148
Session No. 4 Associative and Adaptive Models
THE EVOLUTIONARY PROCESS OF RANDOMLY
t i o n (genotype)
GROWING MUTATED DIGITAL STRUCTURES AS
phenotype i n d e t a i l ,
A MODEL OF EVOLUTION OP
L I V I N G OHGANISMS
FIRST
:)
type.
F u l l I n f o r m a t i o n t o guarantee
s t a b i l i t y is
cyclic
Fialkowski
U n i v e r s i t y o f Warsaw,Poland
achievable from the
environment.
In real l i f e ,
Technical
but only gives
" f r a m e " i n f o r m a t i o n about the phenothe
Konrad R.
does n o t d e t e r m i n e t h e
sufficient
however,
it
i s not
t o achieve s t a b i l i t y .
Sta-
b i l i t y must b e m a i n t a i n e d i n t h e p r e s ence o f t h e m u t a t i o n s . Under t h e s e c o n -
A b s t r a c t
The p a p e r p r e s e n t s
the r e s u l t s of
research concerning the s t a b i l i t y of
an
e v o l u t i o n a r y process f o r randomly
growing d i g i t a l structures.
p u t e r model f o r
the mutated genotype
case is considered.
t h e models
changes
The com-
The g e n o t y p e ( i n
the s e t of r u l e s f o r growth)
in a random e n v i r o n m e n t a l l y
u n o r i e n t e d way, whereas t h e e n v i r o n m e n t assumed a s r a n d o m , f i n i t e a n d
r e p e t i t i v e i n a c y c l i c way i s
bed.
Prom t h e e x p e r i m e n t s i t f o l l o w s
that s t a b i l i t y could be
a
distur-
achieved in
h e u r i s t i c way a f t e r m u t a t i o n o f t h e
genotype and d i s t u r b a n c e s i n t h e e n vironment without
mation
the b u i l t -
in
infor-
t h e o r g a n Isms must s u r v i v e a n d
divide.
The c h a i n o f s u r v i v a l s a n d d i -
visions gives
organism i s
r e s u l t s obtained from
these r e s u l t s are presented.
T h i s sequence c o u l d i n each g e n e r a t i o n
b e ended b y t h e u n s u c c e s s f u l g r o w t h
and d e a t h o f t h e c u r r e n t e l e m e n t o f
sequence.
F o r t h e case w i t h o u t spontaneous mu
tations
i t was
shown i n a p r e v i o u s p a -
per (1)
t h a t w i t h the assumption o f
random environment changing in a c y digital structures,which
c o u l d be a model of v e r y s i m p l e o r g a n isms can grow, d i v i d e and achieve a
(phenotype)
That case i s c a l l e d t h e " d e -
generation*1 of the sequence.
Sometimes
however t h e e v o l u t i o n a r y sequence and
t h e e n v i r o n m e n t a r e i n dynamic b a l a n c e ,
a n d t h e n d e g e n e r a t i o n does n o t h a p p e n .
The b a l a n c e
( i f it exists)
could be
broken by:
1. disturbance of
(the
the
environment
case d i s c u s s e d i n ( 1 ) )
t y p e ( t h e case d i s c u s s e d i n t h i s p a per).
The s e c o n d c a s e i s i m p o r t a n t ,
ment,
"shape"
consideration).
as
t h e c h a n g a b l e g e n o t y p e means d e v e l o p -
Introduction
the
taken i n t o
2 . m u t a t i o n , w h i c h changes t h e g e n o -
t h e computer and a n i n t e r p r e t a t i o n o f
c l i c way,
the evolutionary se-
quence ( i n e a c h g e n e r a t i o n o n l y one
concerning s t a b i l i t y .
The m o d e l ,
stabile
ditions
in spite
o f the f a c t t h a t the b u i l t - i n informsx ) These computer e x p e r i m e n t s were s u p p o r t e d by a grant from the f o r d Found.
increase of complexity,
lutionary
and e v o -
progress.
M o d e l
1.
Phenotype g r o w t h and d i v i s i o n .
The p h e n o t y p e i s c a l l e d i n t h e mo-
del a D i g i t a l Structures
Definition
DI6TRUC.(1).
