Towards an Information-Theoretic Model of Evolution (ITME)

I have started many web projects over the years, but never really got around to finishing any of them. I suppose the issue has always been scope, timing, and funding. So as time has passed, my projects have been driven more towards broader scope, and therefore longer timing. And what has broader scope and greater time than evolution itself? Evolution is timeless, or rather, it is unbounded by time. When we think about evolution, biologists typically think in the scale of thousands or millions of years – geologic time we call it. Slow, like the pace of rocks. Geological time is that of a snails pace through Mother Earth’s history. So maybe that is the pace that evolution deserves. A snails pace.

But sometimes evolution is not so merciful as to move at a pace that humans can comprehend. Sometimes evolution happens in the blink of an eye, in fact, so quick, that if an observer did blink, they would have missed it. In this sense, its easier to think of evolution as a property of the universe rather than only a observational process. Time is a process, but it is also a property of the universe. Space-time (spacetime) is a combination of a physical dimension (space), and a process (time) – so too is evolution. Evolution is the spacetime of biology.

“Evolution is the spacetime of biology.”

In developing a theory of evolution, it is important to define terms and the context they are used in. In this way we can break out the “dimensionality” of evolution into smaller pieces, and develop a more rigorous theory. As it stands, to many people, evolution is a “feeling” – an intuition. We all have an intuitive idea of natural selection and evolution, that is why it was independently discovered perhaps two or three times, all by different researchers, in different parts of the world, as far as we know. There may have been many times that correct ideas about evolution were discovered, and then forgotten, and then rediscovered.

And so what are some of these intuitive ideas about biology and evolution? Things that transcend not just the ideas that Darwin put out, but also general theories of statistics and information. We need for biology what Euclid created for mathematics – the point, the line, and the polygon. So what is the “point” equivalent in biology?

This is problematic because biology doesn’t have a single starting dimension (a 1 dimensional plane) like geometry does – the starting point in biology is always contextual. So we need to conjure a dimensionless unit, a “bit”, that can act as the smallest definable piece of information at the given contextual level. In this case, the bit could be biomolecules (DNA/RNA), in the case of chemistry-level systems or it could be whole organisms, in the case of population-level systems.

Example of the logical, contextual hierarchy of biological systems.

What is the second component of the system then, after the bit (or Euclid’s point)? In this case, adding a second dimension brings about structure – a description of how bits are organized in the system. Structure, in this sense is, is the equivalent to the line in Euclid’s geometry.

A simple example of quantifying information (bits) and structure (spatial components and “interactors” – fields).

The above example looks something similar to a Lewis structure, a graphical way to view the structure of molecules and compounds. In this system, however, the bits can be anything. In chemistry, the “bits” of a Lewis structure are atoms – elements – the smallest units of chemical systems. In the information theoretic model of evolution (ITME), the bits can be atoms, molecules, proteins, cells, organisms, or even populations of organisms. The base unit is always contextual to the level of evaluation, which means that evolutionary systems (or hypothetical evolutionary systems) can be assessed all across nature for their evolutionary properties.

Now as we move up and down through contextual levels (a contextual scientific hierarchy), we can add layered metrics with additional dimensionality on top of the information and structure that we are analyzing. One of the most intuitive metrics that we can look at is a measure of complexity. Intuitively, we’d like to think of complexity as some measure of how information is distributed within a system. In the information-theoretic model, we can think of complexity as the product of information (bits) and the sum of structural components (spatial, interactors, or other structural layers). Under this system, complexity increases for systems with a higher number of base units (e.g., a chemical system with many elements has a high number of bit potential), systems with more diverse structural arrangements (e.g., high degrees of branching or connectivity), and high degrees of “interactors (e.g., a protein with a high number of active sites).

Below is a more complex example of a hypothetical protein, including a complexity calculation:

Hypothetical complexity calculation under the information-theoretic model.

In this example, the number of bits in the system is the number of base units present (amino acids) is multiplied by the number of structural components (the sum of unique spatial arrangements and unique interactors). In this example, each bit is also an interactor, because each bit is contributing a unique piece of information to the way the molecule interacts with other molecules. The number of bits is 18 (there are 18 amino acids in the chain), spatial components is 15 (linear parts are merged, so complexity is reduced), and interactors is 18 (each bit is also an interactor). These are then multiplied to get an overall “complexity metric” – 18 x (15+18) = 594. As we can see this hypothetical protein molecule has quite a bit more potential complexity than the previous example, which might have a complexity value of 25 (5 x (3+2) = 25).

Overall, these are just some hypothetical ways to begin to build an information-theoretic model of evolution. Beginning with a base system of bits, structure, and complexity, the methodology can be expanded into other systems beyond the biologic. This allows researchers to conduct contextual analysis right at, below, or above the traditionally analyzed levels in biology. Under the ITME, abiogenesis, chemical evolution, and other origins-of-life theories can be analyzed within the same framework as classic population genetics, and then expanded into types of social and cultural evolution.

Of course, this is just one way that these calculations could be made as well (should spatial components be combined with interactors?), and those specifics need to be fleshed out more as I develop this into a working theory. With that in mind, I hope everyone enjoyed these musings on some ideas that I’ve been working for more than 10 years now (has it really been that long since I started in Biology?). Stay tuned for more delvings into this new, unique way of conducting evolutionary analysis as I expand and formalize the idea.

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