Re: Applying TDF (was understanding y)
- From: "John Edser" <edser@xxxxxxxxxx>
- Date: Wed, 26 Oct 2005 01:11:46 -0400 (EDT)
"Perplexed in Peoria" jimmenegay@xxxxxxxxxxxxx wrote:-
> > > > JE:-
> > > > Two propositions of r^e exist where one is definitive within just a
> > > > heuristic model but the other is not:
> > > > 1) DEFINITIVE: Inclusive fitness cannot work in this case: the use
> of
> > > > r^e employing sexual selection for the same genotype. IF the AB
> > > > genotype can be
> > > > actively recognized using Dawkins' "green beard" phenotype THEN r^e
> > > > prohibits any such sexual selective event within HR (even after the
> > > > massive wastage of just random sexual selection has been saved) ...
> >
> > > > 2) NON DEFINITIVE: Inclusive fitness cannot be verified in this
> case:
> > > > the use of r^e within just random mating events. If the AB phenotype
> > > > alone acts altruistically then even if each gene can passively
> increase
> > > > the chance that it will become less diluted as the population
> expands
> > > > is not verified.
> > > > The proposition is that A and B becomes more diluted as e increases.
> > > > This is because random mating within an expanding population must
> > > > favor the wildtype
> > > > allele _because_ it is more common. The "duh" case is when no A or B
> > > > exists
> > > > in the population until a and b mutate to A and B. The degree of
> > > > difficultly
> > > > of just "starting" the passive selection of A and B is r^e, i.e.
> > > > inclusive
> > > > fitness cannot start when e>x where x is unknown but I would guess
> to
> > > > be no
> > > > more than a handful of genes. Quite obviously, much more than just a
> > > > handful
> > > > of genes are required to code for any complex phenotype so my
> > > > conclusion is:
> > > > inclusive fitness cannot start.
> >
> > > Haven't you just 'proved', John, that NO complex phenotype can get
> > > started?
> > JE:-
> > No. I have only provided a non definitive explanation as to why a
> complex
> > trait cannot even start to be selected using gene centric inclusive
> fitness.
> > > What is it that you think is special about Hamilton's hypothetical
> > > phenotype in this regard?
> > JE:-
> > Gene centricity within inclusive fitness.
> > > In any case, I do not understand the distinction you are making here
> > > between 'definitive' and 'non-definitive'.
> > JE:-
> > Simplified models can only be definitive for what _cannot_ work
> empirically
> > they cannot be definitive for what appears to work or what remains non
> > verified which is true for the 2nd case (above).
> >
> > > And I don't understand what you mean
> > > by "sexual selection" in the first case. Are you talking about
> assortive
> > > mating? A tendency of A to mate with B (and a with b)?
> > JE:-
> > Sexual selection is the tendency of AB to mate with AB because it can
> > identify the same genotype in the opposite sex.
> Ok, but I am pretty sure this kind of thing is usually called assortive
> mating, rather than sexual selection.
JE:-
Mathematicians, who remain hopelessly biased for just invalidly named
"neutral theory" operating within just heuristic gene centric population
genetics refer to it as "assortive mating". Organism centric biologists
employ the _correct_ biological term: sexual selection.
> > This provides the benefit of
> > not wasting x resources only benefiting aB, Ab or ab.
> I don't follow this. I thought that you talk about 'x resources" with
> regard to acts of altruism. Why mention it when talking about mating?
JE:-
If you spend x resources on p Darwinian recipients who are actually
competing very hard against you in order to raise their group selective
fitness by exactly b, which reduces to an mean increase in their organism
fitness of exactly b/p, costing you a total of c organisms to your own Total
Darwinian fitness leaving you with only R-x resources to now reproduce
yourself with, only because you employed the flawed assumption that each p
recipient is related to yourself by r which is just the probability that
just one identical allele in each p recipient may have been reproduced from
you, then you should make bloody well sure that you are not just wasting
your (and everybody else's) time when doing so...
> > With selective mating
> > you reproduce an AB altruistic phenotype every time and not hardly at
> all or
> > if ever,
> Yes, that 'every time' is true in a haploid model like the one we are
> using, or in a diploid model with the altruism genes recessive. But I
> don't agree with your 'hardly at all, if ever'. In our haploid model,
> if AB mates with aB, they still get half of their offspring as AB and
> the other half as the more fit type aB.
JE:-
No, the proposition is that no altruistic phenotype appears unless you have
AB.
