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Pure Chance Genetics With Inheritance

Using pure chance genetics with inheritance but without fitness describes the situation where we have a random population at the beginning onto them genetic operators will be applied without having additional information by any kind of fitness. This is an artificial case but allows the comparison between (i) pure randomness, (ii) inheritance with genetic operators without fitness as well as (iii) inheritance with genetic operators and with fitness.

The following simple example demonstrates the procedure.

First a new population $ POPX$ is randomly generated by the function popgen(). $ POPX$ has 4 members with a length of $ l=3$. 

-->n=4, l=3,[POPX]=popgen(n,l)
 n  =
 
    4.  
 l  =
 
    3.  
 POPX  =
 
    0.    1.    0.  
    0.    1.    1.  
    1.    1.    1.  
    0.    1.    1.

Then the function gassimple0() is called and $ N=4$ times are the genetic operators applied to this population $ POPX$ (see below). The population starts with four strings repesenting the decimal values '2', '3', '7', and '3'. In the next cycle these strings are changed to '6', '3', '3', '3'. This is repeated in the 3rd cycle with the same positions, then follow the same values '3', '6', '3', '3' but with a different position of the '6'. 

 
-->l=3,p=5,n=4,N=4,
K=1,MThreshold=N+1,MCount=0,show=1,[MCount,DIST2,STD, MEAN, FREQ,STD1,
MEAN1, FREQ1,POP,FX]=gasimple0(POPX,l,p,n,N, K,MThreshold,MCount,show)
 l  =
 
    3.  
 p  =
 
    5.  
 n  =
 
    4.  
 N  =
 
    4.  
 K  =
 
    1.  
 MThreshold  =
 
    5.  
 MCount  =
 
    0.  
 show  =
 
    1.  
 
    1.  

FX after Count

 
    0.    0.    0.    0.  
    1.    0.    0.    0.  
    2.    1.    0.    0.  
    3.    2.    0.    0.  
    4.    0.    0.    0.  
    5.    0.    0.    0.  
    6.    0.    0.    0.  
    7.    1.    0.    0.  

 
    1.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    7.    0.    0.    1.    0.    1.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
POP after Operators
 
    1.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    7.    0.    0.    1.    0.    1.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
 
    2.  

FX after Count

 
    0.    0.    0.    0.  
    1.    0.    0.    0.  
    2.    1.    0.    0.  
    3.    5.    0.    0.  
    4.    0.    0.    0.  
    5.    0.    0.    0.  
    6.    1.    0.    0.  
    7.    1.    0.    0.  

 
    1.    1.    0.    6.    0.    0.    1.    0.    1.    1.    0.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
POP after Operators
 
    1.    1.    0.    6.    0.    0.    1.    0.    1.    1.    0.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
 
    3.  

FX after Count

 
    0.    0.    0.    0.  
    1.    0.    0.    0.  
    2.    1.    0.    0.  
    3.    8.    0.    0.  
    4.    0.    0.    0.  
    5.    0.    0.    0.  
    6.    2.    0.    0.  
    7.    1.    0.    0.  

 
    0.    1.    1.    6.    0.    0.    1.    0.    1.    1.    0.  
    1.    1.    0.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
POP after Operators
 
    0.    1.    1.    6.    0.    0.    1.    0.    1.    1.    0.  
    1.    1.    0.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
 
    4.  

FX after Count

 
    0.    0.     0.    0.  
    1.    0.     0.    0.  
    2.    1.     0.    0.  
    3.    11.    0.    0.  
    4.    0.     0.    0.  
    5.    0.     0.    0.  
    6.    3.     0.    0.  
    7.    1.     0.    0.  

 
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    1.    1.    0.    6.    0.    0.    1.    0.    1.    1.    0.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
POP after Operators
 
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    1.    1.    0.    6.    0.    0.    1.    0.    1.    1.    0.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
 
    0.    0.     0.        0.    
    1.    0.     0.        0.    
    2.    1.     0.0625    50.   
    3.    11.    0.6875    550.  
    4.    0.     0.        0.    
    5.    0.     0.        0.    
    6.    3.     0.1875    150.  
    7.    1.     0.0625    50.   
Number of Events n * N * K = 16
 FX  =
 
    0.    0.     0.        0.    
    1.    0.     0.        0.    
    2.    1.     0.0625    50.   
    3.    11.    0.6875    550.  
    4.    0.     0.        0.    
    5.    0.     0.        0.    
    6.    3.     0.1875    150.  
    7.    1.     0.0625    50.   
 POP  =
 
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    1.    1.    0.    6.    0.    0.    1.    0.    1.    1.    0.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
 FREQ1  =
 
    0.6875    1.  
    0.1875    1.  
    0.0625    2.  
    0.        4.  
 MEAN1  =
 
    0.234375  
 STD1  =
 
    0.2362278  
 FREQ  =
 
    550.    1.  
    150.    1.  
    50.     2.  
    0.      4.  
 MEAN  =
 
    187.5  
 STD  =
 
    188.98224  
 DIST2  =
 
    275.

