocal to prey and
predator. Without predator toxicity, i.e. the prey species
just tastes awful, this argument remains non reciprocal
because it depends on selection acting unilaterally on prey
within one population.

The Darwinian selectee reciprocal argument between prey
individuals, that excludes the predator, suggests that when
fertile parents that contain the toxicity gene have a risk x
of being taken but increase their Darwinian fitness by y
amount because the risk is small enough such that y>x in its
effect on the average Darwinian fitness of selectees, then
the gene can spread. Note that most species are serial
reproducers so that one Darwinian fitness total requires a
finite time frame to complete. While incomplete, altruism
can be _falsely_ diagnosed using Hamilton's rule because it
did not provide a time frame within which to conclude
altruism was the only possible explanation for +c. Measuring
just a relative fitness difference over only one moment in
time makes it impossible to conclude that any cost +c
remained fitness altruistic for a serially reproducing
species. At the end of the time frame +c may become -c in
absolute terms.

Note that the larger the population sharing the risk that a
particular selectee (fertile form) will be eaten over the
predator species learning curve, the smaller the risk each
prey member has to take. This is due to risk reduction
selected by organism fitness mutualism (OFM) between prey
which uses the same logic as an insurance policy: the
premium in risk < gain. Hamiltonian organism fitness
altruism (OFA) is not required for either the reciprocal or
non reciprocal argument, if and only if, Darwinian fitness
remains _correctly_ identified which for Hamilton et al, has
never been the case. It remains impossible to raise this
issue within sbe because most Neo Darwinists that post here
refuse to admit that they did not know what Darwinian
fitness was.

Because Darwinian fitness was not understood by Hamilton et
al, no term for Darwinian fitness could be included within
the rule so the rule cannot diagnose OFA as Hamilton
suggested he could: all cases of +c. The rule cannot
distinguish between -c (mutualism) and a reduced +c (reduced
altruism). OFA can only be proven when Darwinian fitness is
selected within nature to be lowered,
i.e. the total number of fertile forms reproduced by one
parent within one population is selected to be reduced.
Because the rule only measures a relative difference at
just a single point in time and not an absolute
reduction/increase, the rule cannot distinguish between
OFA and OFM which stand as total contradictions to each
other. This means the rule remains unintelligible.

Darwinian fitness is:-
_________________________________________________
The total number of _fertile_ forms reproduced by each
parent within one population
__________________________________________________

Until a general term representing Darwinian fitness is
appended to Hamilton's rule, the rule must remain
biologically unintelligible.

Quoted message said:

snip<

Regards,

John Edser Independent Researcher

PO Box 266 Church Pt NSW 2105

[email hidden]

Quoted message said:

Quoted message said:

Quoted message said:

JM:- I fully agree that most altruism-like behaviors in
nature (excluding parental care, and perhaps the social
insects) are based on reciprocity rather than on the
unilateral altruism covered by the Rule.

Quoted message said:

Quoted message said:

JE:- Proposition: Reciprocity is only stable if Darwinian
fitness gains are mutualised.

Quoted message said:

JM:- I have no problem agreeing with this statement. In
fact, as I have said, I believe that even Hamilton's
unilateral altruism without hope of reciprocation is
favored by natural selection and by Hamilton's Rule, only
if the Darwinian fitness gains are mutualized on average.

JE:- Please note that everything of importance can remain
hidden within an average,
e.g. selective events acting at an _individualised_ level,
unless you invoke group selection.

Quoted message said:

JM:- I think that Hamilton realized this. I think that
many, though perhaps not all, of the defenders of Hamilton
in this newsgroup realize it.

JE:- The missing bit of Hamilton's model is the largest bit:
any objective_ definition of Darwinian fitness to allow an
UNAMBIGUOUS definition as to when organism fitness altruism
(OFA) exists within the rule. This was highlighted within a
previous exchange between Dr Bob O'Hara and myself: --------------quote----------------------

1) 22/01/2004:

JE:- What is the difference between a reduced positive c and
a negative c? If c was an abolute measure of fitness then
yes, a real difference exists. However c is only a relative
fitness cost and not an absolute fitness cost, so what is
the difference?

BOH:-

As far as the rule is concerned, none.

----------- end quote --------------------

I have also requested Prof. J. Felsenstein a senior in this
field who does post to sbe to answer some questions about
this quote. So far he refused my request.

