Enzyme Evolution John Mitchell, February 2010. Theories of Enzyme Evolution.
Numerical Testing of Evolution Theories
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Transcript of Numerical Testing of Evolution Theories
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N U M E R I C L T E S T I N G O F E V O L U T I O N T H E O R I E S
P a r t I I
P R E L I M I N A R Y T E S T S O F P E R F O R M A N C E . S Y M B I O G E N E S I S A N D
T E R R E S T R I A L L I F E . t
b y
N I L S L L B R R I C E L L I
( D e pa r tm e n t o f B io logy , D iv i s ion o f M ole c u la r B iology )
( V a nde r b i l t U n ive r s i t y , N a shv i l l e , T e nne s se e )
( R e e . 27 . X I . I 96 i )
NOTE BY THE UTHOR
I n t h e l a t t e r p a r t o f t h i s p a p e r t h e n a t u r e o f t h e r e l a t i o n s h i p o r s i m i l a r it i e s b e t w e e n
l i v i n g b e i n g s a n d o t h e r s y m b ~ o o r g a n i s m s is d i sc u s s ed . S o m e o f t h e c o n c l u s i o n s m a y b e
s u r p r i s i n g t o t h e r e a d e F . H o w e v e r , i t m u s t b e p o i n t e d o u t t h a t n o t h i n g w h i c h i s p r e s e n t e d
i n t h i s p a p e r c a n j u s t i f y t h e c o n c l u s i o n t h a t a n y o t h e r t y p e o f s y m b i o o r g a n i ~ m e x c e p t
t h e s o c a l le d T e r r e s t r i a l l i f e f o r m s , w h i c h p o p u l a t e t h i s p l a n et , a r e al iv e . A s a m a t t e r
o f f a c t t h i s q u e s t i o n h a s n o m e a n i n g a s l o n g as t h e r e i s n o a g r e e m e n t o n a d e f i n i t i o n
o f l i v ~ l g b e i n g . H o w e v e r , t h e re c i p r o c a l q u e s t i o n w h e t h e r t h e o b j e c t s w e a r e u s e d
t o c al l l i v i n g b e i n g s a r e a p a r t i c u l a r c l a s s o f s y m b i o o r g a n i s m s h a s a m e a n i n g . T h i s i s
t h e q u e s t i o n w e h a v e b e e n t r y i n g t o a n s w e r i n t h i s p a p e r a n d t h e p r e c e e d i n g p a p e r i n
t h i s s e r i e s
BARRICELLI,
1 9 6 2 ) . I f t h e n a t u r e o f t h e a n s w e r a n d i t s c o n s e q u e n c e s s h o u l d
m a k e t h e r e a d e r f e e l s o m e w h a t d i s o r ie n t e d a n a d v i se w h i c h m a y p r o v e u s e f u l f o r
s c ie n c e r e a d e r s a s it i s f o r m o u n t a i n c l i m b e r s i s H o l d o n s o l id g r o u n d . P r o v e n f a c t s
a n d r i g o r o u s d e d u c t i o n a r e t h e s o l id g r o u n d o n w h i c h s c ie n ti ,f ic k n o w l e d g e c a n b e b a se d .
F e e l i n g s a n d o p i n i o n s a n d a n y f o r m o f i n s t i n c t i v e re s i s t a n c y t o n e w i d e a s a r e n o t.
E v e r y t h i n g w h i c h i s s a i d i n t h i s p a p e r s h o u l d b e u n d e r s t o o d , s t a t e m e n t b y s t a t e m e n t ,
t h e w a y i t i s p re s e n t e d . T h e a u t h o r t a k e s n o r e s p o n s i b i l i t y f o r i n f e r e n c e s a n d i n t e r p r e -
t a t i o n s w h i c h a r e n o t r i g o r o u s c o n s e q u e n c e s o f t h e f a c t s p r e s e n t e d . A s i n t h e p r e v i o u s
p a p e r o f t h i s s e r i e s (B A I~ RIC EL LI, I 9 6 2 ) t h e t e r m s u s e d i n c o n n e c t i o n w i t h s y m b i o g e n e t i c
p h e n o m e n a do n o t h a v e t h e s a m e m e a n i n g t h e y h a v e i n bi ol og y . T h e y r e f e r t o m a t h e -
m a t i c a l c o n c e p t s w h o s e r e l a t i o n t o t h e c o r r e s p o n d i n g b i o l o g ic a l c o n c ep t s i s a m a t t e r
o f i n v e s t i g a t i o n .
I T h i s i n v e s t ig a t i o n w a s s u p p o r t e d b y r e s e a rc h g r a n t R G - 6 9 8 o f r o m t h e D i v i s i o n o f
G e n e r a l M e d i c a l S c i e n ce s o f t h e N a t i o n a l I n s t i t u t e s o f H e a l t h , U . S . A . P u b l i c H e a l t h
S e r v ic e . T h e f i r s t p a r t o f t h i s in v e s t i g a t i o n w a s p e r f o r m e d i n t h e f al l, 1 95 9, w h i l e t h e
a u t h o r w a s v ~s i to r t o t h e A . E . C . C o m p u t i n g C e n t e r , N . Y . U . T h e i n v e s t i g a t i o n w a s
c o n t i n u e d i n t h e s u m m e r , I 9 6 O , w h i l e t h e a u t h o r w a s V i s i t i n g R e s e a r c h A s s o c i a t e a t
B r o o k h a v e n N a t i o n a l L a b o r a t o r y , L . I. N . Y . a n d a f t e r h i s r e t u r n t o V a n d e r b i l t U n i v e r s it y ,
N a s h v i l l e , T e n n e s s e e
A c t a B i o t h e o re t ic a , X V I 7
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IO 0 N A BARRICELLI
I I N T R O D U C T I O N
In the first paper of this series
BARRICELLI,
1962) the results of numeric
evolution experiments performed in Princeton, N. J. were presented. In one
of the experiments, the evolutionary improvement was verified by competition
tests between symbioorganisms at different stages of evolution. The tests
clearly showed that symbioorganisms at a more advanced stage of evolution
with a longer evolution history behind them) easily eliminated more primitive
organisms belonging to the same or to a different species see fig. 25,
BARRICELLI,
1962) . Evidently the ability of the various symbioorganisms to
perform operations necessary or useful for their survival was improved
during the evolutionary process.
A question which arises in this connection is whether it would be possible
to select symbioorganisms able to perform a specific task assigned to them.
The task may be any operation permitting a measure of the performance
reached by the symbioorganisms involved; for example, the task may consist
in deciding the moves in a game being played against a human or against
another symbioorganism. Evidently if a measurable improvement in a specific
performance can be obtained by selection, this would open exciting possibili-
ties. The evolutionary development of specialized structures with a specific
function and a specific survival value could be open to investigation.
The problem of testing the improvement in a specific performance will
be the primary subject of the first part of this paper.
A related problem should be mentioned here even though its investigation
has not yet reached a stage where it can give fruitful results. A peculiar
characteristic of the symbioorganisms developed so far is that they consist
exclusively of self reproducing entities, which perform the function of genetic
material. These selfreproducing entities are permitted to interact exclusively
with other selfreproducing entities. No other structures formed or modified
or rearranged by the selfreproducing entities are involved. There is no parallel
to what may be called somatic or non-genetic structures of living organisms.
This peculiarity is evidently due to the reproduction and mutation norms
used. To save labor, computing time, and machine memory, the norms used
did not involve entities which were not selfreproducing and could be dispensed
of in the first evolution experiments. In the tests of performance to be
reported below, the answers or decisions yielded by each symbioorganism will
be expressed by a set of numbers. This will involve the formation of non-
genetic numerical patterns characteristic for each symbioorganism. Such
numerical patterns may present unlimited possibilities for developing
structure.a and organs of any kind to perform the tasks for which they are
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NUMERICAL TESTING OF EVOLUTION THEORIES O
designed. However, since computer time and memory still is a limiting
factor, the non-genetic patterns of each numeric symbioorganism are con-
structed only when they are needed and are removed from the memory as
soon as they have performed their task. This situation is in some respects
comparable to the one which would arise among living beings if the genetic
material got into the habit of creating a body or a somatic structure only
when a situation arises which requires the performance of a specific task (for
instance a fight with another organism), and assuming that the body would
be disintegrated as soon as its objective had been fulfilled.
The experiments are not yet in a stage where the non-genetic patterns
can be expected to yield important information. Only the results of the
preliminary tests of performance and its evolutionary improvement will
be discussed to some extent.
The last part of this paper will be dedicated to a discussion of the possibili-
ties of obtaining symbiogenetic evolution processes by using a dif ferent set
of reproduction and mutation rules (or norm of action ). Particularly the
use of rules applying the reproduction pattern of DN.//-molecules DNA-
norm) and the implications this possibility may have with respect to the origin
and history of terrestrial life are discussed.
2. PERFORMANCE TESTS
As already stated in the previous paper of this series BARRICELLI, 1962),
the genetic pattern of a symbioorganism performs the function of a survival
strategy program developed during the past evolutionary history of the
symbioorganism. The specific operations performed to bring the survival
strategy into action are determined by the norm of action specifying the repro-
duction and mutation rules. This norm is the interpretation of the survival
strategy programs. After this interpretation has been chosen arbitrarily to
begin with, the various symbioorganisms develop their respective survival
strategy programs based on the choice which has been made. Nothing
prevents modifying the interpretation or adding a new interpretation to be
used in special cases, for example, in the case of collision between two diffe-
rent numeric entities moving into the same location.
The last course is the one which will be followed in order to make it
possible for a symbioorganism to perform a specific task. In case of collision
between genes of two dif ferent symbioorganisms, the genetic patterns (or a
part of the genetic patterns) of the two symbioorganisms will be interpreted
as programs for the performance of a specific task according to a particular
code designed for this purpose. The genetic patterns of the two symbio-
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IO2 N A BARRICELLI
o r g a n i s m s w i l l c o n s i s t o f n u m b e r s , a n d n u m b e r s i n t h e m a c h i n e m e m o r y
c a n b e i n t e r p r e t e d a s i n s t r u c t i o n s a c c o r d i n g t o a n y a r b i t r a r y c o d e w h i c h
c a n b e e s ta b l i sh e d b y w r i t i n g a n i n t e r p r e t i v e p r o g r a m .
T h e o p e r a t i o n s t o b e p e r f o r m e d b y t h e t w o c o l l i d i n g s y m b i o o r g a n i s m s
w i ll c o n s i s t i n s e l e c ti n g th e m o v e s i n a g a m e t o b e p l a y e d b e t w e e n t h e m .