1.
A D i g i t a l Structure,DISTRUC,
sequence o f p o s i t i v e ,
(ci)
,
is a
i n t e g e r numbers
i»1,2,...,I
Session No. 4 Associative and Adaptive Models
The numer I i s
149
c a l l e d the l e n g t h of
DISTRUC.
Definition
2.
The sequence o f DISTRUCs c r e a t e d
in
t h e r e c u r s i v e g r o w t h and d i v i s i o n
process is c a l l e d an Evolutionary
Sequence: SB.
E a c h DISTRUC i n £ 8 has i t s g e n e r a t i o n number g , u s e d a s a n i n d e x . The
I n i t i a l Basic S t r u c t u r e ,
g=o.
IBSTRUCs
IBSTRUC has
a r e a l w a y s t h e same
f o r a l l ES (as the r e s u l t of an ass u m p t i o n c o n c e r n i n g t h e common o r i g i n
of
life).
Definition
3.
The g r o w t h p r o c e s s i s
the process
o f n o n - d e c r e a s i n g change o f
ci
val-
u e s p e r f o r m e d i n t h e d i s c r e t e moments
of
time
t,
t = 0 , 1 , . . . , T (measured i n
d i s c r e t e time u n i t s :
DUT),
according
to the following equation:
1
w h e r e : R is a random n u m b e r , a n d F has
v a l u e 1 or 0 according to the s e t of
r u l e s o f g r o w t h shown f u r t h e r .
For a l l g,
for
t=o.
the growth process s t a r t s
F o r t = 0 DISTRUC i s c a l l e d
Basic S t r u c t u r e :
BASTRUC f o r g = 0 .
BASTRUC.
IBSTRUC i s
IBSTRUC i s d e n o t e d
150
Session No. 4 Associative and Adaptive Models
The g r o w t h c o u l d be f i n i s h e d in a
one o f two w a y s :
1. If
t h e g r o w i n g DISTRUC
the rules of growth,
satisfies
the growth is
s u c c e s s f u l l y f i n i s h e d a f t e r T DUTs.
T h e n DISTRUC i s c a l l e d t h e Grown s t r u c ture:
of
GSTRUC.
T is c a l l e d the l i f e time
DISTRUC.
2.
If
t h e g r o w i n g DISTRUC does n o t
s a t i s f y the rules of growth,
TRUC " d i e s " a f t e r T d DUT.
Definition
the DIS-
S t a b i l i t y T r e s h o l d : S T i s a sequence
This is c a l -
l e d " d e g e n e r a t i o n " and Td - t h e degeneration
time.
I n c a s e 1 . GSTRUC d i v i d e s
into
two
paper
taken i n t o
The d i v i s i o n i s p e r -
f o r m e d i n t h e f o l l o w i n g way:
r e a l ( i n t h e ALGOL s e n s e )
numbers:
For a l l
t h e f u r t h e r g r o w t h p r o c e s s and i t s h i s t o r y recorded)•
of p o s i t i v e ,
(Ai)
BASTRUCs o f t h e n e x t g e n e r a t i o n ( b u t
o n l y one o f t h e s e t w o i s
5.
Ai
i= 1,2,...,1,1+1
experiments presented i n
(Ai)
has c o n s t a n t v a l u e s :
=
0.8
A10=
3.0
for i= 1,2,...,9
The L e n g t h o f S t r u c t u r e :
f i n e d b e f o r e . F o r IBSTRUC,
The v a l u e o f D i s
for i =
1,2,3f..., I ,
where E is
the
the integral part of
the number).
med u p
2.
on
the
fig.1.
the S t a b i l i t y T r e s h o l d : ST
I
the I n t e r v a l of Regular Growth:
positive,
D
4.
BG is a sequence of
r e a l ( i n t h e ALGOL s e n s e )
numbers:
(Gi)
,
i=1,2,...,I,I+1
E a c h BASTRUC of g ' s g e n e r a t i o n has BG
determined as:
growth process:
V and F ( s e e e q . 1 )•
are d e t e r -
m i n e d f o r each t i n t h e f o l l o w i n g way:
t h e B a s i c G e n o t y p e : BG
B a s i c Genotype:
two i n d i c a t o r s o f t h e
The v a l u e s o f i n d i c a t o r s
The g e n o t y p e c o n t a i n s :
Definition
t h i s paper,
B o t h o f them h a v e v a l u e 0 o r 1 .