In the quote above the rule is proven not to be able to
distinguish between reduced altruism (any reduced positive
c) and mutualism (any negative c) when organism fitness
altruism (OFA) and organism fitness mutualism (OFM) stand in
total contradiction to each other. This means the rule
remains biologically _unintelligible_.

Hamilton et al have no hope of claiming that (OFA) exists,
even within just a vastly over simplified model of nature
(let alone within nature itself) unless they know what
Darwinian fitness was and can _measure_ a selectee's
_reduction_ of it within the rule. This requires a general
expression for Darwinian fitness to be explicitly
represented within the rule. At the moment, no such
expression exists.

OFA has to prove that the actor has _reduced_ its Darwinian
fitness because of the donation b to recipients related r
(the number of recipients must be > 1 unless the recipient
was a clone) and did not increase it, where Darwinian
fitness can be proven to be:

____________________________________________________
box 1 The total number of fertile forms reproduced into one
population by one parent.
____________________________________________________

The proof of the above definition that I provided is
entirely experimental. When the Darwinian fitness of all
Darwinian selectees (fertile forms) are held artificially
equal within one natural population then all Darwinian
natural selection must cease. You have to ask yourself why
only a single Neo Darwinist who posts here (Dr Guy Hoelzer),
has responded to:

2) The definition of Darwinian fitness in box 1.
3) Its experimental proof.
4) The fact that Darwinian fitness and nothing else must be
proven to reduced within Hamilton's rule in order to
prove OFA.

The fact that the same experiment proves that Dr Moran et al
have not done their Darwinian (or epistemological) homework
because they incorrectly suggest that Darwinian selection
cannot be halted within one population as a control to
varify that random sampling error or any other defined
random process can cause "evolution". This fact alone,
highlights a consistent misuse of mathematical models within
Neo Darwinism let alone the deletion of Darwinian fitness
within Hamilton's model!

I have snipped your argument re: Hamilton's rule works no
matter if absolute or relative fitness measures are
employed. I will argue this view fundamentally flawed and
hope to have in place a detailed reply quite soon

Many Regards,

John Edser Independent Researcher

PO Box 266 Church Pt NSW 2105 Australia

[email hidden]

"Perplexed in Peoria" <[email hidden]> wrote in message news:<[email hidden]>...

<snip>

Quoted message said:

I'm not sure how Hamilton thought of "r". But someone else
on this thread seemed pretty convinced that WDH thought it
was a regression coefficient. If I understand things
correctly, that is exactly what the "r" in my formula
is.

That "someone else" is me. Hamilton agreed. And you are
absolutely correct that your r (which is Hamilton's r) is a
regression coefficient. This view of r is agreed upon by the
majority of experts in the field of social evolution theory.

<snip>

Quoted message said:

I'm still not sure I understand the differences between
Malecot's IBD and Wright's coefficient of relationship in
populations with recent inbreeding.

The two concepts are not rigorously related to eachother in
a general way. Wright was not entirely happy with Malecot's
formalism because of this lack of rigour. But, if we adopt
the standard approach whereby the components of Wright's r
are expressed in terms of prob i.b.d., then even without
inbreeding we get r equal to *twice* the prob i.b.d. between
individuals, so they are not even nearly equivalent.

<snip>

Quoted message said:

Actually, if "r" is calculated by my formula, I don't need
to concede anything. My formula gives the value of "r" as
zero (or actually -1/N) when there is only one carrier of
the allele. So Hamilton's rule still works.

You seem to be on the right track (i.e. your thinking does
seem to be consistent with conventional thought on the
mathematics of kin selection), however, if i understand what
you are trying to do above, -1/N should be -1/(N-1).

1/N + ((N-1)/N)*r = 0

=> r = -1/(N-1)

I think the problem might be that you had not included the
focal individual's allele frequency within the population
allele frequency
p. Although, as I said, I might have misunderstood what you
were doing.

William Morse <[email hidden]> wrote or quoted:

Quoted message said:

I thought Hamilton originally suggested his rule to answer
the question of how a feature like the toxicity of monarch
butterflies could evolve.

