Vicarious Greetings and Salutations,
Stephen Jones has roused me out of a pleasant semi-retirement to
solicit my
thoughts on Glenn Morton's infamous Cambrian Explosion program. His
request
reminded me that I had wanted to write something on this topic, so I
decided
to type my thoughts out and submit them for your consideration.
If my memory serves me, Glenn submitted these programs with a
disclaimer that
went something like the following: "Now before you guys write back
and say
that these programs do not have anything to do with biological
systems, let
me just say that I am fully aware of this fact . . ."
With this sentence (like any true blue Darwinian) he completely
protected
himself from having his Cambrian Explosion program "falsified" in any
meaningful sense. If his program isn't meant to mimic life systems,
what is
the point? Is his point that non-linear dynamics can be used to
create a
drawing that looks (at some level of abstraction) like the Cambrian
diversification?
If this is his point, I have two comments.
1) I will go further then Glenn. I will say that non-linear dynamics
can be
used to simulate any CONCEIVABLE pattern of life. In other words,
give me any
pattern of life you can conceive of and I will simulate it for you on
a personal
computer using a system of linear and non-linear equations. Do you
want
evolution that depends on the phase of the moon? Coming right up.
Evolution
that depends on the number of nose hairs in a given population? No
problem.
Computer modelling is my job. While it may be a stretch to say that I
am an
expert on this subject, it is not much of a stretch. The ONLY way a
computer
model gives significant results is if the assumptions with which it is
written
are close approximations to physical reality. PERIOD. (This is
analogous to
mathematics where you can prove anything depending on what you take to
be
axiomatic.)
2) My second comment would be that despite the fact that he has freed
himself
from the constraints of physical reality, his program STILL doesn't
reproduce
the interesting features of the Cambrian explosion. Let's look at a
crude
representation of the fossil record: X
XXX X
XXXXXXX XXX
X X X X X X X X X X X X X X X X X X X X X X X X X XXXXXXX . . .XXX
XXXXXXX XXX
XXX X
X
<--------------------- 3.2 Billion Years--------->^<-----Stasis->^
| |
Cambrian Subsequent
Explosion diversification
(less than events
5 million years)
In the above diagram, the horizontal axis represents time and the
vertical
axis represents the diversity of life. Now the interesting feature of
this
pattern has always been the long periods of stasis followed by brief
periods
of tremendous diversification followed by long periods of DECLINE in
the
diversity of the higher taxa followed by stasis and again by brief
periods of
diversification. Glenn's program does not (except by artificially
introducing
it as an initial condition) show the initial period of stasis nor does
it
show the other patterns in the fossil record with any degree of
consistency.
Now I am not saying that Glenn COULDN't have written a program that
produced
results that looked like the Cambrian Explosion, I am just saying that
his
program falls short of this goal. To his larger point that non-linear
dynamics can produce behavior that is similar to the behavior of the
fossil
record, I say so what. A program using a system of non-linear
equations could
be written that simulated any pattern you like.
There are two other points I would like to make concerning Glenn's
program.
The first one concerns why Glenn's program has absolutely NOTHING to
do with
biological systems. He has admitted this already, but I think it will
be
useful to go over the exact reasons why his simulation is biologically
meaningless.
I have analyzed his program and it looks like this (for convenience, I
will only
consider the "evolution" of one of the 32 squares in the grid):
Initialization sequence: Draw primary grid and a single point
representing
initial organism.
main loop| sub loop | A* = randomly selected from 1 of 4 values
| | YA' = f(YA,A*)
| | XA' = f(XA,A*)
| | Plot (XA', YA')
| redraw the grid for next "mutation event"
| One of the four A* values is "mutated" to a different value
Now there are any number of problems with this as a simulation of
life.
Most important is the way Glenn generates "progeny". Each "organism"
is represented by a point (XA,YA) but two successive generations are
not related in any way that is even close to physical reality. This
is
because of Glenn's choice of the function f.
XA = ABS ( COS( XA/3 - A*/3))
now if (XA, YA) represents a point in some protein, codon or
nucleotide space,
then f MUST be of the following form to be realistic:
XA' = XA + R
where R is some vector that gets you from the point that represents
the parent
to the point that represents the progeny. Now R can be any function
of XA'
that you like, though it won't be realistic if it is not selected
properly.
If (XA, YA) represents some point in morphology space, then Glenn's
model has
absolutely nothing to do with biological systems from the very start.
The second point I would like to add concerning Glenn's position has
to do with
the information content argument of Hubert Yockey. If you will
recall, Yockey
calculates that the information content of various proteins makes
their
formation by random processes astronomically unlikely. (Specifically,
he
calculates that there are a maximum of 10^93 proteins that could be
functionally
equivalent to cytochrome C in the "high probability set" of 10^137
possible
configurations.) While his calculation does not rule out the
possibility of
GRADUAL evolution, it does suggest that evolution must be gradual
because of
the extreme unlikelihood of forming these proteins quickly. Consider
the
histones which are protein sequences 125 amino acids long that vary in
only
three positions from the pea to the Chicken (according to Yockey), how
could
these proteins have formed without extreme gradualism?
So the question is, how can you reconcile the gradualism that seems to
be
required by the vast improbabilities calculated by Yockey with the
frenetic
level of diversification followed by long periods of stasis shown in
the
fossil record? Just showing that there exist mathematical equations
that
can reproduce this pattern is meaningless in the absence of a credible
genetic mechanism.
Speaking of Yockey, Glenn and I had a bit of an argument a while back
which
I am now able to shed some more light on. I said that Yockey's
calculation
would probably have to be adjusted for the fact that there were
sequences
within his set of 10^93 that would actually be harmful to a given
organism
(and thus these sequences would not be functionally equivalent).
Glenn
asked me if I had any evidence for this and I was unable to answer
him. AS
it turns out, there is a well known phenomena that supports my
contention.
This is the phenomena of inter-species rejection. When (for medical
purposes)
a protein from one species is injected into an individual of another
species,
a common result is rejection by the immune system. This shows that a
protein sequence must be compatible with the organism or it can cause
harmful
effects and that not all of the 10^93 cytochrome C sequences are truly
equivalent.
God Bless,
Robert Van de Water
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| Stephen Jones | ,--_|\ | sjones@iinet.net.au |
| Perth | / Oz \ | http://www.iinet.net.au/~sjones/ |
| Australia | -> *_,--\_/ | phone +61 9 448 7439 |
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