T h e g a m e w h i c h i s u s e d i n th e p e r f o r m a n c e te s t s d e s c r i b e d b e lo w i s a
s im p l e o n e d e n o m i n a t e d T a t T i x . T h e ru l es o f t h e g a m e w e r e p u b l is h e d
i n S c i en t i fi c A m e r i c a n , F e b r u a r y , I 9 58 , p. I o 4 - I I I , a n d w i ll b e e x p l a in e d
b e l o w . T h e r e s u l t o f t h e g a m e w i l l d e c i d e w h i c h o n e o f t h e t w o c o l l i d i n g
g e n e s w il l b e p e r m i t t e d t o o c c u p y th e c o l l is io n p la c e , n a m e l y t h e g e n e o f t h e
w i n n e r . E x c e p t f o r t h e c a s e s o f c o l l i s i o n , w h i c h a r e o f t e n d e c i d e d b y g a m e s ,
t h e n o r m s f o r r e p r o d u c t i o n a n d i n m a n y in s ta n c e s f o r m u t a t io n r e m a i n t h e
s a m e a s i n p r e v i o u s e x p e r i m e n t s ( BA R R IC E LL I, I 9 6 2 ) .
B y t h is p r o c e d u r e , t h e g a m e s t r a t e g y b e c o m e s p a r t o f t h e s u r v i v a l s t r a t e g y
o f t h e c o m p e t i n g sy m b i o o r g a n is m s , a n d a n e v o l u t i o n a r y i m p r o v e m e n t in g a m e
p e r f o r m a n c e c a n b e e x p e c t e d .
3 . R U L E S O F T H E G A M E
T h e r u le s o f t h e g a m e ( T a c T i x ) p l a y e d b e t w e e n c o m p e t in g s y m b i o -
o r g a n i s m s a r e : I n a s q u a r e o f 6 X 6 = 3 6 c o in s t h e tw o p l a y e r s r e m o v e
a l t e r n a t i v e l y o n e o r s e v e r a l c o i n s i n a s i n g l e r o w o r a s i n g l e c o l u m n . O n l y
Fig I Most freq uent game pattern fo r unselected or damaged symbioorganisms
a n u n i n t e r r u p t e d s e q u e n c e o f c o i n s i n a c o l u m n o r a r o w c a n b e r e m o v e d
e a c h t im e . F o r i n s t a n c e , w h e n a r o w ( o r a c o l u m n ) i s r e m o v e d , t h e p l a y e r
w h o h a s h is t u r n c a n n o t ta k e c o in s o n b o th s i de s o f t h e re m o v e d r o w ( o r
c o l u m n ) . T h e p l a y e r w h o g e t s t h e l a s t c o i n o n t h e t a b l e l o s e s t h e g a m e .
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NUMERICAL TESTIN G O EVOLUTION THEOR IES IO3
T o s a v e s p a c e , i n f i g . I a n d 2 t h e 3 6 c o i n s , w h i c h a r e r e p r e s e n t e d b y h o l e s
i n a n I B M c a r d , a r e p l a c e d i n a s i n g l e r o w i n t h e u p p e r l e f t s i de o f e a c h
f i g u r e . B u t t h e g a m e r u l e s a r e a p p l i e d a s s u m i n g t h a t t h e f i r s t 6 c o i ns h o l e s )
f r o m t h e l e f t r e p r e s e n t t h e f i r s t r o w o f a 6 )< 6 s q u a r e , w h i le t h e n e x t 6
c o in s h o l e s) r e p r e s e n t th e se c o n d r o w , e tc . A f t e r t h e f i r s t s y m b i o o r g a n i s m
Fig. 2. Gam e played between two sym bioorganisms aft er I5OO generations of selection
for game performance.
l e f t p l a y e r ) h a d m a d e h i s f i r s t m o v e , th e s i t u a t i o n w a s t h e o n e d e s c r i b e d b y
t h e u p p e r r o w t o t he r i g h t in e a c h f i g u r e . A f t e r t h e s e c o n d s y m b i o o r g a n i s m
r i g h t p l a y e r ) h a d m a d e h i s f i r s t m o v e , t he s i t u a ti o n i n th e g a m e w a s t h e o n e
d e s c r i b e d i n t h e s e c o n d r o w l e f t. A f t e r t h e l e f t p l a y e r h a d m a d e h i s s e c o n d
m o v e , th e s i t u a t i o n w a s t h e o n e d e s c r i b e d i n t h e s e c o n d r o w t o t h e r i g h t
etc
T h e r e a d e r m a y e a s i ly f o l lo w t he p r o g r e s s o f t h e g a m e s i n b o t h f i g u re s .
4 . F R O M G E N E T I C P A T T E R N T O G A M E S T R A T E G Y
T h e p r o c e d u r e a p p l i e d t o se l e c t t h e n e x t m o v e i n e a c h s i t u a t i o n o f t h e
g a m e w i ll n o w b e d e s c r i b e d s u m m a r i l y . T h e i d e a c o n s i s ts i n u s i n g th e s i t u a -
t io n in th e g a m e b e f o re th e m o v e a s d a t a o f t h e p r o b l e m , a n d t he
g e ne ti c p a t te r n o f a s y m b i o o r g an i s m a s a s t r a t e g y p r o g r a m t o b e
i n t e r p r e t e d a c c o r d i n g t o a c o n v e n t i o n a l c o d e . T h e c o d e i s d e t e r m i n e d i n s u c h
a m a n n e r t h a t a n y g e n e t i c p a t t e r n , i n a n y s i t u a t i o n i n t h e g a m e , w i ll , a f t e r
a l i m i t e d n u m b e r o f m a c h i n e o p e r a t i o n s l e a d t o a l e g a l m o v e o f t h e g a m e .
T h e c o m p u t i n g m a c h i n e u s e d w a s 2 ) t h e I B M 7 o 4 o f t h e A . E . C . C o m -
p u t in g C e n te r , N e w Y o r k U n i v e r s i ty , N e w Y o r k . E a c h m e m o r y lo c at io n in
2) Readers who are not fam iliar with machine program ming m ay skip the rest o f
this section and start with the next section.
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IO4 N A BARRICELLI
t h is m a c h i n e h a s 3 6 b i n a r y d i g i t s . T h i s p e r m i t s d e s c r ib i n g th e s i t u a ti o n i n
t h e g a m e ( 3 6 c o in s p r e s e n t o r r e m o v e d ) b y a s in g l e b i n a r y n u m b e r w h i c h
c a n b e s t o r e d i n a s i n g l e m e m o r y l o c a t i o n . I n o t h e r w o r d s , t h e p r o b l e m i s
r e d u c e d t o c a l cu l at e a t t h e n tu m o v e a 3 6 b i t ( n o m o r e t h a n 3 6 d i g i ts b i n a r y )
n u m b e r s n + l a s a f u n c t i o n ~ p (s n) Of a n o t h e r 3 6 b i t n u m b e r s~ : wh e r e
s ~ r e p r e s e n t s t h e p r e s e n t s i t u a t i o n i n t h e g a m e ( a f t e r n t~ m o v e ) wh i l e s ~ 1
i s t h e s i t u a t io n a f t e r n e x t m o v e . T h e f u n c t i o n g p ( X ) s h a ll be c a l le d d ec i si o n -
f u n c t i o n . T h e d e c i s i o n - f u n c t i o n S p X ) m u s t b e d e t e r m i n e d b y t h e g e n e t i c
p a t t e r n o f t h e p l a y e r p i n s u c h a w a y t h a t o n l y l e g al m o v e s a r e p o s s ib l e .
A p a r t f r o m t h i s r e st r ic t i o n ( o n l y l eg a l m o v e s o f t h e T a c T i x g a m e ) t h e r e a r e
n o o t h e r r e q u i r e m e n t s t o t h e d e c i s i o n - f u n c t i o n
S ~ X ) .
I t w o u l d a l s o b e
d e s i r a b l e n o t t o i n s e r t o t h e r r e s t r i c t i o n s d u r i n g t h e p r o g r a m m i n g a n d r a t h e r
l e a v e t o t h e s y m b i o o r g a n i s m s th e m s e l v e s t h e g r e a t e s t p o s s ib l e l ib e r t y t o c h o o s e
t h e d e c i s i o n - fu n c t i o n a n d t o c h o o s e a n y p a r t i c u l a r d e c i s i o n - fu n c t i o n i n t h e
l a r g e s t p o s si b le n u m b e r o f w a y s b y m o d i f y i n g t h e i r g en e t ic p a t te r n s . A n y
r e s t r i c t io n t o t h e c h o i c e o f d e c i s i o n - f u n c t i o n w o u l d l i m i t t h e g a m e s t r a t e g i e s
a v a il a b le a n d m a y p r e s e n t a p o t e n t ia l d a n g e r f o r p r e v e n t i n g o r d e l a y i n g
c e r ta i n e v o l u t i o n a r y i m p r o v e m e n t s .
T h e s o l u t i o n o f t h e p r o b l e m i s s i m p l i f i e d b y t h e f a c t t h a t a n y 3 6 b i t
n u m b e r c a n , b y a s i m p l e o p e r a t i o n , b e t r a n s f o r m e d i n t o a g a m e s i t u a t i o n
s ~ + l w h i c h c a n b e re a c he d b y a l e g a l m o v e f r o m a p r e c ed i n g g a m e
s i t u a t i o n s ~ . T h i s m a k e s i t p o s s i b l e t o s o l v e t h e p r o b l e m i n t wo s t e p s :
A n u n r e s t r i c t e d d e t e r m i n a t i o n o f a 3 6 b i t n u m b e r U ~ + ~ b y a n y f u n c t i o n
U p s ~ ) o f t h e p r e s e n t g a m e s i t u a t i o n s ~ :
~ ) g ~ + l = u , s ~ )
T r a n s f o r m a t i o n o f t h e n u m b e r U ,~ + ~ i n t o a l e g a l s i t u a t i o n s~ + ~ f o l l o w i n g
s ~ b y a l e g a l i z i n g o p e r a t i o n L s~ , U ~ + ~ :
2 ) s n + ~ = L s ~ , U ,~ + 1 )
s ~ i s s u p p o s e d n o t t o b e z e r o ; o t h e r wi s e , t h e g a m e wo u l d a l r e a d y b e d e c i d e d .
T h e f i r s t s t e p c a l l s f o r a m e t h o d t o s e l e c t a s e c t i o n o f t h e g e n e t i c p a t t e r n
o f e a c h p l a y e r t o b e u s e d a s g a m e s t r a t e g y p r o g r a m , T h e m e t h o d s h o u l d
i d e n t i f y t h e g e n e t o b e u s e d a s f i r s t i n s t ru c t i o n i n t h e g a m e s t r a t e g y p r o g r a m .