This feature has nothing to do with reciprocity. It might
not be considered altruism by most, but in fact is, since
being toxic doesn't help an individual at first - the
individual will still be killed by the predator.The
predator is likely thereafter to avoid the species - so it
is only after the toxicity gene has spread that it
provides any advantage to the bearer. The initial benefit
has to be to other individuals who are likely to share the
gene - i.e. kin. Note here that the benefit does not have
to be only to kin - in the monarch butterfly example the
benefit would be to all monarch butterflies - the benefit
to kin only has to exceed the cost to the individual.

Conventionally (i.e. if you avoid species level selection),
then spatialisation is important.

I.e. it would really matter that a predator who had a toxic
monarch for breakfast would be likely to be avoiding
relatives for lunch and dinner - by virtue of the fact
that they are in the same vicinity.

Without spatialisation, benefit would accrue equally to all
monarchs - and the costs would be paid only by those with
the gene - a result which is bound to be a net loss for them
in the competiton between them.

If you permit species-level or group level explanations,
toxic monarchs are no puzzle at all, of course.
--
__________
|im |yler timtyler.orgtimtyler.orgOpen ↗ [email hidden] Remove
lock to reply.

Guy Hoelzer <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

in article [email hidden], William
Morse at [email hidden] wrote on 6/26/04 10:00 PM:

Quoted message said:

It might not be considered altruism by most, but in fact
is, since being toxic doesn't help an individual at
first - the individual will still be killed by the
predator.The predator is likely thereafter to avoid the
species - so it is only after the toxicity gene has
spread that it provides any advantage to the bearer. The
initial benefit has to be to other individuals who are
likely to share the gene - i.e. kin. Note here that the
benefit does not have to be only to kin - in the monarch
butterfly example the benefit would be to all monarch
butterflies - the benefit to kin only has to exceed the
cost to the individual.

I agree that this accurately represents the kin
selection model.

I do not. If the gene benefitted all monarch butteflies
equally, and carries any personal cost, then the gene is
relatively unfit, and will decrease in frequency.

"Name And Address Supplied" <[email hidden]> wrote in
message "]news:[email hidden]...

Quoted message said:

"Perplexed in Peoria" <[email hidden]> wrote
in message

news:<[email hidden]>...

Quoted message said:

Quoted message said:

Actually, if "r" is calculated by my formula, I don't
need to concede anything. My formula gives the value of
"r" as zero (or actually -1/N) when there is only one
carrier of the allele. So Hamilton's rule still works.

You seem to be on the right track (i.e. your thinking does
seem to be consistent with conventional thought on the
mathematics of kin selection), however, if i understand
what you are trying to do above, -1/N should be -1/(N-1).

1/N + ((N-1)/N)*r = 0

=> r = -1/(N-1)

I think the problem might be that you had not included the
focal individual's allele frequency within the population
allele frequency
p. Although, as I said, I might have misunderstood what
you were doing.

You have indeed understood what I was doing. I accept your
correction. Silly mistake for me to have made, given the
current thread on HW. And thanks for confirming that I am on
the right track in my understanding of Hamilton. It is
amazing how many philosophical and mathematical subtleties
go into that simple result "rb>c".

"Name And Address Supplied" <[email hidden]> wrote in
message "]news:[email hidden]...

Quoted message said:

Guy Hoelzer <[email hidden]> wrote in message

news:<[email hidden]>...

Quoted message said:

Quoted message said:

in article [email hidden], William
Morse at [email hidden] wrote on 6/26/04 10:00 PM:

Quoted message said:

It might not be considered altruism by most, but in
fact is, since being toxic doesn't help an individual
at first - the individual will still be killed by the
predator.The predator is likely thereafter to avoid
the species - so

it is

Quoted message said:

Quoted message said:

Quoted message said:

only after the toxicity gene has spread that it
provides any advantage

to

Quoted message said:

Quoted message said:

Quoted message said:

the bearer. The initial benefit has to be to other
individuals who are likely to share the gene - i.e.
kin. Note here that the benefit does

not

Quoted message said:

Quoted message said:

Quoted message said:

have to be only to kin - in the monarch butterfly
example the benefit

would

Quoted message said:

Quoted message said:

Quoted message said:

be to all monarch butterflies - the benefit to kin
only has to exceed

the

Quoted message said:

Quoted message said:

Quoted message said:

cost to the individual.

I agree that this accurately represents the kin
selection model.

I do not. If the gene benefitted all monarch butteflies
equally, and carries any personal cost, then the gene is
relatively unfit, and will decrease in frequency.

