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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    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

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    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

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    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