G e n o t y p e and t h e r u l e s o f g r o w t h
t h e L e n g t h of DISTRUC :
1 = 3.
D = 0.5
There are
The above g i v e n d e f i n i t i o n s a r e sum-
I was d e -
constant f o r a l l
experiments presented in
E n t i e r f u n c t i o n ( f o r p o s i t i v e numbers,
this
Session No. 4 Associative and Adaptive Models
151
l o w i n g f r o m t h e new v a l u e o f BG.
This
change i s p e r f o r m e d b y a d d i n g t o one
r a n d o m l y choosen G i v a l u e t h e random
number f r o m t h e random g e n e r a t o r . These
random numbers
are e q u a l l y d i s t r i b u t e d
from the range:
-1.0,
1.0.
Sometimes t h e r a n d o m l y c h o o s e n
G i ( e . g . G 8 f o r 1=5)
does n o t e x i s t i n
t h e g i v e n g e n o t y p e . Then t h e m u t a t i o n
does n o t o c c u r .
MS can occur d u r i n g each d i v i s i o n
(see f i g . 1 ) .
F o r each t, as l o n g as V = 1 ,
is
zero
t v a l u e V becomes
(V = 0)
s t o p p e d , and
and o n l y i f :
1
d e t e r m i n e d as f o l l o w s :
If f o r c e r t a i n
to
if,
t h e growth
process is continued according to eq.
Then F
I t occurs
equal
the growth process is
it
is
the " d e g e n e r a t i o n "
case.
3.
Mutations
I n t h e p r e s e n t e d m o d e l t h e r e a r e two
kinds
of mutations:
1 . BG's m u t a t i o n s : MG,which change
the
value of (Gi)
2 . E x p a n d i n g m u t a t i o n s : MB, w h i c h
change
the value
I.
B o t h o f them a c c o r d i n g t o t h e g e n e ral
t h e o r y o f e v o l u t i o n are n e i t h e r
environmentaly,
o r DISTRUCtly o r i e n t e d .
M G o c c u r s once f o r t h e d e t e r m i n e d
period of
time i n g i v e n experiment ( e . g .
o n c e f o r 1 5 000
DUTs).
I t changes one
r a n d o m l y choosen v a l u e o f ( G i )
the growth process,
during
and t h e p r o c e s s i s
continued according t o the r u l e s f o l -
The b a s i c a s s u m p t i o n s c o n c e r n i n g
t h e environment were g i v e n i n ( 1 ) .
In
a l l e x p e r i m e n t s t h e e n v i r o n m e n t has
b e e n s i m u l a t e d a s a sequence o f 500 r a n dom numbers t a k e n f r o m t h e random
number t a b l e u s e d i n t h e r e p e t i t i v e ,
c y c l i c way.
The d i s t u r b a n c e s o f t h e
e n v i r o n m e n t were s i m u l a t e d a s s k i p s o f
s e v e r a l ( u s u a l y o n e ) numbers i n t h e
sequence.
In the model,
ment,
f o r the given e x p e r i -
t h e d i s t u r b a n c e o c c u r s once f o r
the determined p e r i o d of time,
on the
Session No. 4 Associative and Adaptive Models
152
same b a s i s as MGrs.
Exeriments
By analogy,
is equivalent of 1 second,
and R e s u l t s
The e x p e r i m e n t s p r e s e n t e d h e r e w e r e
the continuation of the research, which
has been s t a r t e d f r o m s o c a l l e d " v e r s i o n
zero" presented i n ( 1 ) .
In contradistinction
zero"
to
the
"version
a l l f u r t h e r v e r s i o n s were w r i t t e n
i n FORTRAN I V f o r IBM 3 6 0 / 5 0 .
