Evos

Let us define a simple evolutionary scheme, henceforth evos, as made up of the following:

• a genomic language G.
• a phenomic space S.
• a procedure E from G to S, called the egen (for embriogenesis).
• a machine M from G to G, called the mutator.

All genomes are strings in G. E maps genomes to phenomes. M is the reproduction operator, which usually returns a mutated genome.

Given this definition, there are various meaningful ways in which we can compare evos and organize them in hierarchies.

The most obvious way to do this is to look at the subspace of S that is attainable by an evos. If the function defined by E is not surjective, this directly limits the attainable subspace of S. Another possibility is that the iteration of M from a starting genome may never attain certain other genomes. However, I see no good reason to use such schemes; it always seems better to restrict E instead. So we shall focus on schemes where it is possible to attain any genome from any starting genome through an iteration of M (there is a name for such processes, but I don't recall it). This is also why I chose not to include a starting genome (set) in the definition.

For example, if G only contains fixed-length strings, but S is an infinite-dimension space (like it would be in many cases), it is impossible for E to be surjective. Another possibility would be to fix certain parts of the phenome. In this case, E can only affect some parts of the phenome, and so can't be surjective. A similar possibility is to deliberately restrict E to map only to a certain subspace of interest.

With this way of comparison, an evos is higher in the hierarchy than another if its attainable subspace is larger.

Another, perhaps more interesting way is to look at the expressive power of E. A trivial egen is an identity procedure, so that in such an evos, the genome and the phenome of an individual are conflated. At the other end of this hierarchy are Turing-complete egens.

Similarly, we may also look at the expressive power of the mutator, and get a third way of comparing different evos. At the bottom of this hierarchy (keeping in mind the restriction we put on M), we find mutators that mutate genomes at a fixed rate. Another example is a mutator that could mutate the genome at a rate that varies as it goes through the genome, depending on annotations on the genome (these annotations would be part of the genome, but ignored by the egen). At the top of the hierarchy are Turing-complete mutators.