I t w o u l d be a n a d v a n t a g e i f a l w a y s t h e s a m e g e n e i n a s y m b i o o r g a n i s m is
u s e d a s f i r s t i n s t r u c t i o n i n t h e g a m e s t r a t e g y p r o g r a m , s i n c e t h i s w o u l d
p e r m i t t h e s p e c ia l iz a t io n o f a p a r t i c u l a r s e g m e n t o f t h e g e n e t i c p a t t e r n a s
a n o r g a n f o r g a m e s t r a t e g y o p e r a t i o n s . T h e m e t h o d w h i c h h a s b e e n u s e d
i n t h e p e r f o r m a n c e t e st s p r e s e n t e d b e lo w c o n s is t s i n i d e n t i f y i n g th e l a r g e s t
p o s i t i v e n u m b e r i n t h e g e n e t i c p a t t e r n a n d l o c a t i n g t h e f i r s t g a m e s t r a t e g y
i n s t r u c t i o n i n r e l a t i o n t o t h i s l a r g e s t n u m b e r . T h e m e t h o d m a y l e a d t o
c o n s i d e ra b l e a m b i g u i t y if t h e l a r g e s t n u m b e r i s r e p e a t ed s e v e ra l t im e s i n e v e r y
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N U M E R I C L
T S T I N G O F
E V O L U T I O N T H E O R I E S
~o5
p e r i o d o f t h e g e n e t i c p a t t e r n . F o r t h i s r e a so n , m o s t s y m b i o o r g a n i s m s
d e v e l o p e d s e v e r a l g a m e s t r a t e g y p r o g r a m s w i t h d i f f e r e n t c h a r a c t e r i s t i c s a n d
q u a l i t i e s . No s t e p s h a v e b e e n t a k e n a g a i n s t t h i s s o r t o f a m b i g u i t y i n t h e p e r -
f o r m a n c e t e s ts d e s c r i b e d b el o w . B u t t h e s y m b i o o r g a n i s m s t h e m s e lv e s w o u l d
h a v e t h e p o s s i b i l i t y o f p r e v e n t i n g a n y a m b i g u i t y b y a s i n g l e m u t a t i o n i f a n
a d v a n t a g e i n d e v e l o p in g a s i n g le g a m e s t r a t e g y s h o u l d b e r e c o g n i z ed .
T h e d e c i s i o n t o p l a y a g a m e i s t a k e n e v e r y t i m e a c o l l i s i o n t a k e s p l a c e i n
c e r t a i n g a m e - c o m p e t i t i o n a r e a s . C o l l i s i o n s v e r y f r e q u e n t l y o c c u r b e t w e e n
t w o s y m b i o o r g a n i s m s o n e t o t h e r ig h t r i g h t p l a y e r ) a n d o n e t o t h e l e f t
l e f t p l a y e r ) o f t h e c o l l i s i o n p l a c e . B u t t h e r e m a y b e d i s o r g a n i z e d a r e a s
o n e it h e r s id e d i s o r g a n i z e d r i g h t p l a y e r a n d ] o r l e f t p l a y e r ) . W h a t e v e r t h e
s i tu a t i o n , t h e g a m e s t r a t e g y p r o g r a m s o f t h e l e f t p l a y e r a n d r i g h t p l a y e r
wi l l b e i d e n t i f i e d i n r e l a ti o n t o t h e l a r g e s t p o s i ti v e n u m b e r i n a c e r t a i n r e g i o n
t o t h e l e f t a n d r e s p e c t i v e l y t o t h e r i g h t o f t h e c o l li s io n p la c e . E a c h o n e o f
t h e t w o g a m e s t r a t e g y p r o g r a m s i s a r b i t r a r i l y i d e n t i f i e d w i t h 1 6 c o n s e c u ti v e
n u m b e r s c o n t a i n e d i n 1 6 c o n s e c u t i v e m e m o r y l o c a t i o n s o f t h e c o m p u t e r .
B o t h s e q u e n ce s o f 1 6 n u m b e r s a r e c o p i ed i n t o m e m o r y l o ca t io n s r e s e r v e d f o r
t h e g a m e s t r a t e g y p r o g r a m s o f t h e t w o p l a y e r s . T h e l a s t 8 o f t h e i 6 n u m b e r s
a r e u s e d a s p a r a m e t e r s wh i l e t h e o t h e r 8 a r e c o p i e d i n 8 n e w l o c a t i o n s t o b e
u s e d a s i n s t r u c t i o n s . I n t h e s e n e w l o c a t i o n d i g i t s wh i c h c o u l d g i v e m e a n i n g l e s s
o r u n w a n t e d i n s t r u c t i o n s a r e m a s k e d a w a y b y l o g i c o p e r a t i o n s . A l s o d i g i t s
wh i c h c o u l d g i v e a d d r e s s e s o u t s i d e t h e 1 6 l o c a t io n s o f t h e g a m e s t r a t e g y
p r o g r a m a r e r e m o v e d i n t h e s a m e o p e r a t i o n . A c o u p l e o f d i g i t s n e e d e d a r e
i n s e r t e d a n d t h e i n s t r u c t i o n s a r e e x e c u t e d . T h i s p r o c e s s wh i c h i s c a l l e d a
r o u n d o f o p e r a t i o n s i s r e p e a t e d 5 ~ t im e s . E a c h t im e o r i n e a c h r o u n d o f
o p e r a t i o n s ) a p a r t o f t h e I 6 n u m b e r s m a y b e re p l a ce d o r c h a n g e d a n d e a c h
o n e o f t h e 8 i n s t r u c t io n s m a y b e m o d i f i e d a c c o rd i n g l y . A t t h e e n d . o f t h i s
o p e r a t i o n , t h e o r i g i n a l g e n e t i c p a t t e r n h a s b e e n t r a n s f o r m e d i n t o a b o d y o f
1 6 n u m b e r s w h i c h w i l l b e c a ll e d p l a y e r b o d y . T h e s a m e t w o p l a y e r b o d i e s ,
o n e f o r t h e l e f t a n d o n e f o r t h e r i g h t p l a y e r , w i l l b e u s e d t o m a k e a l l t h e
m o v e s o f t h e g a m e . B e f o r e e a c h m o v e , t h e l a s t 4 o f t h e 1 6 n u m b e r s o f t h e
p l a y e r b o d y w h i c h i s s u p p o s e d t o m a k e t h e m o v e a r e r e p l a c e d b y 4 n u m b e r s
g a m e d a t a ) d e r i v e d f r o m t h e p r e s e n t s it u a t i o n s , o f t h e g a m e . T h e 4 n u m -
b e r s C o n s t i t u ti n g t h e g a m e d a t a a r e t h e g a m e s i t u a t i o n s,~ a n d 3 o t h e r n u m b e r s
d e r i v e d f r o m s~ b y o n e o r t w o h o r i z o n t a l a n d ]o r v e rt i c al m i r r o r s u b s t it u t i o n s
i n th e g a m e b o a r d . A f t e r i n s e r t i n g t h e g a m e d a t a 2 o m o r e r o u n d s o f O p e r at io n
a r e p e r f o r m e d . O n c e a g a i n a p a r t o f t h e 1 6 n u m b e r s m a y b e m o d i f i e d o r
s u b s t i t u t e d i n e a c h r o u n d o f o p e r a t io n . T h e n u m b e r t o b e u s e d a s U , + 1 w i l l
b e t h e l a s t o f t h e 1 6 n u m b e r s a f t e r t h e 2 o r o u n d s o f o p e ra t { o n a r e c o m p l e t e d .
T h i s s o lv e s th e f i r s t p a r t o f t h e p r o b le m , t h e d e t e r m i n a t i o n o f U ~ + 1 o n t h e
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io N A BARRICELLI
b a s is o f t h e g a m e s i tu a t i o n s ,, . T h e o p e r a t i o n s w h i c h d e t e r m i n e U s 1 a n d
t h e r e f o r e d e f i n e t h e f u n c t i o n U p i n r e l a t io n I ) a r e to a l a r g e e x t e n t se l e ct e d
b y t h e g e n e s o f t h e p l a y e r , w i t h t h e p o s s ib i l it y a n d , o n e m a y b e te m p t e d
t o s ay , th e l ib e r t y ) t o s e le c t a n d p r o g r a m i n m a n y d i f f e r e n t w a y s a l m o s t
a n y f u n c t i o n U p w h i c h c a n b e c a lc u l a te d w i t h t h e v e r y l i m i te d m a c h i n e t i m e
a n d m e m o r y s p a c e d e v o t e d to t h is p u r p o s e .
T h e l e g a l i z i n g o p e r a t i o n L s n , U s + 1 ) , w h i c h p e r m i t s t r a n s f o r m a t i o n o f a
3 6 b i t n u m b e r U , + 1 in t o a l eg a l g a m e s i t u a t io n s , + 1 f o l l o w i n g t h e p r e s e n t
s i tu a t i o n s , a c c o r d i n g to f o r m u l a z ) , is d e f i n e d b y l og i ca l o p e r a t i o n s w h i c h
s t a r t i n g f r o m t h e n o n - z e r o b i ts c o m m o n t o s,~ a n d U s + ~ o r , i f t h e r e a r e
n o n e , s t a r t i n g f r o m s n) id e n t i f y t h e lo w e s t n o n - z e r o b i t i n t h is p a t t e r n . T h i s
b i t i s r e m o v e d f r o m s , a n d i f i t i s p r e c e d e d b y a c o n s e c u t i v e s e t o f n o n - z e r o
b i ts c o m m o n t o s ~ a n d U ~ + 1 i n t h e s a m e r o w , o r s u b s i d i a r e l y i n t h e s a m e
c o l u m n t h e s e b i t s a r e a l s o r e m o v e d .
5. S E L E C T I O N P R O C E D U R E
W h e n t w o o r m o r e d i f f e r e n t n u m b e r s c o ll id e , t h e f i r s t a n d t h e la s t co l li d in g
n u m b e r s a r e r e c o r d e d . T h e f i r s t o n e is t re a t e d a s a g e n e o f t h e l e f t p l a y e r ,
t h e la s t o n e a s a g e n e o f t h e r i g h t p l a y e r w h i c h i s u s u a ll y b u t n o t a l w a y s
c o r r e c t ) . T h e g a m e s t r a t e g y p r o g r a m s o f t h e l e f t p l a y e r a n d r i g h t p l a y e r
a r e i d e n ti fi e d . F r o m e a c h s t r a te g y p r o g r a m a s e t o f n u m b e r s c a ll ed p l a y e r-
b o d y r e s p e c ti v e l y r i g h t p l a y e r - b o d y f o r th e r i g h t p l a y e r a n d l e f t p l ay e r -
b o d y f o r t h e l e f t p l a y e r ) is d e t e rm i n e d . T h e f i r s t m o v e i s d e t e rm i n e d b y
u s i n g t h e p l a y e r b o d y o f t h e f i r s t p l a y e r a s a s e t o f i n s t r u c t io n s a n d t h e
i n i t i a l s i t u a t i o n o f t h e g a m e a s d a t a o f t h e p r o b l e m . T h e n e x t m o v e i s
s i m i la r ly d e te r m i n e d b y u s i n g t h e p l a y e r b o d y o f t h e s e c o n d p l a y e r a s
a s e t o f i n s t r u c t i o n s a n d t h e s i t u a t i o n i n t h e g a m e a f t e r t h e f i r s t m o v e a s
d a t a . T h e o p e r a t i o n i s r e p e a t e d u s i n g a l t e r n a t e l y t h e r i g h t a n d l e f t p l a y e r
b o d i e s u n t i l a l l c o i n s h o l e s ) a r e r e m o v e d a n d th e is s u e is d e c i d e d .