1 . " f i r s t v e r s i o n " was
the m o d i f i c a -
t i o n o f " v e r s i o n z e r o " f o r IBM 3 6 0 w i t h
the
extension of possible length of
DISTRUC to
I=
23.
duction to " f i r s t v e r s i o n " of the timing
automatic p e r t u r b a t i o n of
the
environment •
which is
a s a t i s f a c t o r y approximation
f o r v e r y simple organisms.
I n t h i s scale
t h e s i n g l e experiment l a s t s app.
6 days
and a l l experiments are e q u i v a l e n t t o
o v e r one y e a r o f c o n s t a n t o b s e r v a t i o n .
The r e s u l t s a r e p r e s e n t e d o n t h e
three hierarchical
1 . Leve
levels:
one ( t h e l o w e s t )
The l e v e l one ( p r e s e n t e d o n f i g . 2 )
a n example o f d i r e c t g r a p h i c r e c o r d
of an experiment.
The e v o l u t i o n a r y s e -
quence p r e s e n t e d o n f i g . 2 d e v e l o p s
the
s t a b i l e environment ( w i t h o u t
disturbances)
the i n t r o d u c -
the "second v e r s i o n " of the
mutations
then the l i f e
in
the
and under t h e i n f l u e n c e
o f b o t h t y p e s o f m u t a t i o n s (MG a n d M S ) .
3 . " t h i r d v e r s i o n " was
t i o n to
t h a t 1DUT
t i m e o f a v e r a g e DISTRUC i s 1 0 m i n u t e s ,
is
2 . " s e c o n d v e r s i o n " was t h e i n t r o and the
i f one assumes
The g e n e r a t i o n number g i s o n t h e
a b s c i s s a ( g = 0 i n d i c a t e s IBSTRUC).
subroutines.
The
arrows under the abscissa i n d i c a t e MG
4 . " f o u r t h v e r s i o n " was t h e i n t r o -
m u t a t i o n s . For the experiment the d i s -
d u c t i o n t o the " t h i r d v e r s i o n " o f l i m i -
t a n c e b e t w e e n two s u c c e s s i v e MG m u t a -
tations for
t i o n s is
the
expansion o f s t r u c t u r e s
( t h e way o f s a v i n g
CPU t i m e )
matic modification of
and a u t o -
the s t a b i l i t y
104
DUT.
The p h e n o t y p e i s
presented as a d o t t e d set of values f o r
given g value.
( A l w a y s BASTRUC c i , o ( g )
t h r e s h o l d ( n o t used i n experiments p r e -
is presented on the diagrams.
sented here).
e x p e r i m e n t s max 1 = 9). The s m o o t h l i n e
For experiments presented here o n l y
is
T(g),
(the l i f e
time).
For these
The p h e n o t y p e
v a l u e s and t h e l i f e t i m e v a l u e s a r e
t h e " f o u r t h v e r s i o n " was u s e d . The
" f o u r t h v e r s i o n " h a d two p r o g r a m r e a l i z a t i o n s : F o u r t h A and F o u r t h B. U s u a l y
F o r t h A was u s e d a s a n e x p e r i m e n t a l
g r o u p , w h e r e a s F o u r t h B was a c o n t r o l
p r e s e n t e d o n t h e same s c a l e . The P ( g )
(expanding c o e f f i c i e n t ,
of
the
diagram)
the upper p a r t
is presented in another
s c a l e and t h e s t a b i l i t y t r e e h o l d (dashed,
constant value l i n e )
is
drawn t h e r e . T h e
g r o u p ( i n t h e same way a s i n t h e b i o l o -
presented diagram is a p a r t of the
g i c a l experiments) •
p e r i m e n t named:
The e s t i m a t e d number
of observed generations
is 50 000 .
The
a v e r a g e l i f e t i m e f o r one g e n e r a t i o n i s
a p p . 6 0 0 DUTs. The s i n g l e e x p e r i m e n t
l a s t s 0 . 5 x 1 0 6 o r 1 0 6 DUTs.
d e t a i l e d data of
level
ex-
1106 F o u r t h B ( f o r t h e
this
e x p e r i m e n t see
two).
