Not as simple as some people think

The combination of natural selection and random mutations appear to too inefficient.
This does not mean that the idea of evolution has to be rejected.
Numerous observations makes the opinion of an evolution to have taken place, to rest upon a quite solid foundation.
But some mechanism different from the neo-Darwinian seems to have been involved.
One possibility could be that life is able to control mutations (epigenetics),
another would be direct intervention from God (Intelligent Design).
A third possibility could be some kind of quantum chemical effect.
I presented such a mechanism, Super Darwinian evolution, at the conference
"Toward a Science of Consciousness", arranged by the Unversity of Arizona.
The essence ot the theory is that the universe is a huge quantum computer,
programmed to couple matter to consciousness, and thus to search the Image of God.
The computer had to work for some 14 billion years before the result was found.
Then it stopped, and here we are.

The picture shows a simulation,
in which a normal population (blue) competes with a mutated (yellow).
In every generation the individuals try to multiply.
The mutated individuals are stronger than the original ones.
According to Darwin's theory of evolution,
only yellow should eventually remain (survival of the fittest).

Darwin's theory is easily converted to a differential equation.
If the fitness of the mutation is one percent better,
its population size should grow according to the sequence
1, 1.01, 1.02, 1.03, 1.041, 1.051, 1.062,....

In reality, the opposite often happens. The reason is that the number of individuals is always an integer.
There does not exist anything like 1.02 individuals.
Due to statistical fluctuations, the sequence rather becomes something like 1, 2, 3, 3, 3, 4, 3, 4, 3, 3, 2, 3, 1, 0.
As soon as the value zero occurs, the mutation is gone.

You may download a program that simulates such a competition.
In order for you to verify that the program does not cheat, you may download the source code.
In this way you are able to verify that the software does what I claim.
You could also compile it (C++), to be sure that the source code describes the correct program.
In addition to these files, there are also user instructions to download.