[From Bill Powers (970801.0815 MDT)]
Bruce Abbott (970731.0915 EST)--
Some added comments after a good night's sleep.
The main doubt I think I'm raising is whether this "sifting process" is
sufficient to account for the changes we see.It seems to me that the "sifting process" is the same in your account and
the traditional one. Where they differ is in the "variation process." In
the traditional account, the rate of variation is essentially constant,
whereas in your account it is tied to error in essential variables.
I think it's just the other way around: the "variation" process in both
cases is a random change in system parameters in which all possible changes
have equal probability before any single mutation. The sifting process,
however, is very different. In traditional natural selection, if one
lineage encounters an unfavorable mutation, it stops there: it dies out.
That's the only selection mechanism. In the PCT model, an unfavorable
mutation simply shortens the interval (the number of generations that
appear) before the next mutation, so that lineage gets a second, and third,
and so on chance. It dies out only if a whole series of "chances" leads to
worse and worse conditions.
In the traditional model, "survival of the fittest" is a qualitative idea.
The only choices are survival or death. In the PCT version, "fitness" is a
continuous variable with many dimensions, and organisms can go on
reproducing even if they have less than maximum fitness. It's this ability
to go on reproducing that gives them multiple chances to mutate in
favorable directions. The assumption, of course, is that most mutations
have small effects, so that while a given mutation may reduce fitness, it
doesn't reduce it very much. The species doesn't die out instantly, in the
very next generation. The "unfitness" will show up only over many
generations, in comparison with other lineages: it is a relative measure.
And as a result, the least fit species will mutate sooner than the more
fit, giving it a chance to recover its relative position or head off in
another direction that reduces competition with other species, or both.
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You have characterized the E. coli method as simply causing a higher
mutation frequency, thus given a apecies "more chances" to find a favorable
mutation. But that isn't quite right. The "decision" as to whether to
mutate again is made continuously during the interval between mutations. If
the result of a mutation is to reduce intrinsic error, the time to the next
mutation is stretched out; if intrinsic error increases, it is shortened.
During the interval, the error signal can fluctuate so the cutoff time can
be changing up and down, but of course the actual delay time isn't
determined until the total elapsed time since the last mutation becomes
longer than the current value of the delay time, tm0 - k*e. It's what
happens during _each cycle_ that matters. If you start thinking in terms of
"increased frequency" of mutation, you're considering many cycles, in a
sort of averaging approach. But in the E. coli method, each cycle is
independent of the others; the critical relationships are found in the
interval between one mutation and the next.
One way of modeling this process is to define a variable that increases
continuously at a rate determined by intrinsic error. When this variable
reaches a fixed upper limit, it is reset and a "tumble" occurs. Obviously,
if intrinsic error is small, this accumulating variable will take a long
time to reach the fixed upper limit, so the next tumble will be delayed,
and so forth. At zero error, the delay will become infinite.
This _sort_ of mechanism is quite probable in the real E. coli's means of
steering. The rotation of the flagellae is driven by some chemical process.
What seems to be the case is that there is a very narrow region over which
the rotational velocity is proportional to chemical concentration, with a
_reversal of rotation_ occurring somewhere within this region. If the six
or seven flagellae have slightly different settings for the zero-rotation
state, there will come a point where some of the flagellae reverse while
some are still turning in the forward direction. This is what creates a
tumble. What Koshland found was that if the rate of change of concentration
were made abnormally large, _all_ the flagellae would reverse, and the
bacterium would actually start backing up. Between the "all reversed" and
the "all forward" conditions, tumbling occurs. The randomness would be
created by the phase relations between the rotating flagellae at the moment
a reversal occurs. It's not really random, of course, but apparently the
result is random enough that the spatial orientations after a tumble are
evenly distributed.
Here, the interval between tumbles would be determined by how rapidly the
chemical driving the forward rotation _decreases_ in concentration after a
tumble (when it is presumably reset). But it's the same idea.
The main reason for going through that was to show how a mechanism could
exist that makes the interval between mutations depend on processes
occurring during each interval. That's the appropriate way to think of the
E. coli principle.
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One more thought. In the standard theory of natural selection, we can think
of the long-term probabilities of changes in different directions as being
equal. In two dimensions (two variables being mutated) the probabilities of
changing in particular directions would be represented by a circle centered
on the origin, the radius being the probability density. When we close the
loop, so that some function of the two variables determines the probability
density in each direction, the circle becomes something like an ellipse
with the origin at one focus. The long axis of the ellipse points in the
direction of most probable change.
On top of this diagram, we could draw another ellipse indicating the
long-term survival rate as a function of change in a given direction. This
would be another figure something like an ellipse, with the long axis
pointing in the direction of the best adaptation. This second ellipse would
correspond to the "natural selection" theory. Organisms that mutated the
two variables in the right proportions would have the maximum survival
potential, while all other combinations would lead to lower fitness.
This shows the difference between natural selection and E. coli selection
in a different way. If the function of the two variables x and y that is
determining the direction of most likely change is not aligned exactly with
the long axis of the ellipse showing the greatest probability of survival,
then the directed evolution will not be optimized. In other words, the
intrinsic variable that is being sensed as the basis for varying the
interval between mutations is not exactly the right one for maximizing
survival rates. The best possible case is the one in which the most likely
direction of change is aligned with the direction of highest survival rates.
From this schematic picture we can draw several conclusions about fitness
from the effect of any one variable on fitness. The best direction of
change for survival is a function of many variables. Looking at the effect
of one variable on fitness does not tell us what the optimal value of that
variable is; _all_ the variables on which fitness depends have to be
considered. If we can imagine an increase of fitness as a result of
increasing one variable, this does not mean that maximum fitness is
achieved by maximizing that variable. Maximizing any variable would
probably take us well off the long axis of the ellipse.
Another conclusion would be that even if the E. Coli type of selection
criterion caused the long axis of the "change" ellipse to point in the
wrong direction, natural selection itself would eventually align its long
axis with the long axis of the "survival" ellipse!
The same would hold for the _shape_ of the "change" ellipse. If this
ellipse were originally a circle, meaning that there are no feedback
effects to make any direction of change more likely than any other, natural
selection would, or at least could, result in acquiring an E. coli type of
mechanism that would change the circle to a modest ellipse, then gradually
increase its eccentricity, and finally align its long axis with the
direction of maximum survival rate.
Of course the net survival rate would be the product of the radii of the
two ellipses in each direction. I think this shows the relationship between
natural selection and directed evolution very neatly.
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One final thought that popped up during an absence from the keyboard.
Long-term survival is not the same thing as maximum short-term reproductive
success (I'm sure this has been said before). As ecological studies
clearly show, a species that reproduces too fast can be as doomed to
extinction as one that reproduces too slowly. The predator can eat up all
the prey and starve to death.
The rate of reproduction per generation is simply another variable in the
equation for long-term survival of a species. And long-term survival of a
species is not really the ultimate criterion, either. If conditions change,
species evolve so that _life_ continues. It does not matter to living
systems, and particularly not to the basic biochemical processes that I
presume drive evolution, what the physical form of an organism is. The
basic picture is that living systems, by varying their forms and functions
in whatever way is necessary, continue to live. The first declaration is
not "Let there be light." It is "Let there be life."
Best,
Bill P.