T h e g e n e o f t h e w i n n e r - - f i r s t o r l a s t c o l l i d i n g n u m b e r b o t h o f w h i c h h a v e
b e e n r e c o r d e d f o r t h i s p u r p o s e - - e n t e r t h e c o l l i s i o n p l a c e . B y t h i s p r o c e d u r e ,
t h e b e s t p l a y e r w i l l i n v a d e t h e c o n t e s t e d a r e a s a n d t h e o t h e r s y m b i o o r g a n i s m s
w i ll b e o b l ig e d to r e t r e a t . O n e o f t h e p l a y e r s c a n b e , a n d o f t e n is , a d a m a g e d
s y m b i o o r g a n i s m o r a c o m p l e te l y d i s o r g a n i z ed s e t o f n u m b e r s . T h e p e r f o r -
m a n c e o f a s y m b i o o r g a n i s m c a n t h e r e f o r e a l s o b e t e s t e d a g a i n s t r a n d o m o r
d i s o r g a n i z e d s e t s o f n u m b e r s .
6 . G A M E Q U A L I T Y A N D C O M P E T I T I V I T Y
I n g a m e s b e tw e e n s y m b i o o r g a n i s m s , a l a rg e f r a c t io n o f t h e g a m e s a r e
l o s t , a s i n f i g . I , b y a s t u p i d m o v e o f t h e l o s e r , w h o t a k e s a l l o f s e v e r a l
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NUMERIC L TESTING OF EVOLUTION THEORIES
Io
remaining coins instead of leaving one of them on the table. These games
are called stupid games or games of quality o. Some other games are decided
by one or several correct final moves of the winner which leave no favorable
choice to the loser. Favorable choice is here defined as a choice which would
give the possibility of winning the game without a mistake from the opponent.
For example, in the game of fig. 2, the winner s last and next to last moves
are both correct decisions which leave no favorable choice for the loser.
The quality of a game which has been played can be measured by the
number of correct final decisions of the winner. For human beginners--
except those beginners who already know a similar game called Nim--the
mean number of correct final decisions by the winner in the first 5 games
played is between I and 2 when both players are beginners.
Unfortunately, the game quality does not only depend on the genetic
strategy program but also on the condition of the players. Damaged symbio-
organisms and disorganized sets of numbers are likely to play bad games.
A quality record of the games played during an evolution process would,
therefore, not only reflect the possible evolutionary improvement but also
the extent of the damages caused by the competition between the symbio-
organisms. For this and other reasons presented below, large fluctuations
of game quality, unrelated to the evolutionary development, are observed.
A record of games won by the left player and by the right player in
relation to the position of the various symbioorganisms and disorganized
regions will therefore be given in fig. 4 and 6 to permit a better evaluation
of the various situations.
7. RESULTS
Attempts to measure evolutionary progress in game performance were
made in 1959 at the A. E. C. Computing Center in New York University
with an IBM 7o4 computer and repeated in 196o with the same computer
while the author was visiting the Brookhaven National Laboratory in Long
Island. In the first attempt, no successful evolution process was obtained
and no measure of evolutionary progress in game performance could there-
fore be made. In 196o the attempt was repeated using primarily the same
combinations of mutation and reproduction norms which had been success-
fully used in Princeton before. However in some regions of the universe,
which in this case had a size of 3o72 numbers, mutations were replaced by
game competitions. With this procedure two successful evolution processes
(respectively called A and B) were obtained and the development of game
performance could be observed and measured. In the later stages, the two
experiments were linked together to observe game competitions between
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IO 8 N A BARRICELLI
the two types of symbioorganisms developed. In each experiment (experiment
A and experiment B) the evolution process started with inefficient game
competition due to unsuccessful coding producing low variability or no
variability at all in the game pattern. In the experiment A efficient game
competition started at generation lO24. In experiment B efficient game
competition started at generation 256o. In fig. 4, upper diagram, the games
played at generation lO24, in the experiment A are marked by dots. Each
dot is approximately at the number location (given by upper scale) where
the collision occurred ( + or - - IO number locations). Above the io24-1ine
(at the level +0 and + I) are the games won by the right player, below the
IO24-1ine at the level ---o) are the games won by the left player. At the levels
Fig. 3. Game of c uali~ty 4 played between two symbioorganisms after a preselected
game-starting.
+o and --o are the dots corresponding to games of quality o (stupid games).
At the level + I is marked a game of quality I which was won by the right
player. The same convention is used in the following diagrams of fig. 4 and
in fig. 6, where dots at the levels +o and ---o mark games of quality o,
dots at the levels + I and -- I mark games of quality I, dots at the levels
+2 and --2 mark games of quality 2. Games of quality 3 or higher are all
marked at the levels +3 or --3. The number of games (dots) in each diagram
is marked in She right margin, the generation in which the games were played
is marked in the left margin. In each diagram the most prominent symbio-
organisms are indicated by horizontal segments (with arrow heads) which
mark the regions in the universe occupied by the respective symbioorganisms.
Tregeners (a type of symbioorganisms of periods 3 and 6) and tregener-
deriva~dves (see fig.4) are related to the parasite recorded in the previous
paper BARRICELLI,1962 fig. 17 and Ig) "'A" is the name of the type of
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A E x p e r i m e n T
1200 1300 1~-00 t500 1600 1700 1800 I r 20 00 210 0 2200 2300
2~-00
2 5 0 0 2 6 0 0
m o f
G~n~.
Tr,9o,er_der i~=t i~es A 9 ~ nes
1 o 2 ~ ' " . > , - , ~ - : . . . . . . . '~o
A
T r e g n e r s
121t0 i
. . . . . . . .9 ~" ": . . . .. . . . < > - ' : " : : . . . . . . . < - ~
> 5 ~
A A r ~ , ~
1S36~-J( - 9 ". ~.'."'::'.':'-:::",::.'.]::: ': :. ~ ' ~ :". ....... " 1 0 5
' A " ' T r e g e n e r s 9
1 ~ A ' -. - '. ~ " .7 . .. .. . :'- ~ - '" . - - -> . 5 3
800 r 1000 1100 1200 1300 lz rOO 150Q 1600 1700 1800 1 :100 200 0 2100 2200
P r e s e l e c l " e d G ~ r n e - S f c t r ' [ i n c a s ~ G ~ m e ' S ' l ' c t r f i n g s
m 2 - ~ " . . " : . ' . " - ~ 2 t
= , :
iq z o ~ } . : . A . . -
A
"" " " - > 1 2 .
B
_ A I 'l ~ ,~ a h ~ p ~ N & d B ( o 4 o o ~ l - A ( ~ o o ~ - s o T ~ ) A
2 o ~ , ~ > ~ : . - . . . . . . . . . . ~ 3 ,1
A . .. . - ... A > 1 %
~ i 7 6 _ ~ . _ :.::- .a ':.- - . ' = ~ ' . . - : "
1 2 0 0 1 3 0 0 1 4 00 1 5 0 0 1 6 0 0 1 7 0 0 1 8 0 0 l q O 0 2 0 0 0 2 1 0 0 2 2 0 0 2 3 0 0 2 4 0 0 2 5 0 0 2 6 0 0
23o~_".~ A : # . . . _ : . . . . . A
. , .:- '.: '.. > 3o~
: ' A A
2.4-32+_~ . . . - . . , _
A A
256o~ :~ . . . . . . . ; . :,
A k
2688L~ . . . . . . . ~- r 5
800 q00 1000 I I00 1200 1300 I }00 1500 1600 1700 1800 Iq00 2000 2100 2200
9
9 " . . . . . ~ q ' 3
2 q ~ @ A . A
. ' ~ - 6
, ~ B - & m Q ~ , d . . A A
3072:e
> ~- .~-- '- " ' " "" ~ ~0
3 z o o } A . . . . . . A
-
" . . . . 9
. . . . . ~- 2 1
: r
: ~ 7
SU BS ID IA R Y E X P E R I M E N T (SSZ 9omes Qnd 15 uta~ons)
2 | i o o 6 z 7 0 0 o o q o o 2 o o o 2 t o o 2 2 0 0 2 3 0 0 2 o o 2 s o o 2 o o
2 m ~ r :y ;' : : :: :. .' .7 . . .. ..~ : : . . A s~-
z 2 4 o ~ , . _ . : . . ~ .y _ . . A A - -
. . . . . >
~1
2 s o ~ , f B + . . : - ._ . : .. . .. : .. . ~ . A .
z ~ a 2 ; ; B . A 9
" y " . " [ . . _ . . < . . .~ . . .
A
'> 3 q
A
) 3 3
A
9 b e 2
F i g . 4. D e s c r i p t i o n o f g a m e s ( d o t s ) p l a y e d i n t h e A - e x p e r i m e n t a n d s u b s i d i a r y
e x p e r i m e n t .
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I l O N A BARRICELLI
s ym bi oo r ga n i s m ( o f pe r i od 5~ o r 5o - ge ne r s ) w h i c h be c om e s p r e dom i na n t
du r i ng the A - e xpe r i m e n t . ' B is t he na m e o f t he t ype o f s ym b i oo r ga n i s m
( 6o - ge ne r s a nd 72 - ge ne rs ) w h i c h be com e s p r e dom i na n t du r i ng t he B-
e xpe r i m e n t .
G a m e s w e r e p l a ye d on l y in c e r t a in a r e a s w h i c h w e r e c ha ng e d s e ve r al ti m e s
du r i ng t he e xpe r i m e n t s , a nd c a n be a pp r ox i m a t e l y i de n t i f i e d by t he pos i t i ons
of the do t s in f ig . 4 and 6 . Be tween number loca t ions 1536 and 2o48 a l l the
games s t a r t ed regula r ly l ike the games in f ig . I and 2 . On both s ides of
th i s reg ion , va r ious prese lec ted game s t a r t ings , a s for example in the game
of f i g . 3 , w e r e u s e d t o p r om ot e t he de ve l opm e n t o f m or e un i ve r s a l ga m e
s t ra teg ies , the va r i e ty of the prese lec ted game s t a r t ings be ing an e f f i c i en t
method to prevent spec ia l i s a t ion .
At genera t ion lO24 in the A-exper iment , when e f f i c i en t game se lec t ion
s ta r t ed , on ly one game out o f 4o (do t in loca t ion 145o) was of qua l i ty I .
The o the r 39 were s tup id games , mos t ly repe t i t ions of the game in f ig . I .
T he s e ga m e s a r e w on by t he r i gh t p l a ye r w h i c h i s a l w a ys t he be g i nne r i n
these exper imen ts . T he reade r wi ll, t he re fo re , n o t i ce tha t a ll bu t 3 games
were wo n by the r igh t p laye r (do t s above the line ) o f genera t ion lO24.