I agree with NAS's quibble, though, as Tyler points out, the
butterfly "altruism" can be shoehorned into Hamilton if
there is spatial structure and the gene benefits local
monarchs more than it benefits all monarchs. Local monarchs
are disproportionately likely to be kin.

However, the sheer weakness of the resulting bias toward kin
is the reason why I don't believe that Hamilton has solved
this puzzle.

in article [email hidden], Name And Address Supplied at
[email hidden] wrote on 6/30/04 8:35 AM:

Quoted message said:

Guy Hoelzer <[email hidden]> wrote in message
news:<[email hidden]>...

Quoted message said:

in article [email hidden], William
Morse at [email hidden] wrote on 6/26/04 10:00 PM:

Quoted message said:

It might not be considered altruism by most, but in fact
is, since being toxic doesn't help an individual at
first - the individual will still be killed by the
predator.The predator is likely thereafter to avoid the
species - so it is only after the toxicity gene has
spread that it provides any advantage to the bearer. The
initial benefit has to be to other individuals who are
likely to share the gene - i.e. kin. Note here that the
benefit does not have to be only to kin - in the monarch
butterfly example the benefit would be to all monarch
butterflies - the benefit to kin only has to exceed the
cost to the individual.

I agree that this accurately represents the kin
selection model.

I do not. If the gene benefitted all monarch butteflies
equally, and carries any personal cost, then the gene is
relatively unfit, and will decrease in frequency.

I should have stated an assumption I always make that I am
convinced is always true. That is that every population is
embedded in space and exhibits isolation by distance. So,
close relatives are generally closer in space than randomly
selected members of a species, and the prey-avoidance
lesson learned by the predator who tasted the toxic
butterfly is more likely to live in the same neighborhood
as the dead butterfly's close relatives than a randomly
chosen butterfly individual. In a viscous population the
kin selection model can work even when altruists practice
random acts of kindness.

Cheers,

Guy

[email hidden] (Name And Address Supplied) wrote
in :"]news:[email hidden]:

Quoted message said:

Guy Hoelzer <[email hidden]> wrote in message
news:<[email hidden]>...

Quoted message said:

in article [email hidden], William
Morse at [email hidden] wrote on 6/26/04 10:00 PM:

Quoted message said:

It might not be considered altruism by most, but in
fact is, since being toxic doesn't help an individual
at first - the individual will still be killed by the
predator.The predator is likely thereafter to avoid the
species - so it is only after the toxicity gene has
spread that it provides any advantage to the bearer.
The initial benefit has to be to other individuals who
are likely to share the gene - i.e. kin. Note here that
the benefit does not have to be only to kin - in the
monarch butterfly example the benefit would be to all
monarch butterflies - the benefit to kin only has to
exceed the cost to the individual.

Quoted message said:

Quoted message said:

I agree that this accurately represents the kin
selection model.

Quoted message said:

I do not. If the gene benefitted all monarch butteflies
equally, and carries any personal cost, then the gene is
relatively unfit, and will decrease in frequency.

Note that I did _not_ state that the gene would benefit all
monarch butterflies equally - only that the benefit does not
have to be _only_ to kin. Now it may well be the case that
once the gene becomes widespread in a population it will be
fixed by drift, but that is not the point. Up until
fixation,in most real populations the gene will still
benefit kin more than non-kin simply because of the
proximity effect. Presumably your argument against equal
benefit is based on the idea that otherwise those who do not
have the gene will gain the benefit without incurring the
cost. Regarding this point,it is interesting to note that in
the real world there are mimicking species, but I am unaware
of significant polymorphism in toxicity occurring for
populations ( this may simply not have been studied).
Perhaps one of the factors that accounts for this is that an
individual who is freeloading will tend to prosper in
relation to nearby individuals, so that there will then be a
local population which does not have the gene. But if a
predator "learns" that monarch butterflies are no longer
toxic, it will tend to demolish precisely the local
population (since the predator will feed in one locale).This
will tend to hasten the fixation of the toxicity gene.

Yours,

Bill Morse

Guy Hoelzer <[email hidden]> wrote in
:"]news:[email hidden]:

Quoted message said:

in article [email hidden], Perplexed
in Peoria at [email hidden] wrote on 6/23/04
9:06 AM:

Quoted message said:

I fully agree that most altruism-like behaviors in nature
(excluding parental care, and perhaps the social insects)
are based on reciprocity rather than on the unilateral
altruism covered by the Rule.