Another example with $ l=3, n=4, N=16$ is given below. 

-->n=4,l=3,[POPX]=popgen(n,l)
 n  =
 
    4.  
 l  =
 
    3.  
 POPX  =
 
    1.    0.    0.  
    1.    0.    0.  
    0.    1.    1.  
    0.    0.    1.  
 
-->l=3,p=5,n=4,N=16,
K=1,MThreshold=N+1,MCount=0,show=1,[MCount,DIST2,STD, MEAN, FREQ,STD1,
MEAN1, FREQ1,POP,FX]=gasimple0(POPX,l,p,n,N, K,MThreshold,MCount,show)
 l  =
 
    3.  
 p  =
 
    5.  
 n  =
 
    4.  
 N  =
 
    16.  
 K  =
 
    1.  
 MThreshold  =
 
    17.  
 MCount  =
 
    0.  
 show  =
 
    1.  
 
    1.  

FX after Count

 
    0.    0.    0.    0.  
    1.    1.    0.    0.  
    2.    0.    0.    0.  
    3.    1.    0.    0.  
    4.    2.    0.    0.  
    5.    0.    0.    0.  
    6.    0.    0.    0.  
    7.    0.    0.    0.  
Mutationcount = 0
 
    0.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    1.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    0.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
POP after Operators
 
    0.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    1.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    1.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    0.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
 
    2.  

FX after Count

 
    0.    2.    0.    0.  
    1.    1.    0.    0.  
    2.    0.    0.    0.  
    3.    1.    0.    0.  
    4.    2.    0.    0.  
    5.    1.    0.    0.  
    6.    0.    0.    0.  
    7.    1.    0.    0.  
Mutationcount = 1
 
    0.    0.    1.    0.    0.    0.    1.    0.    0.    0.    0.  
    1.    0.    0.    7.    0.    0.    1.    0.    1.    1.    1.  
    1.    0.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    1.    1.    0.    0.    0.    1.    0.    0.    0.    0.  
POP after Operators
 
    0.    0.    1.    0.    0.    0.    1.    0.    0.    0.    0.  
    1.    0.    0.    7.    0.    0.    1.    0.    1.    1.    1.  
    1.    0.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    1.    1.    0.    0.    0.    1.    0.    0.    0.    0.  
 
    3.  

FX after Count

 
    0.    2.    0.    0.  
    1.    2.    0.    0.  
    2.    0.    0.    0.  
    3.    2.    0.    0.  
    4.    4.    0.    0.  
    5.    1.    0.    0.  
    6.    0.    0.    0.  
    7.    1.    0.    0.  
Mutationcount = 2
 
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
    0.    1.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    0.    3.    0.    0.    1.    0.    0.    1.    1.  
POP after Operators
 
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
    0.    1.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    0.    3.    0.    0.    1.    0.    0.    1.    1.  
 
    4.  

FX after Count

 
    0.    3.    0.    0.  
    1.    2.    0.    0.  
    2.    0.    0.    0.  
    3.    3.    0.    0.  
    4.    5.    0.    0.  
    5.    2.    0.    0.  
    6.    0.    0.    0.  
    7.    1.    0.    0.  
Mutationcount = 3
 
    1.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    0.    0.    0.    0.    1.    0.    0.    0.    0.  
    1.    0.    0.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
POP after Operators
 
    1.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    0.    0.    0.    0.    1.    0.    0.    0.    0.  
    1.    0.    0.    3.    0.    0.    1.    0.    0.    1.    1.  
    0.    1.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
 
    5.  

FX after Count

 
    0.    4.    0.    0.  
    1.    2.    0.    0.  
    2.    0.    0.    0.  
    3.    4.    0.    0.  
    4.    6.    0.    0.  
    5.    3.    0.    0.  
    6.    0.    0.    0.  
    7.    1.    0.    0.  
Mutationcount = 4
 
    0.    1.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    1.    0.    0.    0.    1.    0.    0.    0.    0.  
    1.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    0.    3.    0.    0.    1.    0.    0.    1.    1.  
POP after Operators
 
    0.    1.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    1.    0.    0.    0.    1.    0.    0.    0.    0.  
    1.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    0.    3.    0.    0.    1.    0.    0.    1.    1.  
 
