"Tim Tyler"  wrote in message
news:c8fujg$31hd$1{at}darwin.ediacara.org...
> Jim Menegay  wrote or quoted:
> > Tim Tyler  wrote in message
news:...
>
> > > The problem is that membranous bags splitting is a stochastic
process -
> > > with no guarantee that the contents are divided equally between
> > > any offspring.  Consequently any information stored as
"proportions"
> > > will be subject to a good deal of drift.
> > >
> > > Maynard-Smith (or more to the point, E. Szathmary) attempted to
address
> > > this issue by using particular (discrete) replicators as the entities
> > > involved - and by having a small number of them.
> > >
> > > In this way is is possible to make a semi-plausible story about
> > > deviations from even assortment between offspring being compensated
> > > for by selection among the offspring.
> >
> > I believe that you have partially misunderstood Szathmary.  Having a
> > small number of instances of a replicator type is not part of the
> > solution, it is the variant of the problem that is most troublesome.
> > Szathmary considered this case to show that selection solve the
> > problem even in the more difficult cases.
> >
> > If there are many instances of each replicator type, the amount of
> > drift is less severe (proportional to SQRT(N)/N), and milder
> > selection against deviations from the optimalproportions can maintain
> > the status quo.
>
> As I said, I was talking about information stored as "proportions".
>
> This contrasts with information being stored as merely the presence or
> absence of particular replicators in the cells.

There is indeed a big contrast between "analog" information such as
proportions and "digital" information such as presence/absense or the
choice of attractor/basin in a dynamical system.

I believe that analog information cannot properly be called "genetic"
information at all, precisely for the reasons you give below.

> If information is stored as a ratio of the numbers of replicators, then
> greater selection is needed to resist stochastic perturbations of the
> proportions of each replicator as the number of replicators involved in
> making up each cell rises - since the mutation rate goes up as the
> chances of each daughter cell receiving exactly the same proportion as
> the parents goes down.
>
> As the mutation rate rises - so the selection needed to combat it
> increases.
>
> Inheritance with stochastic correction is better fidelity than
> without it - but there's still a "low information ceiling".
[snip]
> Szathmary's model used molecular template replicators to function -
> and *they* acted as the primary means of inheritance in the model.
>
> The model was intended to show how numerous small replicators could
> pool their efforts - without being physically connected as chromosomes;
> or suffering an error catastrophe.

Regarding my claim that a small number of replicators is part of the
problem rather than part of the solution:
I think I see how, if a 3:2 ratio between replicators A and B is optimal,
then it is easier to maintain that exact ratio in a balanced fission when
the population of A is 6 and that of B is 4, as opposed to when the
population of A is 60 and that of B is 40.

That is, I see that the information is more digital with a small number of
replicators, and more analog with a large number.  However, when
you consider the steps required in getting a 3:2 population back to 6:4,
I think that my large population of 60:40 and weaker selection for
small deviations from the "exact proportion" is a more viable approach.

> Invoking Szathmary's stochastic corrector in a model of autocatalys
> /without/ template replicators would stretch it to near breaking point.

Hmmm.  I thought YOU were the one who invoked this model as an
argument against autocatalysis.  But I can see now that you were
simply stating the problem (which is common to replicators and
autocats) and describing the Szathmary solution to the replicator
side of the problem without suggesting that it might extend to autocats.

Moving on, it seems to me that the issue of analog vs digital information
has been coming up lately on a number of threads.

*This one.
*Tim, Guy, and Jim on what constitutes "heredity" in complex systems.
*John and Jim on whether natural selection can act on metric traits
   without invoking "genes".
*Jim's insistence that traits for species selection have to be emergent
   at the deme or species level and have to be maintained as an "ESS"
   or attractor at that level for "species selection".
*Tim vs Jim on the usefulness of near-neutral variants.

I also notice an analogy between Szathmary's problem and Eigen's.
Eigen, with the help of selection, maintains a "quasi-species" near an
optimum sequence in the face of variance introduced by mutation.
Szathmary, with the help of selection, maintains a population near
an optimum ratio in the face of variance introduced by sampling
error.

I see both as struggling against the same issue - analog information
is not easily heritable in a long term sense.  (Note that Eigen's
information is digital at a reductionist level, but analog at the level
Eigen is interested in - he talks about a "distance" from the optimal
sequence.  Similarly, Szathmary's information is also digital in some
sense, in that he is counting things, but it is also analog in the "true"
sense.)

Maintaining analog information close to an environmentally specified
optimum can be done using selection, but it takes a huge cut out
of the reproductive excess.  It is far better to have digital information
that is "usually" reproduced exactly, and then to only use selection to
deal with the exceptions to that "usually".  That seems to take a
much smaller cut.
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