Quoted message said:

It's good to know that our estimates of reality are close.

I disagree with both of your estimates of reality. I thought
Hamilton originally suggested his rule to answer the
question of how a feature like the toxicity of monarch
butterflies could evolve.

This feature has nothing to do with reciprocity. It might
not be considered altruism by most, but in fact is, since
being toxic doesn't help an individual at first - the
individual will still be killed by the predator.The predator
is likely thereafter to avoid the species - so it is only
after the toxicity gene has spread that it provides any
advantage to the bearer. The initial benefit has to be to
other individuals who are likely to share the gene - i.e.
kin. Note here that the benefit does not have to be only to
kin - in the monarch butterfly example the benefit would be
to all monarch butterflies - the benefit to kin only has to
exceed the cost to the individual.

Yours,

Bill Morse

"William Morse" <[email hidden]> wrote in message
"]news:[email hidden]...

Quoted message said:

Guy Hoelzer <[email hidden]> wrote in
:"]news:[email hidden]:

Quoted message said:

in article [email hidden], Perplexed
in Peoria at [email hidden] wrote on 6/23/04
9:06 AM:

Quoted message said:

I fully agree that most altruism-like behaviors in
nature (excluding parental care, and perhaps the social
insects) are based on reciprocity rather than on the
unilateral altruism covered by the Rule.

Quoted message said:

It's good to know that our estimates of reality are
close.

I disagree with both of your estimates of reality. I
thought Hamilton originally suggested his rule to answer
the question of how a feature like the toxicity of monarch
butterflies could evolve.

This feature has nothing to do with reciprocity. It
might not be

considered

Quoted message said:

altruism by most, but in fact is, since being toxic
doesn't help an individual at first - the individual will
still be killed by the predator.The predator is likely
thereafter to avoid the species - so it is only after the
toxicity gene has spread that it provides any advantage to
the bearer. The initial benefit has to be to other
individuals who are likely to share the gene - i.e. kin.
Note here that the benefit does not have to be only to kin
- in the monarch butterfly example the benefit

would

Quoted message said:

be to all monarch butterflies - the benefit to kin only
has to exceed the cost to the individual.

I think you are correct that Hamilton's model was intended
to cover this. However, I don't think it succeeds.

There is certainly an odd kind of intraspecific unilateral
altruism involved here. But the situation is complicated by
being interwoven with an even odder kind of interspecific
reciprocity. The butterfly informs the bird that it is
distasteful by its markings. The bird "reciprocates" by not
eating the butterfly. Within the butterfly species, it is
altruistic to be honest with the bird - this maintains the
bird-butterfly bond of trust which is beneficial to all
butterflies.

I have an unpublished model not involving kin selection to
explain this situation. The reciprocity with the bird is
essential for my mechanism to work.

Bill,

in article [email hidden], William Morse
at [email hidden] wrote on 6/26/04 10:00 PM:

Quoted message said:

Guy Hoelzer <[email hidden]> wrote in
:"]news:[email hidden]:

Quoted message said:

in article [email hidden], Perplexed
in Peoria at [email hidden] wrote on 6/23/04
9:06 AM:

Quoted message said:

I fully agree that most altruism-like behaviors in
nature (excluding parental care, and perhaps the social
insects) are based on reciprocity rather than on the
unilateral altruism covered by the Rule.

Quoted message said:

It's good to know that our estimates of reality are
close.

I disagree with both of your estimates of reality.

;-(

Quoted message said:

I thought Hamilton originally suggested his rule to answer
the question of how a feature like the toxicity of monarch
butterflies could evolve.

I think his mind was certainly open enough to include this
sort of phenomenon. I personally see his primary motivation
as one to come up with a plausible model for the evolution
of individual altruism given the crumbling of Wynne-Edwards
style group selection that was happening at the time. The
discrediting (right or wrong) of "for the good of the
species" thinking re-introduced altruistic phenomena as a
big problem begging a Darwin-istic explanation. Hamilton met
this daunting challenge by subtly shifting the target of
selection below (and some argue above) the level of the
individual, although his implicit use of alternative levels
of selection was rather cryptic in his own writings.
However, the success of the theory of kin selection paved
the way for David Sloan Wilson and others to develop
multilevel selection theory as a more general expression of
Hamilton's ideas.

