Re: Hamilton's rule in small population
- From: "John Edser" <edser@xxxxxxxxxx>
- Date: Thu, 3 Nov 2005 19:52:39 -0500 (EST)
Catherine Woodgold wrote:-
> >> > JE:-
> >> > In HR the recipients are equally related r to the actor.
> ...
> >> > the wolf donates x resources to p equally related cubs so
> >> > that each cub grows up and increases it's own mean Darwinian fitness
> by
> >> b/p
> >> > which reduces to a mean gene centric gain per individual of just rb/p
> >> > causing the rule to fail.
> > JE:-
> > Whenever rb>c then rb/p<c/p' where p'= the number of actors which is
> always
> > 1 so Hamilton's allele ALWAYS fails to be able to spread unless the
> actor
> > "inclusively selects" itself.
> > JE:-
> > It means Hamilton's gene always fails to spread when b is corrected by p
> > even on just a 100% relative basis.
> When Hamilton stated Hamilton's rule, what type of situation
> was he referring to? Was it one in which a single actor gave
> x resources to a single recipient?
JE:-
The only possible way that p=1 within Hamilton's rationale so that p can
validly remain ignored as Hamilton et al have ignored it for almost 50 years
is when the actor inclusively selects itself even within a sexually
reproducing population of clones, e.g. Felsenstein's infamous cheetah
population. Forcing Hamilton's actor to inclusively select itself by
pointlessly "donating" x resources to itself is the only situation which
actually works for the rule on an organism or a gene centric basis. On a non
heuristic group centric basis where b is not divided by p you only end up
with just the invalid proposition of attempting to compare "apples" with
"oranges", i.e. compare the b group centric gain with c, an organism centric
loss (or gain whenever c is negative) which of course always was and remains
to this day, invalid.
The direct conversion of b via r to produce a gene centric gain WITHOUT
firstly converting b to an organism centric gain is logically invalid
because the gene centric argument of Hamilton et al only measures gene
replications over organism generations and NOT organism population
generations of that gene. So the only correct gene centric conversion of HR
is rb/p> c where the rule fails to increase Hamilton's allele when rb>c even
on just a 100% relative basis.
> Or one in which a single
> actor gave x resources to multiple recipients? Or some other
> situation?
JE:-
The situation Hamilton envisaged is when x resources are donated to p
recipients where each recipient is related r to the actor. What he failed to
understand is that relatedness cannot subvert fitness.
> Suppose one actor gave x resources to p recipients such
> that each recipient received x/p resources. Suppose the
> result was a cost of c to the one actor and a benefit of
> b/p to each recipient. Suppose they were haploid and
> that there was a 50% chance that each recipient had the
> same gene as the actor, in a large population with
> random mating. (e.g. the actor knew that they were
> siblings.)
JE:-
If it is random mating, which was Hamilton's stipulation, it makes no
difference that "the actor knew that they were siblings" because the actor
cannot act on that information.
> Then the cost of c meant a loss of c units
> of the allele in the actor, and the benefit of b/p
> for each recipient meant a gain of (b/p)(0.5) units
> on average of the allele in each recipient.
JE:-
Yes, where rb/p which is the valid gene centric conversion of a group
centric b by firstly converting it to an organism centric b/p and only then
to a gene centric rb/p. When done _correctly_ gene centricity fails to allow
Hamilton's gene to spread even on just a 100% relative basis
> Totaling
> the losses and gains over all p recipients plus the one
> actor, the total gain in fitness units of the allele
> was p(b/p)(0.5) - c. If this gain is positive, that
> means the action contributes to spread of the
> gene. It's positive if 0.5b > c.
JE:-
Your "totaling" has improperly converted the organism centric (heuristic)
gene based argument back into a group centric (heuristic) gene based
argument WITHOUT the critical intervening organism centric conversion
process. The process of converting the group centric argument to a gene
centric argument has 3 very exact stages:-
1) b
2) b/p
3) rb/p
If you go from 1 to 3 or in your totaling process, from 3 to 1 you cannot
delete 2 because the heuristic gene centric argument of Hamilton et al very
strictly, only counts genes replicated over _organism_ generations and NOT
organism population generations of that gene forcing step 2. It is worth
noting that the only self consistent and therefore valid gene centric
argument is counting genes replicated over gene generations. The closest you
can get to this EMPIRICALLY is a cell centric argument.
Biologically ignorant mathematicians have allowed themselves to smash down
the critical fences that exist between DEFINED independent selectees
whenever it suits them to do so without paying for the damage. This ends up
producing a gene centric rule rb>c which is the equivalent of putting the
organisms concerned through a meat grinder.
Regards,
John Edser
Independent Researcher
edser@xxxxxxxxxx
.
- Follow-Ups:
- Re: Hamilton's rule in small population
- From: Catherine Woodgold
- Re: Hamilton's rule in small population
- Prev by Date: sexually reproducing haploid organism
- Next by Date: Re: positive transmutation
- Previous by thread: Re: Hamilton's rule in small population
- Next by thread: Re: Hamilton's rule in small population
- Index(es):
Relevant Pages
|
