[From Bill Powers (970818.1958 MDT)]
Martin Taylor 970816 12:21--
Negative feedback exists in a system of two variables if
x = f(y) at the same time that
y = -g(x)
I'd be _much_ happier with this if you put the time dimension in explicitly.
I knew somebody was going to bring this up; since you've brought it up
before, you're the appropriate one, I guess. I will repeat my answer,
perhaps better than before.
It is true that perturbations take time to propagate around a loop, so the
effect of a change in a variable that is fed back arrives at some time
after the initial perturbation. The _value_ of the variable does not affect
itself. However, the variable itself (such as a muscle tension) _does_
affect itself via the closed loop -- at a later time. This is radically
different from the case of lineal causation, in which a variable is
affected only by _other_ variables.
A second point is that in a stable negative feedback system there must some
variable or combination of variables that is limited in speed of change, so
that the feedback gain s prevented from being more negative than -1 at or
above frequencies where the phase shift due to the delay is 180 degrees or
more. In time-domain terms, this means that the system's state can't change
more than a small fraction (approx. 1/gain) during one loop delay (whether
the speed limit is set in one element or distributed). At low frequencies,
well within the frequency limits for good control, the system approaches
the performance of a system with zero delay. So under those conditions, the
algebraic equations give the correct solution, the approximation improving
rapidly as the speed of changes gets slower. In fact, the algebraic
solutions are the correct steady-state solutions of the differential
equations for conditions under which transients have died out, with or
without time delays.
···
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Evolutionary dynamics are treated as a negative feedback loop
in which the feedback control quantity (x or y above) is _in an individual_.
There may or may not be negative feedback in evolutionary dynamics, but it
cannot be through an individual who has no influence on the evolution of
the species once it has died.
That is my conclusion also.
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While I'm on that subject (perhaps long since laid to rest), could someone
explain wherein the "stress" is in an individual who dies because of one
"unfortunate" action such as failing to withdraw a gill cover when touched?
This is a bit exaggerated; an Aplysia struggling to breathe with a badly
injured gill doesn't necessarily die, but its oxygen content is going to be
chronically low and its mobility could be affected.
With respect to the theory I have put forward, this alone would not lead to
an "adaptive mutation". What would lead to such an adaptation would be a
side-effect: failing to protect against disturbances of variables on which
accuracy of replication depends. The theory of adaptive mutation (just
thought of that name -- not bad, huh? I hope it's not already registered)
is not Lamarkian. All you have to remember is that the basis of adaptive
mutation is simply the failure to maintain the conditions that are
neccessary for accurate replication. That automatically guarantees a
"mutation." No external cause of mutation is required, although external
causes like cosmic rays are not ruled out. But cosmic rays do not arrive at
the opportune moment, while failure to replicate accurately always does.
So far as I can see, the individual is happily unstressed until it is dead.
How, then, does increased stress in the individuals of the population lead
to mutations that decrease the likelihood of the "unfortunate" action
(or in this case, inaction)?
Living vs dying is not the issue under either theory. I have lately been
corrected on this matter when I raised the same objection to natural
selection -- organisms can reproduce to varying degrees, especially those
that produce multiple offspring over their reproductive years. In the same
way, there can be degrees of failure to control the variables on which
accuracy of replication depends; this is a continuous variable, not a
binary one. The superficial appearances of "stress" are irrelevant, unless
they are associated with loss of control over variables critical for
accurate replication.
A simple example. How long would a species last if it developed a taste for
a kind of food that contained a mutagen? It wouldn't necessarily fail to
reproduce -- it might even reproduce more rapidly. But if you came back
after a while you would find different creatures swimming around, and none
of the originals. The _species_ would die out, but not because of the
failure of the individuals to reproduce. It would die out because, for a
time, the individuals failed to reproduce _accurately_.
At the very least, the concept of reproductive success has to be expanded
to include not just quantity of reproduction, but precision of
reproduction. I think we will find that precision is the governing factor
in evolution.
Best,
Bill P.
Normal "natural selection" can account for
the evolution of individuals that don't perform the "unfortunate" action,
if random genetic variation happens to yield some that don't, because
those individuals are more likely to survive to produce progeny. But
even those that continue to act "unfortunately" are unstressed until
they are dead, aren't they?
See the above. The critical question is how effective the two modes of
evolution would be, relative to each other. I can see that there would be
some reluctance to give up natural selection as the primary force behind
evolution without some even more effective mechanism to take its place,
because after all we do have to account for evolution. But once such a
mechanism is found, it ought to be easier to review natural selection with
an eye to its actual effectiveness, and perhaps admit that, as originally
conceived, it never was able to account for the speed of the actual changes
we observe.
Best,
Bill P.