Evident ly , a s long as the qua l i ty of the games i s low, the r igh t p laye r has
a dva n t a ge s i n t he r e g i on o f r e gu l a r ga m e s t a r t i ngs . T he A - s ym bi oo r ga n i s m
to the l e f t o f loca t ion 18oo has the re fore no chance to pene t ra te the game
a r e a t o the r i ght , be f o r e it s ga m e p e r f o r m a nc e is i m pr ove d . O n l y a t ge ne r a ti on
1664, a f t e r A had invaded the game reg ion to the l e f t (be tween 128o and
1536 ) thu s imp roving i ts gam e s t ra t eg y by adapta t ion to th i s gam e a rea , i t
s t a r t ed making some progres s in the game reg ion to the r igh t .
A t ge ne r a ti on 2o48 a nd e ve r y 256 ge ne r a t ions a f t e r t ha t, B - s ym bi o -
o r ga n i s m s f r om t he pa r a l l e l B - e xpe r i m e n t w e r e i n t r oduc e d i n t he r e g i on
O-lOO7 . A l a r ge num be r o f ga m e c om pe t i t i ons ( do t s ) i n t he ga m e r e g i on
to the r igh t o f loca t ion
lO 4
i s the resul t (see f ig . 4 generat ions 2o48, 2816,
a nd 3o72 ) . I n g e ne r a ti ons 23o 4 a nd a nd 256o t he r e w a s no ga m e r e g i on i n t he
proximi ty of loca t ion lOO7 and only loca t ions above 12oo a re recorded in the
f igure for these genera t ions .
A g lance a t f ig . 4 shows tha t the qua l i ty of the games and the pe r cen t o f
t he ga m e s w on by t he r igh t o r t he le f t p la ye r a r e ve r y d i f f e r e n t i n d i f f e r e n t
regio ns and, a t leas t in som e places ( l ike locat ion I9OO at gen erat ion 1664 and
loca t ion i lOO a t genera t ion 2176) , a re s t rongly re la t ed to the respec t ive
pos i t ions of com pe t ing sym bioorg ani sm s and]or d i sorganized reg ions . A c lose r
inspec t ion of f ig . 4 can of t en t e l l i n which pos i t ions the symbioorgani sms
are who win the games , o r who a re l ike ly to p lay good games a t l eas t aga ins t
a pa r ti c u l a r opp one n t w h os e ta c ti c s t he y ha ve l e a r ne d b y m u t a t ion a nd
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N U M E R I C L T E S T I N G O F E V O L U T I O N T H E O R I E S
l
selection. On the other hand, there is no clear evidence that the nature of
game startings (regular or preselected startings) has any direct influence on
the quality of the games or on the fraction of left (or right) victories after
A-organisms had invaded the whole universe. No discontinuity in the quality
or type of games can be seen in position 1536 which marks the frontier
between preselected game startings (to the left) and regular game startings
(to the right) at the generations 1792 192o, 2048, 2176 2816, 2944 etc. A
difference can, however, be observed in the number of games played to the
left of location 1536, compared with the number of games played to the right
of this location. The difference, which is manifest at the generations 1792
192o, 2048, 2944, etc. indicates a greater variability of the symbioorganisms
in the preselected game starting's sector to the left of location 1536 than
in the regular game starting's sector to the right of this location. The large
variety of preselected game startings seems to promote variability. Usually
variability will produce changes and permit evolution. But there is one case
in which a stable situation with some variability in the region between
location 137o and 15oo was maintained for 128 generations without further
changes. A glance at the games (dots) in this region on fig. 4 shows that the
same games were played with the same results at generations 2944 and 3072.
The quality of the games, measured by the per cent of dots above the +o
level and below the --o level, showed a tendency to increase during the
A-experiment, but also large fluctuations. In fig. 5 the solid line shows the
per cent of games with quality not lower than I for each generation repre-
sented in fig. 4. The significance of each value can be judged from the
number of games on which it is calculated. This number is represented by
vertical solid lines in the lower part of fig. 5. For example, the very low
value (based on 5 games) at generation 2432 and the very high values (based
respectively on 6 and 7 games) at generations 2954 and 3328 are not very
significant. Some of the fluctuations are, however, significant and their
interpretation is still a matter of investigation. In spite of the mentioned
fluctuations, the solid line of fig. 5 suggests an increase in the percentage of
games with quality I or higher by lO to 15' every IOOO generations. From
generation 1792 (or 768 generations after efficient game-selection had been
started) disorganized areas appeared only in places where two symbioor-
ganisms competed. A disorganized set of numbers had no longer any chance
against symbioorganisms which had improved their game strategy for that
many generations.
After generation 2o48 a different continuation (subsidiary experiment)
of the above experiment was attempted. The purpose o f this subsidiary
experiment was to keep the B-symbioorganism alive for a large number of
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I I 2 N A B A R R I C E L L I
generations rather than re-introducing it once every 256 generations in the
region O-lOO7 of the A-universe. In the game areas, the B-symbioorganisms
are at a disadvantage in the competition with A-symbioorganisms to the right,
as 10ng as the game quality is low, for the reasons explained above. However,
a reduction of the game frequency obtained by leaving about 15 of the
1 0 Z q - l S 3 2 0 4 g Z S 6 o 3 0 7 Z . ' ; G e ~ e v o . ' ( 'i o ~ S
oz
/ \ /
~ ; v
lZ
1 1
IO
q
8
7o
O
~G
3C
Zc
1
t
?
t
t
Fig. 5. Game number and quality diagrams in the A-experiment
subsidiary experiment (dotted diagram).
T
(solid diagrams) and
collision places empty (while the remaining 85 of the collision places were
occupied by the winner of a game) proved sufficient to give the B-symbio-
organism a fighting chance. In the subsidiary experiment (see lower part
of fig. 4) the B-symbioorganism was able to survive in a region below
location 13oo which is mostly outside range of fig. 4. The quality of the
games is represented by the dotted curve of fig. 5. The lower quality at
generations 23o 4 and 2423 coincides with the situation in which most games
are played in a disorganized area between the two symbioorganisms A and B
(see fig. 4 lower part). The players are, therefore, mostly damaged or
disorganized.
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N U M E R I C L T E S T I N G O F E V O L U T I O N T H E O R I E S
II 3
B Experi menl
t200 1300 1400 1500 I (o00 1700 1800 IqO0.200012 1 00 2 2 0 0 23 0 0 2 ~ 0 0 2 5 00 2 ~ o f
25~ ; . . . . . " . . . . . . . . el ~
1 5
B B
B B
- ( - 1
ixTure
E x p e r im e n t A o - loo 7) - B looe-3o71)
8 00 q eo 1 0 0 0 1 10 0 1 2 0 0 1 3 0 0 t4 0 0 1 5 0 0 1 6 0 0 1 7 0 0 l S 0 0 I q 0 0 2 0 0 0 2 1 00 2 2 0 0
P re s elecl ed
G a m e - S ~ a r f i n g s R e g u l a r G a m e - S t = r t i n g s
A B * B
~ 3 Z S ~ k > < : ' : ' : : : ' : ' . . . . . l... " , " " ii. i " > 3 ~
. B B
~ ~ ; g . . . . . . . . . r " " " ' ' l } 1 3
353~
_
>
< ' : : : . f . . . . . . . . . . . . . . . 9 . . . . " . . . . . . . . > 6 8
. , B - i n f e c d B infected
3 71 2 ~ < l 9 : . . . . . . . . . . . . l ill 9 . . . . . . . . . . . ~ . . 9 . . . . . . . . i : i l > 8 t
-=
1200 1300 l ifO0 1500 11100 1700 1800 I90 0 2000 2100 2200 2300 20,00 25 00 2600
~o B - c lamacjed B - damacjecl
1 1
~ B - da. oged B - dam=~ea
B d o m a ~e ~ l E l a m a g e d
B - d a m a g e d [ 3 ; d am a ~ ec l
~ 2 2 ~ ~ I ~ I I l : ' i , I ~
2 G
F i g . 6 . D e s c r i p t i o n o f g a m e s d o t s ) p l a y e d i n t h e B - e x p e r i m e n t .
The B-experiment is recorded in fig. 6 and the quality of the games in this
experiment is recorded in fig. 7. Eff icient game selection started at generation
256o which is the first generation recorded in fig. 6 and 7. At generation
3328 and every 256 generations after that A-organisms from the parallel
A-experiment was introduced in the region O-lOO7 . The collisions between
A and B-genes are the cause of the large number of games dots) to the right
of location lO24 at generations 3328 and 3584 in fig. 6.
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I I 4 N. A. BARRICELLI
A r o und ge ne r a ti on 3456, t he B- s ym b i oo r ga n i s m de ve l ope d a n i n f e c t ion b y
a pa ras i t e which apparen t ly damaged but d id no t k i l l t he hos t . In f ig . 8A
a n d B i n w h i ch b i n a r y n u m b e r s - - o r g e n e s - - a r e r e c o rd e d v e rt ic a ll y , e a ch
c o l um n r e p r e s e n t i ng a b i na r y num be r ) t w o s pe c i m e ns o f B- s ym bi oo r ga n i s m s
a r e p re s e n te d . T he f i r s t s pe c im e n f i g . 8A ) i s t a ke n f r om ge ne r a t i on 3328
loca t ions 1224- I296 be fore the in fec t ion deve loped . The second spec imen
Q
tJ
5 0 ~ a 3
e ~ _~
~ O ~
3 o ~
z o z ~
0% ~
l n~ ect ion
2560
qO
8O
7
6 0 E
5 0 0
q -O
3 0 : ~
20
0 o l
3 0 7 2 3 5 8 4
Oq6 - - G e n e r a T i o n s
w [ 1
Fig. 7. Game number and quality diagrams in the B experiment.
f ig . 8B) i s t aken f rom genera t ion 3712 loca t ions 2232-2304 a t a s t age of
advan ced infec t ion . At th i s s t age eve ry th i rd gene see f ig . 8B) of the hos t
ha d be e n r e m ov e d o r r e p l a c e d by t he pa r a si te . T h e ge ne s o f t he pa r a s i t e c a n
e a s i l y be d i s t i ngu i s he d f r om t hos e o f t he hos t be c a us e t he y do no t ha ve a I
o r ho l e) i n t he uppe r r ow s e c ond r ow f r om t op w h i c h is f i ll e d i n t he
un i n f e c t e d ho s t - - f i g . 8 A - - w h i l e e ve r y th i r d p l a c e i n th i s r ow i s e m p t y in
t he i n f e c t e d on e - - f i g . 8B ) . S om e c a s e s o f pa r t ia l r e c ove r y ha ve be e n
obs e r ve d , bu t i t i s no t know n w he t he r t he B- s ym bi oo r ga n i s m s c a n r e c ove r
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NUMERICAL TESTING OF EVOLUTION THEORIES
II
c o m p l e t e ly o r w h e t h e r t h i s s p e c t a c u la r i n f e c t i o n w i lt e v e n t u a l l y d e v e lo p i n t o
a s y m b i o t i c r e l a t i o n s h i p .
