Re: Fundamental theorems, dilemmas, fitness, and information
- From: "Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx>
- Date: Thu, 30 Jun 2005 12:07:41 -0400 (EDT)
"John Edser" <edser@xxxxxxxxxx> wrote in message news:d9tb6n$1r37$1@xxxxxxxxxxxxxxxxxxxxxx
> "Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx>
> >
> > > JE:-
> > > I don't wish to appear overly argumentative but the definition of
> > > Darwinian fitness which is entirely empirically based is very exact
> > > and has to be appreciated as such. It is: the _total_ number of fertile
> > > forms reproduced into _one_ population by _each parent_, i.e. it is
> > > not just an incomplete count of "fertile offspring" produced by anybody
> > > within any population.
>
> > > > JM:-
> > > > Fisher prefers to define it as
> > > > a growth rate. To get from an Edser fitness to a Fisher fitness,
> > > > just take the logarithm.
>
> > > JE:-
> > > I don't think so. Take the logarithm of a biological count of
> > > exactly what?
>
> > JM:-
> > Take the logarithm of "the _total_ number of fertile
> > forms reproduced into _one_ population by _each parent_", of course.
> > Take the logarithm once per individual (parent).
>
> JE:-
> Ok.
>
> > JM:-
> > Or, average together
> > the fitnesses of a bunch of individuals, and take the log of
> > that. Once for each bunch. It depends on what you are trying to
> > accomplish.
>
> JE:-
> When you combine TDF's you erase the one and only independent fitness
> interface that actually exists within evolutionary theory. When you
> erase the empirical line that critically exists between all independent
> selective events and fail to even attempt to re-establish this line
> within your conclusion you repeat the "error" of Enron accounting
> allowing debits to become credits by eliminating independent events.
>
> > > > JM:-
> > > > Individuals that you say have zero fitness are individuals that
> > > > Fisher would say have huge negative fitnesses.
>
> > > JE:-
> > > I do not agree. My understanding of Fisher's concept of fitness is
> > > that he measures it per gene and not per organism and does not
> > > discriminate between the fitness of an allele reproduced within
> > > a mature fertile form and exactly the same allele reproduced
> > > into just an immature infertile form. [snip]
>
> > JM:-
> > OK. There are three issues here. One is the "gene fitness" vs
> > "organism fitness" issue. The second is the logarithms. The
> > third is how to measure the fitness of an individual organism.
> > Lets take them in that order.
>
> > It is probably incorrect to say that Fisher deals with fitnesses of
> > "genes". What you should say is that Fisher deals with fitnesses of
> > "types". A "type" is simply a set of organisms, all of which have
> > the same allele(s) at some locus. (For simplicity, I am going to
> > assume that our organisms are haploid.) The fitness of a type is
> > defined as the average fitness of all individuals of that type -
> > that is, the average fitness of the individuals with a particular
> > allele.
>
> JE:-
> If fitness is now the trait type but fitness per gene was not simply
> additive then fitness isn' heritable or selectable according to Fisher,
> i.e. Fisher had deleted all gene fitness epistasis as just non heritable
> and non selectable when all empirical gene fitnesses were then and
> remain today, gene fitness epistatic.
You seem to be objecting to the procedure of averaging together the
fitnesses of a collection of individuals of the same type. There are
two ways I can respond to this. The second is to point out that you
that you don't really HAVE TO average. The first is to claim that
averaging is the right way to do things, even if there is epistasis.
Yes, John. I see the contradiction. But I am allowed to speak
contradictions. I am an American. Just ask Walt Whitman:
http://www.quotationspage.com/quote/26914.html
The reason averaging is the right thing to do is that Fisher is trying
to calculate the increase (over a generation or over time) in the
frequency (when using relative fitnesses) or population (when using absolute
fitnesses or logarithms of absolute fitnesses) of alleles. He is not
calculating the frequencies or populations of epistatic combinations
of alleles. Why not? Well, he doesn't have to! If you want the
frequencies of the epistatic combinations, you can easily calculate
them from the individual allele frequencies. (There are various
assumptions embedded in this argument - linkage equilibrium & HW
equilibrium both before and after, etc. Those assumptions are pretty
close to valid in most cases. If they are not valid, there are more
complicated variants of the basic Fisher models that do not make these
assumptions. Now there is one thing that makes me a little uneasy here.
These assumptions are probably not much of a stretch if you calculate
fitnesses birth-to-birth as I would prefer. But they are more of a stretch
if you calculate fitnesses maturity-to-maturity as you prefer. So, I am
not yet absolutely certain that your worries about epistasis are totally
groundless.)
But then you don't absolutely have to average (much) to use Fisher's
models. Earlier in this thread, I defined a type thus:
A "type" is simply a set of organisms, all of which have
the same allele(s) at some locus.
That was an oversimplification. I should have written "...at some loci."
If you wish, you can define the two-locus type AB, which "competes" against
types Ab, aB, and ab. Compute the fitness of each of these types by averaging.
But you can extend this by looking at three-locus types, or ten-locus
types. In the ultimate extension, you look at all-locus types. Now, the
only averaging that takes place is if you have identical twins. (I assume
you would not object to averaging in this case.)
But there is a difficulty with this. In the simple one-locus case, for
a sexual species, we "know" that half of the offspring of a type A individual
will be of type A "by descent" from the focal parent, and that some more
will be of type A "by descent" from the other parent. But in the two locus
case, only a quarter of the offspring of a type AB individual will be of
type AB "by descent". And the calculation of how many other AB offspring
get produced is complicated by the fact that some of them get A from the focal
parent, some of them get B, and some get neither. The "heritability" of a
two locus type is lower than the heritability of a one-locus type. (Unless
one of the two loci has an allele nearly fixed in the population).
> Darwinian fitness is TDF which is
> entirely, an epistatic fitness. If TDF is not mostly heritable then
> Darwinian theory _fails entirely_.
Well, you don't need "mostly heritable" for Darwinian theory to work.
All you need is "partly heritable". But there is no question - the more
heritable that fitness is, the better for the theory. Luckily, even
though most (or all?) gene fitnesses involve some epistasis, there is
still enough heritability there to make Darwinism work. And even if
all genes involve some consideration of epistasis in figuring their
fitnesses, that doesn't mean that all of the fitness that you has to
be treated as epistatic fitness. There is a single-locus component
of the total fitness that is very heritable, a two-locus component that
is less heritable, a three-locus component that is even less heritable
yet, and so on. (Malcolm or someone else may correct me on this
interpretation.)
.
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- From: John Edser
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