S t a r t i n g f r o m IBSTRUC,
g l e expansion (MSs
a f t e r the s i n -
effect)
a nonperi-
153
Session No. 4 Associative and Adaptive Models
o d i c sequence e x i s t s
r a t i o n.
t i l l the 8 t h gene-
I n t h e 9 t h and 1 0 t h t h e r e are
t h e same, b u t t h e y h a v e d i f f e r e n t l i f e
t i m e s . The M G m u t a t i o n o c c u r s a t t h e
two M E s ( t h e e f f e c t s a r e v i s i b l e i n t h e
end o f l i f e o f t h e 2 9 t h g e n e r a t i o n .
v e r y n e x t g e n e r a t i o n a n d marked " x " o n
According
the diagram).
G5 value of BG from 2,00 to 1.76.
to
6.
The I v a l u e becomes e q u a l
The n e x t two MEs o c c u r i n 1 3 t h
to
t h e r e c o r d i t changes
the
It
does n o t i n f l u e n c e BASTRUC o f t h e 3 0 t h
a n d 1 4 t h g e n e r a t i o n s a n d one i n 1 6 t h •
g e n e r a t i o n ( w h i c h has b e e n a l r e a d y d e -
A f t e r t h a t I is equal
t e r m i n e d b y GSTRUC n e a r l y c o m p l e t e l y
to 9.
From t h e
1 8 t h g e n e r a t i o n the p e r i o d i c sequence,
f o r m e d a t t h e t i m e o f MG), b u t i n f l u -
described in (1)
ences t h e g r o w t h o f DISTRUC i n 3 0 t h
starts,
with a period
equal
t o 1 0 ( s e e p e r i o d i c changes o f
g e n e r a t i o n . A s o n l y BASTRUCs a r e r e -
T(18)
to T ( 2 9 ) ) .
corded the e f f e c t o f M G are v i s i b l e i n
All
the phenotypes are
154
Session No 4 Associative and Adaptive Models
t h e BASTRUC o f 3 1 s t g e n e r a t i o n .
most probable phenotype
smaller,
is
The new,
statisticaly
CPU t i m e ) •
The p a r t o f t h i s e x p e r i m e n t
was p r e s e n t e d a s f i g . 2 f o r l e v e l o n e .
than the previous one, b u t is
O n f i g . 3 t h e numbers o f MG's
muta-
n o t e x a c t l y d e t e r m i n e d a n d one c a n see
t i o n s a r e o n t h e a b s c i s s a . The number
o t h e r values
o f g e n e r a t i o n s o b s e r v e d b e t w e e n two
"shapes")
of
the phenotype ( o t h e r
in 33rd,
rations (the last
4 3 r d and 4 9 t h g e n e two a r e l a r g e r
t h e p h e n o t y p e s b e f o r e MG6).
quence
than
The s e -
successive mutations are on the o r d i nate.
The e x p a n d i n g s e q u e n c e ( t h e e f -
f e c t o f MEs
is nonperiodic.
mutations),
the p e r i o d i c
a n d t h e n o n p e r i o d i c sequences a r e d i s -
MG7 does n o t change a n y t h i n g .
changes G9 v a l u e f r o m 2 . 0 0 to
It
1.99
tinguished.
and
In the experiments,
d i a t e l y a f t e r the
imme-
d e g e n e r a t i o n o f one
t h a t has n o v i s i b l e i n f l u e n c e o n t h e
s e q u e n c e a new s e q u e n c e s t a r t s f r o m t h e
growth process.
IBSTRUC w h a t i s m a r k e d o n t h e d i a g r a m s
MG8 changes ( a c c i d e n t a l l y t h e same
a s MG6)
This
by " _ " .
The t i m e b e t w e e n t h e two s u c m u t a t i o n s i s 1 0 4 DUTs ( t h e
t h e G5 v a l u e f r o m 1.76 to 1 . 6 1 .
ces
causes a f u r t h e r s t a t i s t i c a l
a b s c i s s a i s s c a l e d w i t h MGs o r w i t h t h e
decrease of phenotype v a l u e s ,
exceptions in the 7 0 t h ,
w i t h some
MG's
1 0 4 DUTs).