> > so you speed up the time taken for x resources to be donated back
> > to you with interest. However, this benefit cost r^e which is much more
> than
> > the benefit selective mating can provide so it cannot evolve as a
> definitive
> > statement of evolutionary theory. Dawkins' green beard hypothesis was
> and
> > remains incorrect, yet it persists as a part of the folk lore of HR.
> >
> > > What is this
> > > "massive wastage of just random selection" that you mention?
> > JE:-
> > It is just a waste for AB to randomly mate with anything else besides AB
> re:
> > quickly advancing the AB altruistic phenotype via gene centric inclusive
> > fitness.
> Ok. I understand a little better now. You have discussed two rationales
> (you called them propositions) that might be offered for how altruism
> spreads. You reject the first, which involves assortive mating. That is
> OK with me, because I wasn't suggesting assortive mating. I don't
> completely
> understand your reasoning here, but it doesn't matter.
JE:-
It matters a WHOLE LOT. Any tautological argument, even the most
sophisticated mathematical treatment of one such as the mathematical
expansions of HR by Cathy, Felsenstein, yourself and many others here all
remain _circular_. At best a tautology misused as a valid theory of nature
can only describe two contrary propositions (relatively opposite
propositions like "up" and "down") but it will never be able to tell them
apart no matter what you do with it mathematically unless you define at
least one constant algebraic term to beak the circularity. Without one, as
much as anybody attempts to break the mindless circular reasoning somewhere
it simply reforms somewhere else because you cannot get something for
nothing. In this particular case e is maximized because A and B are defined
to be on different chromosomes obeying Mendel's law of random assortment
making e as hard and as costly possible. They could be defined to be next to
each other on the same chromosome so they remain linked making e as easy as
cheap as possible. However, now the probability that random mutation mutates
a to A and B to b on loci next to each other is much less than the
proposition they remain apart from each other so the cost blows out here to
pay for it because if it didn't you would end up get something for nothing.
> The second rationale is the one I was suggesting. It says that if rb>c
> and if the frequency of the alleles A and B is not vanishingly small,
> then both A and B will increase in frequency just as they would if
> the altruism trait were not epistatic (well, actually, a little slower -
> but they DO increase in frequency if Hamilton's logic for the non-
> epistatic
> case is correct). And since both A and B increase in frequency, then
> ultimately AB must increase in frequency.
JE:-
Not if A and B increase relatively less than a and b within an _expanding_
population.
> Let me try to paraphrase your objection to this rationale. You accept
> the logic, but claim that there is no way that A and B could ever rise
> in frequency from their initial 'vanishingly small' starting frequencies.
> And furthermore, if e > 2, it is even more difficult to get started.
> Do I understand your argument?
JE:-
As e increases just slightly, the probability that HR can start becomes an
effective zero.
> You wrote: "The degree of difficultly of just "starting" the passive
> selection of A and B is r^e". You know what, John? I believe you are
> right. But that doesn't mean that the rule should be written as
> (r^e)b > c. Once the process DOES get started, however it starts, the
> correct form of the rule is rb > c.
JE:-
A well meaning parent sits a wide eyed 10 year old on his lap and eloquently
expounds to the child about what they will do with a million dollars. The 10
year old listens intently. At the end the child tells the parent that they
do not have a million dollars. However, the child does so in a compassionate
and loving way only because that child knows, like any 10 year old child
knows, adults are just fools.
Since I am not an all knowing 10 year old I will say it in a non
compassionate way: If HR cannot start then it is idiotic to assume that it
has and then just carry on from there within evolutionary ***SCIENCE***.
Hamilton's Rule is like a perpetual motion machine. It cannot start and but
it you start it heuristically, it cannot stop....
> It might be interesting to consider a model in which the cost 'c' is not
> epistatic, but the altruistic behavior is epistatic. That is, if you
> are 'A' rather than 'a', you bear a cost c/2. If you are 'B' rather
> than 'b', you bear another cost c/2. And if you have both 'AB', then
> you bear a total cost c but you can bestow benefits b on your kin.
> In a model like this, it is quite possible that your version of the
> rule - (r^e)b > c - might be the right rule. I haven't done the math,
> but it is pretty clear that the altruism would have to pay a lot of
> 'interest' to be worthwhile in this scenario.
Your proposition, while heuristically interesting, cannot be resolvable
empirically until you include the total fitness of the actor on just one
side of the calculation.
Regards,
John Edser
Independent Researcher
edser@xxxxxxxxxx
.
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