I n t h e e a r l y a c u t e p h a s e o f i n f e c t i o n , a l a r g e n u m b e r o f g a m e s a r e p l a y e d
see do ts in f ig . 6 , genera t ions 3584 and 3712 , and ve r t i ca l l ines in f ig . 7
s a m e g e n e r a t i o n s ) a s a r e s u l t o f t h e l a r g e n u m b e r o f c o l li s io n s b e t w e e n
p a r a s i t e a n d h o s t - g e n e s . I n t h e l a t e r s t a g e s o f i n f e c t i o n g e n e r a t i o n s 3 8 4 o ,
3 96 8, 4 o 9 6 , 4 2 2 4 ) t h e c o l l is i o n f r e q u e n c y is g r e a t l y r e d u c e d .
i
/
| | | l l I ii i i | l l i i ~ | l l i | | i i i B ~
i i | i i | | i I I i i | i 1 | JiJ i i } I i l l j i l l | ~ i l l H l i | ~11 i~ I liD I l l i i | i i iH i i } ~ i i g iQ | l J i i
I |
I l l n
l l l
I I n l
i i i
i i i i
i i i l l
I I I I I I I I I I I I I I I I I I
I I I I I I I I I I I I I I I I I I I l U l l
I I I 1 I I I I I I I I I I I I I
I I I I I I I I I I I I I I I I I U I lU U I
I I I I I I I I I I I I I U I I I I I I I
I I U I I I I I I I I I I I U I I I I I I
I I I I I I I I I I I I I I U I I I I I
Fig. 8. A. Normal B specimen. B. Infect ed B specimen.
T h e i n f e c t i o n s e e m s t o p r e v e n t a t l e a s t t e m p o r a r i l y a n y f u r t h e r p r o g r e s s
i n g a m e p e r f o r m a n c e a s s u g g e s t e d b y f i g . 7. T h e p a r a s i te n e v e r d e v e l o pe d i ts
o w n i n d e p e n d e n t g a m e s t r a t e g y . I t s i n v a s i o n t e c h n i q u e i s b a s e d o n i t s a b i l i t y
t o m a k e u s e o f t h e g a m e s t r a t e g y p r o g r a m o f t h e h o s t i t s e lf , in o r d e r t o
b e a t t h e h o s t i n a l a r g e f r a c t i o n o f t h e g a m e s . T h i s t e c h n i q u e , h o we v e r ,
c a n n o t w o r k i f t h e h o s t i s r a p i d l y d i s o r g a n i z e d o r s e r i o u s l y d a m a g e d . A n y
d r a s t i c r e d u c t i o n o f g a m e p e r f o r m a n c e i n a n i n f e c t e d a r e a w o u l d p r e v e n t
Acta Biotheoretica, X VI 8
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I I N. A, BARRICELL
furthe~ progress of the parasite from this area, and may locally produce
a partial recovery of the host. This way a balance between host and parasite
is obtained and the destruction of the host is prevented in game areas. Outside
game areas a much more pronounced disorganization of the host is
occasionally observed.
8. SIGNIFICANCE OF THE PERFORMANCE TESTS
The performance tests described in the previous section cannot give a true
measure of the rapidity of improvement obtainable by the selection method
used. These performance tests are the first combined experiment which suc-
ceeded at all. The choice of experimental conditions and parameters has
primarily been based O a guess, and there is no information available which
could help in deciding whether and how much the result could be improved
by modifying the experiment.:,
A new Combined 'experiment in which the game areas have been extended
while the founds of operations before each game (after the formation Of the
player body) are reduced from 2o to IO has recently been started. This
'experiment i s being carried on in two different universes, and the conditions
for periodical interchanging, of symbioorganisms between the two universes
are radically di fferen t from previous experiments. It is hoped that this
experiment can give some of the information necessary to decide whether
and how much the exiolutionary progress of performance can be-speeded
up. With present speed, it may take io,ooo generations (about 8o machine
hours on the IBM 7o4 or between 5 and Io machine hours on the Atlas,
Ferranti machine)to reach an average game quality higher than I. The best
averages obtained so f a r ar e around o.4. Human beginners in the first 5
games show averages between I and 2. All these data must be taken with
reservation due to the large fluctuations an d the irregular character of the
progress. However, there is no doubt that the progress is significant and
t'hat the symbio.organisms are learning the game by a sort of evolutionary
learning process based on mutation, crossing and selection.
A fundamental question for practical application is: how would the
evolutionary learning process work out in a more complicated game like,
for instance, chess ? Itwould seem that in a complicated game the evolutionary
learning process would be much slower. However, the evolutionary learning
process is very different from human learning. The learning of a seemingly
simple operation like leaving a single pawn on the board in the Tac Tix
game at the first given opportunity, may take a rather long time. On the other
hand, the crossing mechanisms which play a fundamental role in this proces's
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N U M E R I C L T E S T I N G O F E V O L U T I O N T H E O R I E S
II7
make evolutionary learning extremely well suited to make progress in many
different directions at the same time (cf. FISI-tER'S law and the independent
spreading of many different mutations). This may be rather difficult for
humans who largely prefer to learn one thing at a time. There is no evidence
that human standards can be used to evaluate machine time for evolutionary
learning processes. The only way to decide the question is to try. The
programming difficulties are greater with the chess game than with the
game used above. On the other hand, chess-programming for high speed
computers has already been successfully accomplished (BERNSTEIN, 1958).
There is no doubt that the difficulties can be overcome.
At any rate, the value of the results presented does not primarily rest on
the possibilities for practical applications, but on their biotheoretical
significance. It has been shown not only that the symbioorganisms can
improve by evolution, but how the improvement takes place in a particular
set of operations necessary for their survival. It has been shown that given
a chance to act on a set of pawns or toy bricks of some sort the symbio-
organisms will *'learn how to operate them in a way which increases their
chance for survival. This tendency to act on any thing which can have
importance for survival is the key to the understanding of the formation of
complex instruments and organs and the ultimate development of a whole
body of somatic or non-genetic structures.
9- THE CHOICE OF REPRODUCTION NORMS
The development in game performance presented in this paper was made
possible by a minor change in the reproduction and mutation rules (or norm
of action ) used. This norm of action was designated as a shif t norm
]~ARRICELLI,1957) and this designation will still be maintained in spite of
the change performed. A question which arises is: what would happen if
more radical changes were applied or if a completely different norm were
used.
As already pointed out in the previous paper (BARRICELLI, 1962) a norm
which does not require symbiosis as a condition for reproduction or survival
would not lead to the formation of symbioorganisms and hardly to any
structure of complexity or evolutionary possibilities comparable to living
organisms. Only norms of action requiring symbiosis (symbionorms) shall
therefore be considered.
An extension of the shift norms to a two-dimensional universe in which
each generation consisted of vectors (pairs of numbers) scattered on a cros-
section paper instead of a single row--has been tried in Princeton (BARRI-
8
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I Ig N A BARRICELLI
CELLI, 1957). The experiment was not carried very far because of the much
larger machine time and machine memory requirements of two-dimensional
experiments. The phenomena observed were, however, of the same nature
as those which have been described in the one-dimensional experiments.
Of fundamental interest for the understanding of the nature of terrestrial
life is the fact that the Well-known reproduction rules for
DN/t
molecules
are an example of a symbio-norm. In this norm, the nucleotides play the role
of elementary selfreproducing entities numbers); the polynucleotide chains
or DNA molecules play the role of symbioorganisms. Proteins and other
molecules which are constructed, rearranged, or modified by the catalytic
action of the
DNA
and the associated enzymes tiave apparently the role of
non-genetic objects, instruments, and products of the action of symbio-
organisms example: pawns in a game and numerical devices constructed
or used to act upon them).
It is easy to show that the DNA reproduction rules constitute a symbio-
norm. Each nucleotide would be unable to reproduce alone. In this respect a
single nudeotide behaves like a single number in the numeric experiments
already presented, tt is the association of several nucleotides into polynucleo-
tide chains symbioorganisms) which confer to them the catalytic abil ities
necessary both for the construction by the intermediate action of enzymes
and other molecules) of new nucleotides and their associat ion into new poly-
nucleotide chains identical to the parental chains. The DN-A-norm requires
a symbiotic association into specific groups of nucleotides as a condition for
reproduction.
The simplest known DNA-symbioorganisms viruses) show the biopheno-
mena listed in the previous paper B~RtlCELLI, 1962, section 6), except
spontaneous formatiOn which cannot be observed in nature today BARRI -
CELLI, 1962, section IO).
It is important that the biophenomena observed are a consequence of the
symbio-norm followed by the DNA-molecules. If the nucleotides, the amino
acids, and other essential features involved were substituted by numbers
in the memory of a computer instructed to apply the same symbio-norm
DNA-norm), one would observe exactly the same biophenomena, assuming
successful programming. Obviously there may be technical difficulties, and
our present knowledge is hardly sufficient to construct a true numerical
model of the chemical phenomena involved in any particular DNA or
polynucleotide dupiication. An incomplete model describing only some funda-
mental aspects of DNA-duplication is the best one might be able to do for
the time being. The question of present practical feasibility is however of
no consequence for the argument, as long as no theoretic principle like
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NUMERIC L TESTING OF EVOLUTION THEORIES
I I 9
He i s e n b e r g ' s u n c e r t a i n t y p r in c i p l e , E i n s t e i n ' s c r i ti c o f s i m u l t a n e i t y ) i s i n -
v o l v ed , w h i c h w o u l d p r e c l u d e t h e f e a s i b i li t y o f t h e e x p e r i m e n t . T h e q u e s t i o n
w h e t h e r n u m b e r s o r n u c l e o t i d e s o r m a g n e t i c c h a r g e s o r a n y o t h e r g a d g e t s
i n t h e m e m o r y o f a h i g h s p e e d c o m p u t e r a r e u s e d a s s e l f r e p r o d u c i n g e l e m e n t s
h a s n o i n f l u e n c e o n t h e r e s u l t .
A l e s s o n w h i c h c a n b e l e a r n e d f r o m t h e p e r f o r m a n c e t e s ts d e s c r ib e d i n
t h i s p a p e r i s th a t t h e n a t u r e o f t h e b i o p h e n o m e n a o b s e r v e d i s n o t r a d i c al l y
c h a n g e d b y a m o d i f i c a t i o n o f t h e s y m b i o n o r m w h i c h d o e s n o t d i r e c t l y i n t e r -
f e r e w i t h t h e r e p r o d u c t i o n m e c h a n i s m . N e i t h e r A n o r B n o r a n y o t h e r
s y m b i o o r g a n i s m d e v el o p e d i n th e p e r f o r m a n c e t e st s s h o w p r o p e r t ie s o r
b i o p h e n o m e n a w h i c h a r e f u n d a m e n t a l l y d i f f e r e n t f r o m t h o se o b s e rv e d i n th e
s y m b i o o r g a n i s m s d e v e lo p e d d u r i n g t h e P r i n c e t o n e x p e r i m e n t s o f I 9 5 4 a n d
1 95 6. T h e i n f e c t i o n d e v e o p e d b y t h e B - s y m b i o o r g a n i s m s ( f i g . 8 B ) m a y
s e em m o r e s p e c t a c u la r , b u t n o t f u n d a m e n t a l l y d i f f e r e n t f r o m s o m e o f th e
o t h e r p a r a s i t ic p h e n o m e n a o b s e rv e d i n p r e v i o u s e x p e r i m e n t s .
