# How does evolution get around the combinatorial problem?

Imagine a combinatorial tree showing all the possible arrangements of nucleotides. Some arrangements are functional, meaning they can be plugged into a cell and create a living organism capable of reproducing. Some arrangements are nonfunctional, meaning they can't sustain any living system at all.

In evolution, new information is created as the result of what are essentially an accumulation of copying errors. My question is, would the ratio of functional to nonfunctional arrangements have to be relatively large so that enough genetic information can arise in response to natural selection? If so, what scientific studies have led biologists to conclude that this combinatorial space is rich with functional arrangements. If it isn't necessary please explain why.

• The ratio is incredibly low with almost all possible combinations being nonfunctional. If you have, by chance, a functional combination, evolution is extremely conservative and works in a step-wise trial-and-error manner, usually not taking large steps in the space of possible sequence combinations. If no one else answers your question in greater detail, I will provide an answer in the coming days. Jun 16 '17 at 8:31
• What exactly do you mean by "genetic information"? Are you thinking of some Shannon entropy-type thing, or do you just mean new genetic variants that increase fitness? Please clarify. Jun 17 '17 at 10:30

No, with some caveats. First, about the actual value of the ratio: it's probably tiny, with almost all possible genetic sequences failing to lead to living organisms.

Why does this not make evolution impossible? Each sequence can have billions* of neighbors in sequence space. If even a very small number of those are functional, evolution can proceed. More importantly, the functional sequences are clustered in sequence space. If you pick 3 billion nucleotides randomly, you'll get nonsense, but if you mutate a single nucleotide in a human you'll most likely get a perfectly good human.

There are interesting open questions here, though, especially regarding the origin of life, and whether natural selection tends to drive populations to regions of sequence space that are especially dense with functional sequences.

*Just looking at point mutations. Including the full mutational spectrum gives many more.

would the ratio of functional to nonfunctional arrangements have to be relatively large so that enough genetic information can arise in response to natural selection?

Evolution does definitely not explore all possible combinations of a DNA. It just try things out. Of course a new gene is not necessarily recreated from scratch. A gene often get copied and then the two copies can diverge (this is called neo-functionalization).

So, no not the all possibility space is explored but this is in no way a trouble. It is not like a mutation would cause a whole brand new sequence out ov the void and hope for it to be beneficial. A path is being taken through this possibility space.

"would the ratio of functional to nonfunctional arrangements have to be relatively large so that enough genetic information can arise in response to natural selection?"

Yes it is very large. Because most mutations are synonymous mutations. Take a look at the part about the degeneracy of the genetic code.

Another reason, and this one only helps evolution move on is called gene duplication. Many proteins in a genome are duplicated, meaning there is some redundancy involved. If we delete one protein, the fitness of the organism may/may not be affected but survival won't be affected. One example that comes to mind is Histone H1 (because I studied about it a bit). To clearly affect a change we need to delete at least three H1 genes, any less and one of its variants act as replacements.

Bonus answer, evolution does not always lead to the best possible combination, it leads to functional combinations.

• I am not the down voter. But I think the first part does nothing to explain a large fraction of functional arrangements. It merely simplifies the problem to a smaller number of arrangements, but we don't know the ratio of functional ones among these!
– Ludi
Jun 16 '17 at 8:46