Quoted message said:

This feature has nothing to do with reciprocity.

I don't want to quibble, but I am not so sure about this
claim. After all, if we are both toxic to predators, then I
benefit by being near you and you benefit by being near me.
I think that reciprocity is fundamentally about positive
feedback whether or not social interaction is involved.

Quoted message said:

It might not be considered altruism by most, but in fact
is, since being toxic doesn't help an individual at first
- the individual will still be killed by the predator.The
predator is likely thereafter to avoid the species - so it
is only after the toxicity gene has spread that it
provides any advantage to the bearer. The initial benefit
has to be to other individuals who are likely to share the
gene - i.e. kin. Note here that the benefit does not have
to be only to kin - in the monarch butterfly example the
benefit would be to all monarch butterflies - the benefit
to kin only has to exceed the cost to the individual.

I agree that this accurately represents the kin
selection model.

Cheers,

Guy

"Guy Hoelzer" <[email hidden]> wrote in message
"]news:[email hidden]...

Quoted message said:

in article [email hidden], William
Morse at [email hidden] wrote on 6/26/04 10:00 PM:

Quoted message said:

I thought Hamilton originally suggested his rule to
answer the question of how a feature like the toxicity
of monarch butterflies could evolve.

[snip GH opinions regarding history which are debatable,
but not worth debating]

Quoted message said:

Quoted message said:

This feature has nothing to do with reciprocity.

I don't want to quibble, but I am not so sure about this
claim. After all, if we are both toxic to predators, then
I benefit by being near you and you benefit by being near
me. I think that reciprocity is fundamentally about
positive feedback whether or not social interaction is
involved.

I agree that "reciprocity is fundamentally about positive
feedback", but I strongly disagree that "I benefit by being
near you and you benefit by being near me" constitutes
feedback. For feedback, you require something like "I
benefit *because* you benefit". Or, to look at it in another
way, the distinguishing feature of a feedback *loop* is that
it can be broken. If I cease to provide benefit to you, then
thru some chain of causality, this must result in you
ceasing to provide benefit to me.

You don't have feedback just because you have causal
"arrows" pointed in both directions. Those arrows have to be
connected.

In Guy Hoelzer said:

phenomenon. I personally see his primary motivation as one
to come up with a plausible model for the evolution of
individual altruism given the crumbling of Wynne-Edwards
style group selection that was happening at the time. The
discrediting (right or wrong) of "for the good of the
species" thinking re-introduced altruistic phenomena as a
big problem begging a Darwin-istic explanation. Hamilton
met this daunting challenge by subtly shifting the target
of selection below (and some argue above) the level of the
individual, although his implicit use of alternative levels
of selection was rather cryptic in his own writings.

I saw an interesting paper showing how kin selection can
be modeled mathematically with Price's Theorem in terms
of group selection. I also recall a paper by Maynard-
Smith showing how to model kin selection in terms of
individual selection. But I can't remember the titles --
can anybody help?

As to level at which selection is _really_ occuring, I liked
Sean Rice's essay, pantheon.yale.edugroup.htmlOpen ↗

I noticed an article by H. Allen Orr in the New York Review
of Books, in which he implies that kin selection requires
selection at the level of the gene. I was surprised that he
would make that statement. Sober addressed this belief on
pages 335 to 355 of his book, "The Nature of Selection."
Hamilton wrote that the classical models "admit no
possibility of the evolution of any characters which are on
average to the disadvantage of the individuals possessing
them," and Dawkins wrote that Hamilton got biologists to
stop focusing on organisms and start focusing on genes, but
both these statements are misleading. Population genetics
models had always paid attention to individual genes, and
they show how characters that are to the disadvantage of
individuals can evolve. Sober argues that inclusive fitness
is not a substitute for Darwinian fitness; instead, it is a
rule of thumb that approximates fitness. The fitness of a
trait is commonly defined as the average fitness of the
organisms possessing them. Sober writes, "Hamilton's insight
was that there are many ways for a gene to be advantageous
on average...Classical models of selection show how a
phenotype can be selected against without being
eliminated...On the other hand, this and other standard
models of selection do imply that a gene that is on average
deleterious must be eliminated, if selection is the only
force at work. Kin selection does not alter this fundamental
fact. Indeed, the greater average fitness of a gene is an
absolute criterion for increase under selection, regardless
of the level at which selection occurs." Hamilton simply
showed how the mean fitness of a gene or a trait can be
caused by interesting interactions among kin. Presenting
inclusive fitness as a new definition of fitness or as
evidence that all selection is genic selection obscures the
basic point.