I t s e e m s l i k e ly t h a t t h e n a t u r e o f t h e b i o p h e n o m e n a a p p e a r i n g i n a s y m b i o -
g e n e t i c e x p e r i m e n t i s p r i m a r i l y , i f n o t c o m p l e t e l y , d e t e r m i n e d b y t h e r e p r o -
d u c t i o n n o r m u s e d i r r e s p e c t i v e o f p o s s i b l e i n t e r a c t io n s w i t h o t h e r e n t i t ie s ;
I f t h i s a p p l i es a l s o f o r t h e DAT A r e p r o d u c t i o n n o r m , t h e i n t e r a c t i o n b e t w e e n
DN- A a n d p r o t e i n s o r o t h e r m o l e c u l e s m a y h a v e l i t tl e i n f l u e n c e o n t h e g e n e r a l
f e a t u r e s o f t h e b i o p h e n o m e n a , i r r e s p e ct i v e o f t h e i n f l u e n c e t h e y m a y h a v e o n
t h e s e l e c t i o n o f s y m b i o o r g a n i s m s . I t m i g h t t h e r e f o r e b e p o s s i b l e a l r e a d y
w i t h t h e s c a n t y k n o w l e d g e p r e s e n t l y a v a il a bl e t o a t t e m p t n u m e r i c a l e v o l u t io n
e x p e r i m e n t s b a s e d o n t h e D N A - n o r m i n o r d e r t o g a t h e r i n f o r m a t i o n o n t h e
m a n n e r i n w h i c h a D N A - e v o l u t i o n p r o c e s s w o u l d d e v e l o p .
io. DNA SYMBIOGENE SIS
A N D C R O S S I N G
As a f i r s t s t e p t o wa r d t h e u s e o f a
DNA norm
as a bas i s fo r a symbio-
g e n e t ic e v o l u t io n e x p e r i m e n t , o n e m a y a t t e m p t t o f i n d i n a d v a n c e s o m e
o f i t s c h a r a c t e r i s t i c s a n d p r o s p e c t s . S o m e q u e s t i o n s wh i c h we r e i n v e s t i g a t e d
b e f o r e t h e s h i f t n o r m s w e r e u s e d a n d w h i c h m a y b e w o r t h i n v e s t i g a t i n g
b e f o r e a D N A - n o r m i s u s e d a r e th e f o l lo w i n g : ( I ) w h a t ar e th e p ro s p e c t s
o f d e v e l o p i n g c o m p l e x s y m b i o o r g a n i s m s ; ( 2 ) w h a t a re t h e p r o s p e ct s o f
d e v e l o p i n g a c r o s s in g m e c h a n i s m e a r l y i n t h e e v o l u t i o n p ro c e ss . W i t h o u t
a c r o s s i n g m e c h a n i s m e v o l u t i o n w o u l d p r o c e e d a t a n e x t r e m e l y s l o w r a t e ,
a n d i t is d o u b t f u l w h e t h e r t h e e x p e r i m e n t w o u l d b e w o r t h w h i le .
T h e i n t e r p r e t a t i o n o f c r o s s i n g p h e n o m e n a ( p a r t i c u l a r l y o f t h e c r o s s o v e r
m e c h a n i s m ) o n a p o l y n u c l e o t i d e b a si s i s a p r o b l e m w h i c h h a s p u z z l e d m a n y
i n v e s t ig a t o r s . T h e s i m p le s o l u t io n o f t h e p r o b l e m p r e s e n t e d b e l o w m a y t h e r e -
f o r e h a v e p a r t i c u l a r b i o t h e o r e t i c i n t e r e s t .
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120 N.A. BARRICELLI
Bot h c om pl e x i t y a nd c r o s s i ng w ou l d r a p i d l y de ve lop in D N A - s ym bi o -
o r ga n i s m s i f t he phe nom e non , t e r m e d c om pl e m e n t a r y a s s oc ia t ion , w h i c h
i s desc r ibed be low, can be expec ted to t ake p lace dur ing the dupl i ca t ion of
a po lynuc leo t ide cha in . I t i s unknown whe the r complementa ry as soc ia t ion
w ou l d be pos s i b l e w he n DN dup l i c a t e s unde r t he a c t i on o f a n e nz ym e
l ike po lymerase . I t may be necessa ry to a s sume tha t the dupl i ca t ion process
i s t ak ing p lace under more pr imi t ive condi t ions pe rhaps s imi la r to those
exi s t ing be fore l i fe o rg ina ted (poss ib ly wi th a ca ta lys t o f non-b io log ic
or ig in) . The consecut ive s t eps in the dupl i ca t ion process a re a s sumed to be :
( I ) S e pa r a t i on o f t he t w o D N A - s t r a nd s . ( 2 ) A t t a c hm e n t o f s ing l e nuc l e o ti de s
t o e a ch s t r a nd i n t he p l ac e s w he r e t he y f i t w i t h t he c om pl e m e n t a r y nuc l eo t ide .
H ow ev er , un der th is co ndi t ion i t is conce ivable tha t n o t on ly s ing le
nuc leo t ides , bu t occas iona l ly a complementa ry s ing le s t randed polynuc leo t ide -
s e gm e n t m a y be inc o r po r a t e d i n t he doub l e s tr a nde d m o l e c u le w h i c h i s
f o r m e d ( hypo t he s i s o f c om pl e m e n t a r y a s s oc ia t ion ) . I f t he t w o s ing l e s tr a nde d
po l ynuc l e o t i de c ha i n s a r e c om pl e m e n t a r y on t y i n a bo r de r s e gm e n t ( ove r l a p )
shor te r than e i the r o f the tw o cha ins ( f ig . 9 B ) the resu l t can be a longer
doub l e s t r a nde d po l ynuc le o t ide ( f i g . 9C ) . T he p r oc e s s m a y , f o r e xa m pl e ,
s t a r t w i th a longi tud ina l a s soc ia t ion ( f ig . 9A) . Thi s condi t ion i s uns tab le
s ince on ly a low percentage of the nuc leo t ides fac ing one anothe r a re comple -
m e n t a r y bu t m a y e nd up i n a c om pl e m e n t a r y a s s oc ia t ion ( f ig . 9 B) w h i c h i s
s t ab le s ince a l l nuc leo t ides fac ing one anothe r a re complementa ry .
T h i s c om pl e m e n t a r y a s s oc ia t ion m e c ha n i sm p r ov i de s a pos s ib l e i n t e rp r e -
t a t ion of evolu t ionary growth and inc rease of complexi ty in po lynue leo t ides .
A fac t o f cons ide rab le in te res t i s , however , tha t i t a l so provides a p r imi t ive
( A ) A G A A C A A
A T A T C T T
B)
G
T
A A G A A C A A
A T A T C T T T
T
T
(C ) T A T A G A A C A A
A T A T C T T G T T
Fig. 9- A) Longitudinal association of two single stranded polynucleotides with a
complementary segment AGAA complementary to TCT T) . B) Complementary
association and insertion of single nucleotides. C) Formation of a double-stranded
polynocleotide longer than both original chains permitt ing evolutionary growth in
size and complexity).
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N U M E R I C A L T E S T I N G O F E V O L U T I O N T H E O R I E S
1 2 1
c r o s s i n g m e c h a n i s m f o r p o l y n u c l e o ti d e s . I n f a c t t h e t w o s i n g l e - s t ra n d e d
p o l y n u c l e o t i d e s i n f i g . 9 A a n d B c o u l d b e t h e r e s u l t o f i n c o m p l e t e d u p l i c a t i o n
( p a r t i a l r e p l i c a s ) o f l a r g e r p o l y n u c l e o t i d e s i d e n t i c a l o r h o m o l o g o u s t o t h e
d o u b l e - s t r a n d e d p o l y n u c l e o t i d e i n f i g . 9 C , S u c h i n c o m p l e t e r e p l ic a s o r p a r t i a l
r e p l i c a s c o u l d f o r i n s t a n c e b e t h e r e s u l t o f p o s s i b l e d a m a g e s o r t o o e a r l y
s e p a r a t i o n o f t h e t w o s t r a n d s a f t e r d u p l i c a ti o n ( s e p a r a t i o n b e f o r e a ll
n u c l e o t i d e s a r e f i l l e d i n ) . I n t h i s c a se , t h e p r o c e s s e s r e p r e s e n t e d i n f i g . 9
w i l l o n l y r e s t o re t h e o r i g i n a l s iz e o f t h e p o l y n u c l e o ti d e s a n d c a n b e c o n s i d e r e d
a r e p a i r i n g m e c h a n i s m ( li k e m u l t i p li c i ty r e a c t iv a t i o n in v i r u se s ) r a t h e r t h a n
a g r o w t h m e c h a n i s m . O n t h e o t h e r h a n d i f t h e t w o s i n g l e - s t r a n d e d p o l y -
n u c l e o t i d e s i n f i g . 9 A c o n t a i n e d g e n e t i c m a r k e r s ( a s a r e s u l t o f m u t a t i o n s o r
c o p y i n g m i s t a k e s ) , t h e d o u b l e - s t r a n d e d p o l y n u c l e o t i d e o f f ig . 9 C m a y b e
r e c o m b i n a n t ( c o n t a in i n g c o p y i n g m i st a k es i n h e r i t ed f r o m b o t h p a r e n t s ) .
E v i d e n t l y t h e p r o c e s s d e s c r ib e d i n f i g . 9 c a n o p e r a t e a s a c r o s s i n g m e c h a n i s m .
P a r t ia l r ep l ic a m o d e l s f o r v ir u s c ro s s in g a n d r e p r o d u c t io n ( D o E ~ N N ,
I 9 5 3 ; D O E R M N N
] ~ O E H N E R
1961; ] ~ A R R I C E L L I 1952 , 1955, 196o;
BARRICELLI DOERMANN, 1960 , 1961 ) m igh t be based on som e mec ha nism
o f t h i s o r s i m i l a r n a t u r e .
T h e a b o v e p i c t u r e o f a p o l y n u c l e o t i d e - c ro s s i n g m e c h a n i s m m a y o r m a y
n o t b e t h e a n s w e r o n e w o u l d f i n d b y DNzl norm s y m b i o g e n e s i s e x p e r i m e n t s .
B u t i t s h o w s a t l e a s t t h a t s o m e s i m p l e c r o s s i n g m e c h a n i s m s f o r
DNzt
m o l e c u l e s c a n b e c o n s t r u c t e d o n t h e b a s i s o f t h e DN/1 reproduction m o d e l
a n d m i g h t h a v e a p o s s i b i l i ty t o d e v e l o p i f a
DNH symbiogenesis
e x p e r i m e n t
w e r e a t t e m p t e d .