7 1 s t and 72nd
The sequence o f MGs
mutations in
g e n e r a t i o n . From t h e 6 9 t h g e n e r a t i o n
t h e b o t h cases ( p a r t A a n d B )
a p e r i o d i c sequence s t a r t s w i t h t h e
a c t l y t h e same,
p e r i o d e q u a l t o 1 0 . T h i s dynamic b a l a n c e
conditions.
is
occurs
broken in the
8 4 t h g e n e r a t i o n b y MG9.
of
it
t i o n occurs
1.21.
the G7 value from 2.00 to
The DISTRUC o f 6 4 t h g e n e r a t i o n
does n o t f i n i s h i t s g r o w t h .
generates
the sequence.
From t h e r e c o r d o f
follows
The MG9 d e -
the
experiment it
t h a t t h e DISTRUC o f t h e 8 4 t h
"shape"
pansions,
From ( 1 )
it follows
sequence,
two h i s t o g r a m s ,
the
which
two d i f f e r e n t
6
0 . 5 x 1 0 D U T / 4 2 m i n . 3 7 s e c . o f IBM 3 6 0 / 5 0 )
CPU t i m e ) .
B) lower p a r t (1106 F o u r t h B, l a s t e d
D U T s / 3 7 m i n . 4 6 s e c o f I B M 360/50
not
that a nonperi-
a f t e r s u f f i c i e n t l y long
can e a t h e r a c h i e v e p e r i o d i c i t y
or degenerate.
A) upper p a r t (1006 F o u r t h B, l a s t e d
0.5x10
the p e r i o d i c and n o n p e r i o d i c
sequences d e s c r i b e d b e f o r e o n l e v e l
time,
experiments:
6
alone.
MG5 a n d MG9 was p r e s e n t e d in a n o t h e r
odic
Level two.
the records of
I n case B t h e m u t a -
one.
w i t h c 1 0 = 171 a f t e r 299 DUTs.
are
the environment.
The f r a g m e n t o f B r e c o r d b e t w e e n t h e
( c i ) = ( 2 , 4 , 9 , 19, 3 1 , 63,127,255,407)
Fig.3 presents
But i n case A t h e m u t a t i o n
f o r m o n f i g . 2 . One c a n n o t i c e t h e e x -
g e n e r a t i o n " d i e s " w i t h the
2.
as w e l l as the o t h e r
together w i t h the disturbance
According to the experimental r e c o r d s ,
changes
is ex-
P e r i o d i c sequences a r e
interesting for
the
n o t h i n g c o u l d happen
experiments, as
there
till
the
nearest mutation or disturbance of env i r o n m e n t . On the o t h e r s i d e , under
severe
c o n d i t i o n s a n o n p e r i o d i c sequence
lasts f o r a very short
time.
The c o n d i -
t i o n s f o r the presented experiments
were n o t too severe (see the l o n g n o n p e r i o d i c sequence a t p a r t A ,
fig. 3),
Session No. 4 Associative and Adaptive Models
155
Session No. 4 Associative and Adaptive Models
156
a n d t h e f r e q u e n c e o f MGs
repetition
Z:
2705 F o u r t h B, l a s t e d
can n o t i c e
One
P:
2905 F o u r t h B ,
t h a t the degenerations are
more f r e q u e n t i n c a s e B .
To determine
the p r o b a b i l i t y of degeneration,
generation coefficient
DUTs
( 1 h o u r , 1 2 m i n . 5 8 s . o f GPU t i m e )
was c h o s e n h i g h enough f o r a p e r i o d i c
sequence n o t to be t o o p r o b a b l e .
10 6
l a s t e d 0 . 5 x 1 0 6 DUTs
( 4 0 m i n . 2 7 s . o f CPU t i m e )
Q:
5005 F o u r t h A ,
the de-
l a s t e d 0 . 5 x 1 0 6 DUTs
( 5 8 m i n . 2 5 s . o f CPU t i m e )
d w i l l be i n t r o
duced.