Paul

in article [email hidden], Perplexed in Peoria at
[email hidden] wrote on 6/30/04 8:35 AM:

Quoted message said:

"Guy Hoelzer" <[email hidden]> wrote in message
"]news:[email hidden]...

Quoted message said:

in article [email hidden], William
Morse at [email hidden] wrote on 6/26/04 10:00 PM:

Quoted message said:

I thought Hamilton originally suggested his rule to
answer the question of how a feature like the toxicity
of monarch butterflies could evolve.

[snip GH opinions regarding history which are debatable,
but not worth debating]

Quoted message said:

Quoted message said:

This feature has nothing to do with reciprocity.

I don't want to quibble, but I am not so sure about this
claim. After all, if we are both toxic to predators, then
I benefit by being near you and you benefit by being near
me. I think that reciprocity is fundamentally about
positive feedback whether or not social interaction is
involved.

I agree that "reciprocity is fundamentally about positive
feedback", but I strongly disagree that "I benefit by
being near you and you benefit by being near me"
constitutes feedback. For feedback, you require something
like "I benefit *because* you benefit". Or, to look at it
in another way, the distinguishing feature of a feedback
*loop* is that it can be broken. If I cease to provide
benefit to you, then thru some chain of causality, this
must result in you ceasing to provide benefit to me.

You don't have feedback just because you have causal
"arrows" pointed in both directions. Those arrows have to
be connected.

Good point. So it may be more accurate to describe this
model, let's call it the "proximity=mutual benefit" model,
as something more like quantum entanglement than positive
feedback. I agree that this models lacks what we might call
reciprocity, but don't you think that the symmetry of
positive effect alone is sufficient to drive the reciprocal
altruism model?

I was actually going to say something about symmetry, rather
than "positive feedback" originally, but I wasn't sure that
I could express myself well enough in that framework to find
a resonance with this audience.

Regards,

Guy

"Paul Gallagher" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

In <[email hidden]> Guy Hoelzer
<[email hidden]> writes:

Quoted message said:

I saw an interesting paper showing how kin selection can
be modeled mathematically with Price's Theorem in terms of
group selection. ... But I can't remember the titles --
can anybody help?

There have been many. If you're the kind of person who wants
original sources, you want Selfish and Spiteful Behavior in
an Evolutionary Model
W. D. Hamilton, Nature 228, 1218-20 (1970) But also see
what Hamilton says about this paper in retrospect in
Chapters 5, 6, and 8 of Narrow Roads. And follow the
paper's reference to Price's paper in Nature.

My favorite paper on the topic is a big one: "A geometric
view of relatedness", Alan Grafen, 1985
users.ox.ac.ukoseb.pdfOpen ↗

Also good is: "The Price Equation, Fisher's fundamental
theorem, kin selection, and causal analysis", Steve Frank,
1997 stevefrank.org97Evol CausalOpen ↗
R.html

Quoted message said:

I also recall a paper by Maynard-Smith showing how to
model kin selection in terms of individual selection.

I also would be interested in seeing a reference for
that paper.

Quoted message said:

As to level at which selection is _really_ occuring, I
liked Sean Rice's essay,
pantheon.yale.edugroup.htmlOpen ↗

I liked it less well. See my reply to Edser on the thread
"Hamilton's Rule: light at the end of a LONG tunnel?" Also,
notice what Frank and Grafen say about the dynamic
insufficiency of Price's equation. This means that a group
selection interpretation of kin selection needs to make some
auxiliary assumptions about the breeding structure, so as to
restore the variance within groups that gets discharged by
selection. It is difficult to do so in a way that also
maintains the variance between groups.

"Guy Hoelzer" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

in article [email hidden], Perplexed
in Peoria at [email hidden] wrote on 6/30/04
8:35 AM:

Quoted message said:

"Guy Hoelzer" <[email hidden]> wrote in message
"]news:[email hidden]...

