Re: Ernst Mayr: Where Are We (1976)
- From: "Malcolm" <regniztar@xxxxxxxxxxxxxx>
- Date: Sat, 4 Jun 2005 13:03:35 -0400 (EDT)
"Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx> wrote
>
> Because it is an "empirically true fact" that epistatic gene fitnesses
> (as you seem to use this term) are not heritable.
>
"Empirical" means "of experience". It is difficult to measure fitness, or
the contribution of any one gene to fitness, directly.
John Edser's argument goes; we know that it is unlikely that a a gene could
produce something as complex as altruistic behaviour all on its own. If
several genes are involved it is likely that mutations affecting the trait
are present on more than one gene within the population. So let's assume we
have three loci, a, b, and c, with alternate allele A, B, C, such that the
combination ABC gives a certain level of altruism. Now the chance of a
relative also having the combination ABC is r^3 (skating over Washburne's
fallacy here). Therefore, and here is where I beleive he goes wrong, the
combination will only spread if benefit exceeds cost by a ratio of r^3.
However the argument is not empirical, but mathematical. Joe Felsenstein
posted a model a while back. Unfortunately he is not on speaking terms with
John Edser so other sbem denizens never got to find out who was right.
>
> There do exist models of two epistatic loci dependently selected at the
> organism level. The key issue in such models is the degree of linkage
> (segregation independence) between the two loci. It turns out that if
> the loci are unlinked (on different chromosomes, say), then
> **under the assumption of random mating**
> the process of recombination undoes any linkage disequilibrium created
> by selection. Hence, the standard "independent selection of loci" model
> are close to correct, as long as you allow the fitness of alleles at one
> locus to depend upon the frequency of alleles at another locus.
>
> On the other hand, if the loci are tightly linked (close together on the
> same chromosome, say), then recombination will disrupt the linkage
> disequilibrium only rarely. Under these circumstances, you can think of
> the two loci (each with two alleles) as a single locus (with four alleles)
> and the situation is again well handled by the standard models.
>
> Models exist for the cases of close (but not too close) linkage, but they
> are not exactly *simple* models. Models also exist which relax the
> assumption of random mating, and which thereby make the epistasis somewhat
> > "heritable" in that way. These models are definitely NOT simple. As I
> understand it, this is the kind of issue which distinguishes Wright's view
> of
> selection in structured populations from Fisher's view of selection in
> well-
> mixed populations. One of these days, I am going to have to dig up a good
> tutorial on Wright's F-statistics and see how they work.
>
It not obvious to me that epistatic interactions, if we relax assumptions
such as random mating or random meiosis, won't also lead to some rethink of
Hamilton's rule. Also the "green beard effect", implausible for single
genes, becomes less implausible if we start talking about groups of genes.
Maybe someone will post a model. However I cannot see how b > c r^e will
come out of any such model.
>
> You also demand that the models work at the "fertile organism level of
> selection" rather than just at the "organism level". I understand this
> to mean that the selective fate of an immature organism is taken to be
> a function of its parents' genomes, rather than its own. But this is also
> empirically untrue, at least in part. While the parents' genomes are
> important (in plants and in animals with parental care, at least), the
> genome of the immature organism is different from that of its parents
> and it is very important in determining the fate of the immature organism.
>
Not really. Many organisms don't influence their own success significantly
until quite an advanced stage of development. A baby bird, unless it has a
serious defect, will hatch if the parents incubate and not if they don't. As
a chick, when huge mortality takes place, its fate will be determined
largely by the parent's ability to bring food, parasites, and other
nestmates. Only when it leaves the nest and begins to find food for itself
will its genetic make-up really begin to be very important in determinig
whether it reproduces or doesn't.
I don't however see the relevance to models of altruism.
>
> Models which make selection dependent upon two or three genomes are
> definitely NOT simple. They are also unnecessary, since Hamilton has
> shown us how to work with a simple model in which the *inclusive* fitness
> of an organism is taken to be dependent upon only its own genome.
>
You could have a relatively simple model in which fitness of A depends on
whether father is A or a. Let's say it is gene for alcohol dehydrogenase and
the organism in question, the beer monster, relies on sneaking some of dad's
supplies in early development. If dad is A, then dad cannot drink, and baby
beer monster may die of thirst. If dad is a, plenty of beers in the fridge,
and he's away.
>
> I invite people who understand pop gen better than I do to comment upon
> my summary.
>
Is that a disinvitation to those of us who understand it worse?
Seriously, once you understand maths it is yours. Given the assumptions, it
is no more possible that the chance of a new mutation being fixed by drift
is not1/(2N) than it is that 2+2 = 5.
.
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