For the g i v e n experiment and the
given p e r i o d of time
the d value is
c o u n t e d b y d i v i d i n g t h e number o f n o n s p o n t a n e o u s d e g e n e r a t i o n s b y t h e number
o f MGs
m u t a t i o n s . F o r t h e A and B case
the d values are ;
dA = 5 / 5 0 = 0 . 1
,
dB=10/50
= 0.2
( i n e a c h case one s p o n t a n e o u s d e g e n e r a t i o n was o b s e r v e d , f o r A b e t w e e n M C 4 8
a n d MG49, a n d f o r B b e t w e e n MG9 a n d
MG10).
The e x p e r i m e n t s p r e s e n t e d o n f i g . 3
are rather t y p i c a l .
records e.g.
There a r e o t h e r
306 F o u r t h A w i t h t h e p a r a -
m e t e r s o f t h e p r o c e s s t h e same a s f o r
1006 F o u r t h B ,
where d = 0 . 0 7 4 .
From t h e c o m p u t e r e x p e r i m e n t s p r e s e n t e d here and c o n s i d e r e d i t f o l l o w s
that
for
the p r o b a b i l i t y o f
e v o l u t i o n a r y sequences
when
the mutations
the disturbance
3.
degeneration
of
occur
increases
w i t h o u t
the environment.
Fig.4.
Level three.
Distribution of lethal
i n f i v e experiments.
cases
O n t h e f i g . 4 t h e d e g e n e r a t i o n cases
for
the f i v e
d i f f e r e n t experiments
are
p r e s e n t e d . The e x p e r i m e n t s named t X, Y,
For a l l these experiments
the
time
Z , P and Q have t h e f o l l o w i n g c h a r a c t e r -
p e r i o d b e t w e e n t h e t w o s u c c e s s i v e MG's
istic:
mutations,
x: 2805 F o u r t h A
,
lasted 106
DUTs
( 1 h o u r , 1 1 m i n . 4 5 s . o f CPU time)
Y : 2905 F o u r t h B ' ,
lasted 106
DUTs
( 1 h o u r , 1 4 m i n . 5 6 s . o f CPU t i m e )
o r two s u c c e s s i v e d i s t u r b a n c e s
o f t h e e n v i r o n m e n t was
1.5x104
DUTs •
From t h e d e t a i l e d r e c o r d s o f t h e e x periments
1.
it
follows
that:
I f the mutation i s l e t h a l f o r se-
quence i t
is
usualy l e t h a l
in
the very
Session No. 4 Associative and Adaptive Models
157
n e x t g e n e r a t i o n ( s e e marks w i t h o u t d e lay on f i g . 4 )
2.
ment
lethal for
usualy lethal
(see
the e n v i r o n
t h e sequence
it
is
a f t e r several generations
creases w i t h the
shift.
that
it follows
that
the phase
i n c r e a s e o f the phase
The p r o b a b i l i t y o f t h e d e g e n e r a -
t i o n is highest f o r
the
fig.4).
From t h a t
it follows
the p r o b a b i l i t y o f degeneration i n -
If the disturbance of
is
From t h e above t a b l e
the disturbance of
environment being d i r e c t l y preceded
by the m u t a t i o n (Q e x p e r i m e n t ) .
s h i f t b e t w e e n t h e m u t a t i o n and t h e d i s -
The d e g e n e r a t i o n s c a u s e d b y m u t a t i o n
turbance of the environment could be
comparable f o r each e x p e r i m e n t .
an important f a c t o r ,
p r o b a b i l i t y of degeneration
which influences
the p r o b a b i l i t y of degeneration.
The phase s h i f t f a c t o r i s
The
is
lowest
when MG and a d i s t u r b a n c e of t h e e n -
counted
v i r o n m e n t o c c u r i n t h e same
time ( t h e
experiment is considered as n o n t y p i c a l
a n d shown
only
a s a n example o f t h e
e x i s t e n c e o f such r e c o r d s ) .
interpretation.
The p r e s e n t e d c o m p u t e r m o d e l i s a
model of the e v o l u t i o n p r o c e s s .
The
DISTRUCs b e i n g t h e o b j e c t s o f s i m u l a t e d
The d c o e f f i c i e n t c o u l d b e c o u n t e d
f o r a l l degeneration cases,
or for
d e g e n e r a t i o n s c a u s e d by MGs o n l y .
second w i l l be denoted as dMG. .
fig.4
the k f a c t o r ,
the
The
From
d c o e f f i c i e n t and
d MG ,
c o e f f i c i e n t could be determine f o r
the
a l l f i v e presented experiments.