Quoted message said:

After all, if we are both toxic to predators, then I
benefit by being near you and you benefit by being near
me. I think that reciprocity is fundamentally about
positive feedback whether or not social interaction is
involved.

I agree that "reciprocity is fundamentally about
positive feedback", but I strongly disagree that "I
benefit by being near you and you benefit by being near
me" constitutes feedback. For feedback, you require
something like "I benefit *because* you benefit". Or, to
look at it in another way, the distinguishing feature of
a feedback *loop* is that it can be broken. If I cease
to provide benefit to you, then thru some chain of
causality, this must result in you ceasing to provide
benefit to me.

You don't have feedback just because you have causal
"arrows" pointed in both directions. Those arrows have
to be connected.

Good point. So it may be more accurate to describe this
model, let's call it the "proximity=mutual benefit" model,
as something more like quantum entanglement than positive
feedback.

A very evocative analogy! I share what it evoked in me
below. But first...

Quoted message said:

I agree that this models lacks what we might call
reciprocity, but don't you think that the symmetry of
positive effect alone is sufficient to drive the
reciprocal altruism model?

Symmetry of positive effect, along with some other
conditions, may well be enough to lead to the increase in
altruism in an evolutionary model. It does so in Hamilton's
model. My main concern here was to defend the received
meaning of "reciprocal". In both common usage and in
Trivers' model, the word assumes a causal linkage in the
feedback. It also assumes that the feedback is directed to
an individual. A reciprocator is not "repaying a debt to
society". He is repaying a "debt" to an individual. In
Hamilton's kin selection model, by contrast, there is
symmetry of positive effect, but not "reciprocity".

"Reciprocity" need not involve intentionality, however. I
think that the interchange of materials between cytoplasm
and mitochondria is reciprocal, in that the various antiport
machinery constrains the cytoplasm to stoichiometrically
supply food to the organelle to the extent that it extracts
energy. That is perfectly good reciprocity, by my
definition. In operation, it is not even teleonomic - merely
teleomatic, if that.

Quoted message said:

I was actually going to say something about symmetry,
rather than "positive feedback" originally, but I wasn't
sure that I could express myself well enough in that
framework to find a resonance with this audience.

One of the first things they teach you in an applied
statistics text is that "correlation" is not the same thing
as "causation". And one of the canonical examples of how you
can have a correlation without direct causation is when the
two things that are correlated are both results of the same
fundamental cause.

However, in spite of this warning, we continue the practice
in mathematical science of reasoning by writing down
equations in which the two sides are joined by the symmetric
equal sign. One cannot tell by inspection which side of the
equation is causal of the other. And, in fact, in our
mathematical reasoning, the direction of the causality is
not important. Models can still work, and can be
explanatory, even though they may involve what looks like
causal nonsense.

A prime example of this is Hamilton's kin selection. It is
essential to that model that there be genetic correlation
between the donor and the recipient. In the case of
siblings, or cousins, neither the donor nor the recipient is
the cause of the genetics of the other. However, there is a
correlation between them, caused by a shared fundamental
cause - namely the genetics of a shared ancestor. It was
Hamilton's genius to recognize that correlation is enough,
that you don't need causality, or rather that the math still
works if some of the causal arrows must be traced backward.
Edser doesn't seem to accept this. Similarly, in physics
Bohr recognized that correlation is enough, that you don't
need conventional causality. But Einstein, along with
Podolsky and Rosen, couldn't seem to accept this. (I don't
know whether the stroking implicit in this analogy will
soften or harden John's position. Time will tell ;-)

All of this tends to weaken my claim that "causality",
rather than "symmetry" is important in the meaning of
"feedback" or of "reciprocity". I guess that it is not
absolutely essential that an explanatory model have all of
the causal arrows connected and pointing in the same
direction. But still, I would like to reserve the words
"feedback" and "reciprocity" for those (most common) cases
in which the arrows DO all connect properly.

One final observation, or perhaps speculation: The reason
why science so rarely needs to consider explanations in
which causal arrows run in the wrong direction is that such
explanations usually don't work. Something else, not yet
considered here, is needed before backward causality - the
future determining the past - can actually be effective. It
is evocative, for me at least, that physicists sometimes
refer to this "something else" as a "selection rule".
Wilkins is perhaps wise in trying to rein in my use of
teleological language before I say something really
dangerous. ;-)