Tuesday, November 11, 2014

Evolution

While thinking about the evolvability of different artificial life simulations, as discussed some in my last posting, I realized that it would be helpful to talk about what is required for a system to evolve. It comes down to four basic traits.

1. Reproduction: Some unit in the system has to reproduce. This unit could be bacterial cells in your gut, or it could be numerical representations in a computer. (Even fire can be described as reproducing when it spreads through a house or forest.)

2. Inheritance: During reproduction, each new unit in the system has to gain traits from its parent(s). The traits could be hidden, as in recessive alleles, or it could be obvious, as in dominant alleles. The number of parents can be one or more than one. (We have two, but maybe some aliens have three or more.)

3. Mutation: At some point in the reproductive cycle, there has to be the potential for changes in the traits (mutations) that are inherited.

4. Death: Death is generally required to remove individuals from a population, thus freeing up room for the next generation. However, there are scenarios where death isn't required. If the population is continuously expanding into new territory, the front-line sub-population can evolve over time without individual death. In this case, the older organisms being left behind fills the same role of actual death.



It is relatively easy to prove mathematically that a system with these four traits will experience evolution.

Lets give it a go in a simulation that has a maximum population of four organisms represented by letters and driven by the following rules.
  1. Reproduction with inheritance: A -> AA; B -> BB
    • A or B can duplicate.
  2. Mutation: A -> B.
    • A can mutate into B.
  3. Death: A -> A 
    • Only A can die.
We start the simulation with "A" .

"A" -> "AA" -> "AAAA" -> "AAAB" -> "AAAB" -> "AB" -> "AABB" -> "AABB" -> "ABB" -> "ABBB" -> "ABBB" -> "BBBB"

This may not look like the sort of math you are familiar with, but it is math nonetheless. Math is the manipulation of abstract symbols that represent precise concepts with the extremely rigid rules of logic. 2+2 always equals 4. A system with the described traits will always experience evolution.

Now, this little toy system I've described has an extremely low evolvability. The starting state of the system ("A") does meet the four requirements and thus evolves. However, once the system has reached the final state ("BBBB"), it no longer meets the four requirements and thus cannot evolve further.



If you argue that life doesn't evolve, then you are logically arguing that life does not meet one of the four requirements discussed above. Unequivocally, life meets the four requirements.

Life evolves. The math doesn't provide any other possibility.