    6.  

FX after Count

 
    0.    4.    0.    0.  
    1.    3.    0.    0.  
    2.    1.    0.    0.  
    3.    4.    0.    0.  
    4.    7.    0.    0.  
    5.    4.    0.    0.  
    6.    0.    0.    0.  
    7.    1.    0.    0.  
Mutationcount = 5
 
    0.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
    0.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    0.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
POP after Operators
 
    0.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
    0.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    0.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
 
    7.  

FX after Count

 
    0.    4.    0.    0.  
    1.    4.    0.    0.  
    2.    2.    0.    0.  
    3.    4.    0.    0.  
    4.    8.    0.    0.  
    5.    5.    0.    0.  
    6.    0.    0.    0.  
    7.    1.    0.    0.  
Mutationcount = 6
 
    0.    0.    1.    2.    0.    0.    1.    0.    0.    1.    0.  
    0.    1.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
POP after Operators
 
    0.    0.    1.    2.    0.    0.    1.    0.    0.    1.    0.  
    0.    1.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
 
    8.  

FX after Count

 
    0.    4.    0.    0.  
    1.    5.    0.    0.  
    2.    3.    0.    0.  
    3.    4.    0.    0.  
    4.    9.    0.    0.  
    5.    6.    0.    0.  
    6.    0.    0.    0.  
    7.    1.    0.    0.  
Mutationcount = 7
 
    0.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
    1.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
POP after Operators
 
    0.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
    1.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    1.    0.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
 
    9.  

FX after Count

 
    0.    4.     0.    0.  
    1.    6.     0.    0.  
    2.    4.     0.    0.  
    3.    4.     0.    0.  
    4.    10.    0.    0.  
    5.    7.     0.    0.  
    6.    0.     0.    0.  
    7.    1.     0.    0.  
Mutationcount = 8
 
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    0.    1.    2.    0.    0.    1.    0.    0.    1.    0.  
    1.    1.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
POP after Operators
 
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    0.    1.    2.    0.    0.    1.    0.    0.    1.    0.  
    1.    1.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
 
    10.  

FX after Count

 
    0.    5.     0.    0.  
    1.    7.     0.    0.  
    2.    4.     0.    0.  
    3.    4.     0.    0.  
    4.    10.    0.    0.  
    5.    8.     0.    0.  
    6.    1.     0.    0.  
    7.    1.     0.    0.  
Mutationcount = 9
 
    1.    1.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    0.    1.    6.    0.    0.    1.    0.    1.    1.    0.  
    0.    0.    0.    0.    0.    0.    1.    0.    0.    0.    0.  
POP after Operators
 
    1.    1.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    0.    1.    6.    0.    0.    1.    0.    1.    1.    0.  
    0.    0.    0.    0.    0.    0.    1.    0.    0.    0.    0.  
 
    11.  

FX after Count

 
    0.    6.     0.    0.  
    1.    8.     0.    0.  
    2.    4.     0.    0.  
    3.    4.     0.    0.  
    4.    10.    0.    0.  
    5.    9.     0.    0.  
    6.    2.     0.    0.  
    7.    1.     0.    0.  
Mutationcount = 10
 
    0.    0.    1.    6.    0.    0.    1.    0.    1.    1.    0.  
    1.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    1.    0.    0.    0.    0.    1.    0.    0.    0.    0.  
POP after Operators
 
    0.    0.    1.    6.    0.    0.    1.    0.    1.    1.    0.  
    1.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    1.    0.    0.    0.    0.    1.    0.    0.    0.    0.  
 
    12.  

FX after Count

 
    0.    7.     0.    0.  
    1.    9.     0.    0.  
    2.    4.     0.    0.  
    3.    4.     0.    0.  
    4.    10.    0.    0.  
    5.    10.    0.    0.  
    6.    3.     0.    0.  
    7.    1.     0.    0.  
Mutationcount = 11
 
    0.    1.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    1.    0.    0.    0.    1.    0.    0.    0.    0.  
    1.    0.    0.    6.    0.    0.    1.    0.    1.    1.    0.  
POP after Operators
 
    0.    1.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
    0.    0.    1.    0.    0.    0.    1.    0.    0.    0.    0.  
    1.    0.    0.    6.    0.    0.    1.    0.    1.    1.    0.  
 
    13.  

