模倣子 Natural Selection Game

 Introduction

My idea is to invent a "game" that illustrates some principles of evolution by natural selection. Initially there would be no mutations, and no "junk genes" or such.

The way it works is an individual is a set of three numbers, zero to nine, rolled up on a ten-sided die (d10). The reproductive process is that two individuals average each of their numbers (1), one, two, three, to produce a new individual. The fitness function works of the total of the three numbers, for example, one is fit if the total is between 14 and 16.

Set-Up

Decide how many individuals to make for the first generation, about a half-dozen. Roll up each individual with three d10 rolls.

A	B	C	D	E
9	8	0	0	2
3	2	6	5	7
8	1	8	5	3
20	11	14	10	12

Second Generation

We make the fitness determinator to be that the total for an individual's three numbers be between fourteen and sixteen. I'm rounding down, i.e., throwing away half values, and this is arbitrary (1) for a reproductive algorithm.

A+B F	A+C G	A+D H	A+E I	B+C	B+D	B+E	C+D	C+E
8	4	4	5	4	4	5	0	1
2	4	4	5	4	3	4	5	6
4	8	6	5	4	3	2	6	5
14	16	14	15	12	10	11	11	12

Third Generation

We take the individuals that survived the fitness test and mix them together, and continue this as long as we like, until we end up with nobody passing the fitness test, hitting an unchanging condition, or we give up.

F+G J	F+H K	F+I	G+H L	G+I M	H+I
6	6	6	4	4	4
3	3	3	4	4	4
6	5	4	7	6	5
15	14	13	15	14	13

Fourth Generation

J+K N	J+L O	J+M P	K+L Q	K+M	L+M R
6	5	5	5	5	4
3	3	3	3	3	4
5	6	6	6	5	6
14	14	14	14	13	14

Fifth Generation

N+O S	N+P T	N+Q	N+R U	O+P	O+Q	O+R	P+Q V	P+R	Q+R
6	6	6	4	4	4	4	5	4	4
3	3	3	3	3	3	3	3	3	3
6	5	4	7	6	5	6	6	6	6
15	14	13	14	13	12	13	14	13	13

Sixth Generation

S+T W	S+U X	S+V Y	T+U Z	T+V	U+V
6	5	5	5	5	4
3	3	3	3	3	3
5	6	6	6	5	6
14	14	14	14	13	13

Seventh Generation 

W+X	W+Y	W+Z	X+Y	X+Z	Y+Z
5	5	5	5	5	5
3	3	3	3	3	3
5	5	5	6	6	6
13	13	13	14	14	14

So at this point there is only one genotype left, so it will just continue, and in principle grow and grow and grow, since every new individual in each new generation will be the same and will be equally viable.

Summary & Conclusions

In the example we give here, five random individuals converge to a homogenous genotype in seven generations.

One wonders what effect making average rounding a random thing, eg., a coin-flip. As in the example, if one parents contributes a 5 and another a 6, this information is lost, in a way, that is, both become one or the other. Some other way of varying the rounding might also be interesting.

There is no concept of "junk DNA" at this point. All of the numbers contribute to the individual's "value" and thus their fitness determination.

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(1) One can round up or down, or even flip a coin (which would effectively introduce a random mutation) when producing new individuals.