While the theory of evolution by natural selection has become the well established basis for all biological science, and while further developments in genetics and molecular biology have confirmed the theory, it continues to suffer from an affliction that has always plagued all of biology – the lack of any mathematical rigor. To date there is no useful mathematical law that fully encompasses the meaning of Darwininian evolution. Fisher’s famous “genetical theory of evolution” published in 1931, describes the general idea of the statistical nature of genetic variation, and posits that fitness must always increase. That is useful, but not comprehensive.

It is often held that biology has been resistant to mathematical treatment due to the enormous complexity of the subject. That is not quite true. Science has never actually described its subjects by mathematics, that is impossible for either physics or chemistry, whose subjects are also extremely complex. What science does do is describe a model of reality with mathematics. The laws of motion are based on models, as are the laws of chemistry. Because such models, (eg a frictionless inclined plane, or an ideal gas) do closely resemble their real world counterparts, the equations generated to fit the models, do a pretty good job with reality as well.

Biological models are rare. When they are produced, the results are often quite brilliant. The literal model building by Watson and Crick led to the solution of the DNA structure, which some consider to be another revolution in biological science. Models of predator prey interaction, using difference equations, led to the understanding of the role of chaos and nonlinear dynamics in biology. Even Mendelian genetics, including the Hardy Weinberg equilibrium law is a model (which is why Mendel’s actual experimental data didn’t quite fit his theory).

But no useful, mathematically describable model of Darwinian evolution has yet been constructed. Actually, there are hundreds of such models, but none that has risen to the status of universally accepted law. Does it matter? Does a theory need to have a mathematical expression in order to be true? Not at all. The mass of data supporting evolution, and the absence of any real data opposed to it are sufficient. Still, it does matter for other reasons, not for establishing the truth of the basic theory, but for demolishing the pseudo-science that seems to accompany scientific ideas that are not easily contained in a set of fairly straightforward (and often simple, elegant) equations.

For example, once we know that laws of thermodynamics and electromagnetism are both true, and easily described by mathematical equations, we can test any future ideas to see if they violate these laws by mathematics as well. However, in biology, especially evolutionary biology, such tests don’t exist, and this allows for many misinterpretations, misunderstandings and even fraudulent distortions of the basic theory to gain some measure of credence.  

An example of an extension of Darwinian theory to an area that is actually not supported by either the theory itself, nor any other scientific underpinning, is evolutionism, which includes social Darwinism, evolutionary psychology and other ideas. Evolutionism (a branch of scientism) is the fundamental concept that the principles of Darwinian theory can be applied to all aspects of life on Earth, and perhaps to many other phenomena as well. A good example of evolutionism is the concept of the meme, invented by Dawkins, which is the mental equivalent of a gene. According to the idea, memes compete and reproduce, follow the rules of natural selection, go extinct, and so on. Religion is considered a meme, as is prejudice, fashion statements, popular tastes in food and hair styles, philosophical and political ideas, and so on.

This idea is quite charming, and makes considerable sense. But it isn’t science. Technology also seems to follow similar evolutionary rules. The fittest (meaning most useful, cheapest, etc.) new devices survive and edge out those that do not compete as well. One can even talk about the evolution of everything from pianos to telephones, to calculating devices. Clearly there is something about change that is quite universal, and that applies to living creatures as well as to human artifacts, thoughts, nations, and so on. But let’s be very clear. These simple observations about the nature of change, and how so many competing entities survive and prosper, or don’t, are NOT what Darwinian theory is about. The theory of natural selection in biology does not at all apply to memes, disc players, or societies. Any more than the attraction felt by two lovers is explained by gravitational theory.

Natural selection, as outlined by Darwin, and then as explained by our current understanding of molecular genetics, involves very specific biological parameters that are not found in these analogous systems. Those parameters, which are uniquely part of biological systems, include reproduction of the informational DNA molecule with a close genotype phenotype interaction, variation produced and controlled to a very fine degree, and a method of change that depends on random and non-random mutational events followed by strong interaction with the total environment. Electronic devices do not reproduce themselves, so the target of selection is not the device, but the people who decide if the device is worth manufacturing.

In other words, there are some very general laws of change, and biological evolution is a very specific special case of change. If we are ever able to formulate a useful model for biological evolution, I’m sure we will find that it will be highly useful in combatting the excesses of evolutionism as well as putting biology on a much sounder scientific footing.