These v a l u e s a r e p r e s e n t e d i n t h e t a b l e
e v o l u t i o n a r e a b s t r a c t and a r e n o t t h e
image o f s t r u c t u r e o f any l i v i n g o r ganisms.
But
t h e i r behavior simulates
the behavior of organisms,
i.e.,
they
c a n g r o w , d i v i d e and m u t a t e . The p r o c e s s
of e v o l u t i o n ,
t h e r e a l one a s w e l l a s
t h e s i m u l a t e d , has a s a g o a l :
chievement
the a-
o f dynamic s t a b i l i t y f o r a n
e v o l u t i o n a r y sequence.
s t a b i l i t y is
I n t h e model
a c h i e v e d when t h e p e r i o d i c
sequence s t a r t s . A n o n p e r i o d i c sequence
is
t h e phase o f s e a r c h i n g f o r s t a b i l i t y .
F o r t h e g i v e n g e n o t y p e and t h e e n v i r o n ment
t h e r e a r e many p o s s i b l e s t a b i l e
s t a t e s ( i . e . p e r i o d i c sequences).
examples
and the
The
o f d i f f e r e n t s t a b i l e sequences
d i f f e r e n t ways o f f i n d i n g them
one can see o n f i g . 3 .
Not a l l o f p o s s i b l e
as
t h e m u t a t i o n and t h e d i s t u r b a n c e o f
t h e e n v i r o n m e n t o c c u r i n t h e same
time
a n d t h e cause f o r d e g e n e r a t i o n i s u n detectable.
quences a r e l o o k e d u p .
any)
stabile seO n l y one ( i f
is found in the h e u r i s t i c search.
From t h e e x p e r i m e n t s f o l l o w s
that:
158
Session No. 4 Associative and Adaptive Models
1 . The s t a b i l e ( t h e same i n t h e d i f f e r e n t generations)
phenotype c o u l d be
achieved a f t e r mutation of
and disturbances
w i t h o u t
in
the
the environment
b u i l t - i n informa-
t i o n concerning s t a b i l i t y .
sion,
the genotype
In conclu-
the r e l a t i v e l y simple
which could only
v i d e
g r o w
organisms,
and
d i -
and had n o b u i l t - i n i n f o r m a t i o n
about the f i n a l "shape" could be the
f i r s t l i v i n g organisms,
able
to de-
v e l o p and t o c o m p l i c a t e t h e s t r u c t u r e s .
2 . The d i s t u r b a n c e s o f t h e e n v i r o n ment were n o t n e c c e s s a r i l y t h e d e s tructive factors
t i o n of
the
could b e
e v o l u t i o n a r y sequences.T h e y
h e l p f u l
s t a b i l i t y if
proper
causing the degenera-
t h e y have
t o achieve
occured i n
the
" phase s h i f t " w i t h t h e m u t a -
tion.
The r e s u l t s p r e s e n t e d i n t h i s p a p e r
were o b t a i n e d f r o m a n a b s t r a c t model
of
the e v o l u t i o n process simulated on
t h e c o m p u t e r . They may b e t r e a t e d a s
i n d i c a t i o n s o f some p r o b l e m s ,
any e x t r a p o l a t i o n s
but f o r
towards b i o l o g y t h e y
should be tested in biological experiments •
References
1.
K.R. F i a l k o w s k i ,
C y c l i c Behavior of
Randomly G r o w i n g D i g i t a l S t r u c t u r e s
i n F i n i t e Random E n v i r o n m e n t ( P r o c .
of I n t .
J o i n t Conf.
Intelligence,
on A r t i f i c i a l
W a s h i n g t o n D.C.
1969,
pp.347-359)
2.
K.R.
Fialkowski,
F i n a l Report f o r
the Ford Foundation
3.
L . J . F o g e l , A . J . Owens, M . J . W a l s h ,
Artificial
Intelligence
through
Simulated Evolution ( J . W i l e y ,
1966)