I I . C H E M O - A N A L O G I C A L A N D D I G I T A L C O M P U T E R S
A q u e s t i o n o n e m a y a s k is : W h y u s e a c o m p u t e r , r a t h e r t h a n a c h e m i c al
m e t h o d t o p e r f o r m a n e v o l u t i o n e x p e r i m e n t b a s e d o n t h e
DNA norm
? T h e
a n s w e r i s: O n e m e t h o d d o e s n o t e x c l u d e th e o t h e r a n d t h e d i s t in c t i o n b e t w e e n
t h e t w o m e t h o d s m a y n o t b e a s f u n d a m e n t a l a s o n e w o u l d b e i n c li n e d t o
b e l i e v e . As a m a t t e r o f f a c t , i f
DNd norm
e x p e r i m e n t s s h o u l d b e c o m e a
f r e q u e n t p r o c e d u r e , t h e q u e s t io n w o u l d a r i s e w h e t h e r i t w o u l d b e p o s si b le
a n d c o n v e n i e n t t o c o n s t r u c t a n a n a l o g ic a l c o m p u t e r e s p ec i al ly d e s i g n e d f o r
t h i s t y p e o f e x p e r i m e n t s . S u c h a c o m p u t e r c o u l d e s s e n t i a l ly co n s i s t o f a n
a u t o m a t i c , p r o g r a m m e d c h e m i c a l l a b o r a t o r y w i t h r e a d - i n a n d r e a d - o u t
d e v ic e s a n d o t h e r g a d g e t s t o p e r f o r m t h e f o l l o w i n g o p e r a ti o n s : I n t e r p r e t a n d
t r a n s f o r m i n f o r m a t i o n c o n t a i n e d i n I B M c a r d s o r m a g n e t i c t a p e i n t o a
s p e c i fi c a r r a n g m e n t o f n u c le o t id e s a n d o t h e r m o l e cu l es . P e r f o r m t h e c h e m i c a l
o p e r a t i o n s s p e c i fi e d b y th e p r o g r a m ( a ls o c o n t a i n e d i n I B M c a r d s o r m a g n e t i c
t a p e ) . P u n c h o r r e a d o u t t h e re s u l ts i n t o I B M c a r d s o r m a g n e t i c t a pe .
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I22 N . A . B A R R IC E L L I
T h i s c h e m o - a n a l o g i c a l c o m p u t e r w o u l d p r o b a b l y d o n o t h i n g w h i c h
c o u l d n o t b e d o n e b y a c o r r e c t l y p r o g r a m m e d d i g it a l c o m p u t e r , i f s u f f i c i e n t
i n f o r m a t i o n w e r e a v a il a b le t o w r i t e a c o r r e c t p r o g r a m . H o w e v e r , i ts v a l u e a t
l ea s t a s a c h e ck f o r c o r r e c t p r o g r a m m i n g a n d a c h e c k f o r t h e t h eo r ie s u s e d
i s e v i d e n t .
A f a c t w h i c h e m e r g e s f r o m t h i s t y p e o f c o n s , i d e r a t i o n i s t h a t t h e d i s t i n c t i o n
b e t w e e n a n e v ol u ti o n e x p e r i m e n t p e r f o r m e d b y n u m b e r s i n a c o m p u t e r o r
b y n u c l e o t i d e s i n a c h e m i c a l la b o r a t o r y i s a r a t h e r s u b t l e o n e . A s a m a t t e r
o f f a c t , i t is c o n c e i v a b l e t h a t th e u s e o f a d i g it a l c o m p u t e r a n d a c h e m o -
a i~ a lo g ic a l c o m p u t e r c o u l d b e a lt e r n a t e d i n t h e s a m e e v o l u t io n e x p e r i m e n t
d e p e n d i n g o n w h i c h c o m p u t e r is a v a il a b le a t a n y p a r t i c u l a r m o m e n t .
T h e s e c o n s i d e r a t i o n s w i l l m a k e i t c l e ar f o r t h e r e a d e r t h a t t h e f u n d a m e n t a l
d i f f e r e n c e b e t w e e n v a r i o u s t y p e s o f s y m b i o o r g a n i s m s i s t h e d i f f e r e n c e i n
t he n o r m s u s ed . T h e q u e s t i o n w h e t h e r o n e t y p e o f s y m b i o o r g a n i s m is
d e v e l o p e d in t h e m e m o r y o f a d i gi ta l c o m p u t e r w h i le a n o t h e r t y p e i s d e v e l o p e d
i n a c h e m i c a l l a b o r a t o r y o r b y a n a t u r a l p r o c e s s o n s o m e p l a n e t o r s a te l li te
does no t add a ny th in 9 fun da me nta l to th i s d i f f e rence .
i 2 . S Y M B I O G E N E S I S A N D T E R R E S T R I A L L 1 F E
I t is d o u b t f u l w h e t h e r a s y m b i o g e n e t i c e v o l u t io n e x p e r i m e n t b a s e d o n
D N A - n o r m c o u l d b e c a r r i e d f a r e n o u g h t o s e e p o l y n u c l e o t i d e s d e v e l o p t h e
a b i l it y t o a c t o n p r o t e i n s . A s a m a t t e r o f f a c t, t h e r e i s n o a s s u r a n c e t h a t t h e
c o n t ro l o f p r o te i n f o r m a t i o n w o u l d b e a m o n g t h e i n v e n t io n s o f th e s y m b i o -
o r g a n i s m s d e v e l o p e d d u r i n g a n e v o l u t i o n e x p e r i m e n t b a s e d o n D N A - n o r m
n o m a t t e r h o w f a r th e e x p e r i m e n t w e r e c a r ri e d o n . P r o b a M y , i n o r d e r t o
s u r v i v e , t h e
D N A - s y m b i o o r g a n i s m s
w o u l d h a v e t o d ev e lo p s o m e m e a n s o f
c o n t r o l l in g t h e i r c h e m i c a l e n v i r o n m e n t . B u t w h e t h e r t h i s w o u l d h a v e t o b e
d o n e b y e n z y m e s o r w h e t h e r s o m e o t h e r c a t a ly s ts m i g h t b e u s ed a n d p o s s ib l y
d e v e l o p e d i n t o c h e m i c a l i n s t r u m e n t s o f c o m p a r a b l e p o w e r , i s st il l a n o p e n
q u e s t i o n a ) .
3) The problem of programming a norm permit t ing act ion of polynucleot ides ol l
protein : format ion (or any ot h er act ion by a symbioorganism) is in several respects
similar t o the problem, al ready handled in this paper, to pro gram a noi 'm p erm it ting
symbioorganisms to act in the determinat ion of the moves in a game. T her e i s how ever
the fol lowing fundame ntal di ffere nce ; the rules for gam e-act ion we re chosen arbi t rarily
and the symbioorganisms were pu rposeful ly giv en a large num ber of w ays in which
they could ac t on the game pa t t e rn or mo di fy the i r game s t ra t egy . O n the cont rary ,
a p rog ram m ed
DNA-norm
if i t shall have anything, to do with.
D N A
must he a t rue
copy of the reactions Occurring in a particular chemical environment realizable, in a
hypothetical experiment. W e can not choose arbi t rari ly the wa ys in w hich polynucleotides,
wou ld ac t o n pr ote in synt l- /eSis. 'The possibi li ties of interfer ing wi~h the phenomena
would ha ve to be restricted to th e possibil it ies w hi ch would ex ist in a tru e chem i'cal
experiment.
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NUMERIC L TESTING OF EVOLUTION THEORIES
123
W ha t e l s e a n e vo l u t i on p r oc e s s ba s e d on D N A - nor m w ou l d s how , be s i de s
the usua l b iophenomena a l ready quoted , i s ha rd to pred ic t . However , i t i s
obv i ous t ha t a s uc c e s s fu l e xpe r i m e n t m i gh t g i ve re s u lt s o f f und a m e n t a l
theoret ic interes t .
T he num e r i c e vo l u t i on e xpe r i m e n t s w h i c h ha ve be e n p r e s e n t e d do no t
g i ve i n f o r m a t i on a bou t t he o r i g i n a nd h i s t o r y o f t e r r e s tr i a l l if e . N e ve r t he l e s s, '
a f e w f unda m e n t a l no t i ons ha ve be e n e s t a b li s hed w h i c h m a y g i ve s om e
leads on the na ture of the processes involved .
T h e v e r y fa c t t h at t h e D N A - n o r m is a s y m b i o n o r m ( se c ti o n 9 ) w i t h
charac te r i s t i c s sugges t ing a s imple so lu t ion of the hybr id iza t ion (c ross ing)
p r ob l e m , s t r ong l y s uppo r t s t he i de a t ha t t he s ym bi oge ne s i s o f t e r r e s t r i a l
l i fe form s m ay have s t a r t ed by an as soc ia t ion of nuc leo t ides in to po ly-
nuc leo t ide cha ins . The on ly na tura l envi ronment in which po lynuc leo t ides
(v i ruses or ce l lu la r gene t i c ma te r i a l ) reproduce nowadays i s the in te r ior ,
p r imar i ly the nuc leus , o f l iv ing ce l l s . In v iew of the conse rva t ive na ture of
b ia log ic sys tems
c f .
chemica l s imi la r i t i e s be tween b lood and sea wa te r ) i t
i s t empt ing to a s sume tha t the envi ronmment in which t e r res t i a l symbiogenes i s
occur red may have presen ted cons ide rab le chemica l s imi la r i t i e s to the nuc le i
of l iving cel ls (p roto plasm ic env iron m en t) (c / . RAPOPORT & RAI?OPORT,
1958 ) . Th e chemica l s imi la r i ti e s be tw een nuc le i o f m any d i f fe r en t Ce ll s
suppor t th i s no t ion . The poss ib i l i ty for syn thes i s o f s evera l complex organic
compounds in the absence of l iv ing organi sms has a l ready been es tab l i shed
(U 'REY & M ILLER , I959; F o x , 196o ) .
O ne o f t he f i r s t s t e p s i n t he e vo l u t i ona r y p r oc e s s l e a d i ng t ow a r d t he
f o r m a t i on o f c e l l s , m a y ha ve be e n a m e m br a ne ( p r o t o t ype o f t he p r e s e n t
nuc l e a r m e m br a ne s ) . T he f unc t i on o f t h i s m e m br a ne m a y ha ve be e n t o
p r o t e c t a s m a l l f r a c t i on ( p r o t onuc l e us ) o f t he m e d i um i n w h i c h a nuc l e i c
a c i d s t r uc t u r e pe r f o r m e d i t s a c t i v i t y , f r om c he m i c a l c ha nge s p r oduc e d by
e x t e r na l c ond i ti ons o r o t he r nuc l e ic a c id s ( c om pe t i t o r s a nd ] o r p a r a s i t e s ) . A t
t h e s a m e t im e t h e m e m b r a n e w o u l d p r e v e n t t h e d i sp e r si o n o f e n z y m e s
a nd o t he r c a t a ly s t s p r odu c e d i n t he p r o t onuc l e us . T he m e m br a ne m a y
or ig i na l y ha ve be e n f o r m e d a nd d i s so l ve d a c c o rd i ng t o ne c e s s i ty a t va r i