The Increasing Non-beneficial Gap Problem
As it turns out, with each increase in the minimum size and/or specificity requirement of a system (or any informational language system, such as English, French, Russian, Morse Code, computer codes, DNA, proteins, etc.), the average number of mutational changes that are required to get from one such system to the next closest system (at the same level of functional complexity or higher) increases in a linear manner. And, with each linear increase in minimum number of modifications required to find something functionally new, the average number of random mutations or modifications required to achieve success increases exponentially. This results in an exponential stalling-out effect of evolutionary progress at very low levels of functional complexity.
For example, consider the evolutionary sequence:
Is this not a clear evolutionary sequence where every single character change results in a new meaningful word? What then is the problem for the evolutionary algorithm of random mutations and function-based selection?
Consider that it is relatively easy to move around between three-letter words because meaningful three-letter words are so close together in “sequence space” (a space that contains all possible arrangement of characters of a certain length). In fact, the ratio of meaningful vs. meaningless three-letter sequences in the English Scrabble Dictionary is about 1 in 18. However, what happens when the minimum size requirement is increased to 7-character sequences comprised of one or more “words”? Well, 7-character sequences are not so closely spaced on average because the ratio of meaningful vs. meaningless decreases, exponentially, to about 1 in 250,000 at this level of functional complexity (within the English language system). So, the average time to success for the evolutionary algorithm must also increase exponentially with each step up the ladder of functional complexity.
The very same thing happens in biology with DNA and proteins. For example, direct experimentally-determined degrees of protein sequence flexibility by those like Durston, Sauer, Olsen, Bowie, Axe, and others show that the vast majority of possible protein sequences, of a given size, are unstable and cannot even be maintained within living things, much less produce any beneficial effect.1-5 Consider a fairly small 150aa protein, for instance. The total number of possible sequences of 150aa in length is 20150, or 1e195 sequences. This is an enormous number of sequences. After all, the total number of atoms in the visible universe is only about 1e80. So, out of this total number, how many of these protein sequences could actually produce a stable protein? Experimental studies by those like Thirumalai (2000) and Axe (2011) show that only about 1 in 1074 sequences of 150aa in size are even capable of forming stable protein folds.6-7 As it turns out, this ratio decreases, exponentially, with each linear increase in the minimum size requirement of the protein-based system. In other words, as sequence space grows by 20N, the number of stable protein structures only scales by the natural log of N.6 Now, consider that protein stability isn’t the only thing that makes a protein beneficial. Requiring that a protein not only be stable, but beneficial as well before natural selection can preferentially maintain it reduces the ratio of such proteins in 150aa sequence space to about 1 in 1077. And, with each step up the ladder of functional complexity, this ratio gets exponentially worse and worse.
What this means is that when one starts considering protein-based systems that require more than 1000aa with an average degree of specificity, the minimum likely distance between any such system and the next closest system in sequence space is well over 150 non-selectable mutational changes. In other words, it would take well over 150 modifications to the protein-based system to get it to produce a qualitatively new kind of function at the same level of functional complexity or higher.9 How long would 150 non-selectable mutations take to achieve within a large population?