FX after Count

 
    0.    7.     0.    0.  
    1.    10.    0.    0.  
    2.    5.     0.    0.  
    3.    4.     0.    0.  
    4.    11.    0.    0.  
    5.    11.    0.    0.  
    6.    3.     0.    0.  
    7.    1.     0.    0.  
Mutationcount = 12
 
    1.    0.    1.    2.    0.    0.    1.    0.    0.    1.    0.  
    0.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    1.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
POP after Operators
 
    1.    0.    1.    2.    0.    0.    1.    0.    0.    1.    0.  
    0.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    1.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
 
    14.  

FX after Count

 
    0.    7.     0.    0.  
    1.    11.    0.    0.  
    2.    6.     0.    0.  
    3.    4.     0.    0.  
    4.    12.    0.    0.  
    5.    12.    0.    0.  
    6.    3.     0.    0.  
    7.    1.     0.    0.  
Mutationcount = 13
 
    1.    0.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    0.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
POP after Operators
 
    1.    0.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    0.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
 
    15.  

FX after Count

 
    0.    7.     0.    0.  
    1.    12.    0.    0.  
    2.    7.     0.    0.  
    3.    4.     0.    0.  
    4.    13.    0.    0.  
    5.    13.    0.    0.  
    6.    3.     0.    0.  
    7.    1.     0.    0.  
Mutationcount = 14
 
    0.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    0.    1.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    0.    1.    2.    0.    0.    1.    0.    0.    1.    0.  
POP after Operators
 
    0.    0.    1.    4.    0.    0.    1.    0.    1.    0.    0.  
    0.    1.    0.    5.    0.    0.    1.    0.    1.    0.    1.  
    1.    0.    0.    1.    0.    0.    1.    0.    0.    0.    1.  
    1.    0.    1.    2.    0.    0.    1.    0.    0.    1.    0.  
 
    16.  

FX after Count

 
    0.    7.     0.    0.  
    1.    13.    0.    0.  
    2.    8.     0.    0.  
    3.    4.     0.    0.  
    4.    14.    0.    0.  
    5.    14.    0.    0.  
    6.    3.     0.    0.  
    7.    1.     0.    0.  
Mutationcount = 15
 
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
    1.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
    0.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
POP after Operators
 
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
    1.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
    0.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
 
    0.    7.     0.109375    87.5   
    1.    13.    0.203125    162.5  
    2.    8.     0.125       100.   
    3.    4.     0.0625      50.    
    4.    14.    0.21875     175.   
    5.    14.    0.21875     175.   
    6.    3.     0.046875    37.5   
    7.    1.     0.015625    12.5   
Number of Events n * N * K = 64
 FX  =
 
    0.    7.     0.109375    87.5   
    1.    13.    0.203125    162.5  
    2.    8.     0.125       100.   
    3.    4.     0.0625      50.    
    4.    14.    0.21875     175.   
    5.    14.    0.21875     175.   
    6.    3.     0.046875    37.5   
    7.    1.     0.015625    12.5   
 POP  =
 
    1.    0.    1.    1.    0.    0.    1.    0.    0.    0.    1.  
    0.    1.    0.    2.    0.    0.    1.    0.    0.    1.    0.  
    1.    0.    0.    4.    0.    0.    1.    0.    1.    0.    0.  
    0.    0.    1.    5.    0.    0.    1.    0.    1.    0.    1.  
 FREQ1  =
 
    0.21875     2.  
    0.203125    1.  
    0.125       1.  
    0.109375    1.  
    0.0625      1.  
    0.046875    1.  
    0.015625    1.  
 MEAN1  =
 
    0.1116071  
 STD1  =
 
    0.0809748  
 FREQ  =
 
    175.     2.  
    162.5    1.  
    100.     1.  
    87.5     1.  
    50.      1.  
    37.5     1.  
    12.5     1.  
 MEAN  =
 
    89.285714  
 STD  =
 
    64.779847  
 DIST2  =
 
    81.25

Below are 6 experiments reported: three with gassimple0() and three with frequCheck(). All 6 experiments have the parameters $ l=3, n=4, N=2048$.

The first three experiments with gassimple0() shows the results by starting with a certain population $ POPX$ and then apply only crossover without fitness in $ n \times N$ many events. Comparing the empirical values gives the following table:

DIST2 gassimple0() frequCheck()
1 56.054688 3.8085938
2 100.83008 2.6855469
3 6.4453125 6.9824219

These examples of gassimple0() demonstrate that the application of the corssover operator without fitness compares to a pure random procedure badly.

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Next: gasimple0 1 Up: Pure Chance Genetics Previous: Approaching the Solution   Contents
Gerd Doeben-Henisch 2012-03-31