In physics, chemistry, geology, climatology and even some of the social sciences, theories and laws are born from models of systems, generally based on observations or experimental data. Molecular biologists also use the term model in their papers and presentations.  These so-called models or cartoons of mechanistic pathways tend to resemble roadmaps with lots of arrows pointing to and from long lists of gene products. But such cartoons are not really models; they are summaries of data. Models have specific purposes, one of which is to simplify and focus the experimental work; another is to lead to new hypotheses for testing. Building a real model is usually difficult and requires a good deal of creative effort.

And what a model needs, by definition, is a mathematical treatment of the idea being modeled. Mathematics has been successfully applied to certain areas of biological science, such as ecology, enzymology, and genetics. But there are surprising gaps in how mathematical models are used in biology. One of the most surprising to me is the lack of any mathematical laws of evolution.

The usefulness of a mathematical theoretical approach to evolution becomes clear when one considers the enormous complexity of the systems being studied. Evolutionary biology has become very broad and now covers most aspects of molecular biology, developmental biology, genomics, physiology, systematics, ecology and genetics. There has been a great deal of theoretical work done on many of these areas, and the overall theory has been described, elaborated and modified continuously.

There have even been a number of mathematical treatments of various aspects of evolutionary theory, such as the use of fitness differences in the Hardy-Weinberg law to predict allele frequencies over time. A search of the literature for math in biology will reveal a plethora of equations related to theoretical treatments of evolution. But despite a wealth of formulas (many of which are not comprehensible to non-mathematicians), there are none that rise to the level of a law of nature,  because they are either speculative, or too specialized in their application, or because some terms (fitness being notorious for this) are impossible to define.

On the face of it, it does seem strange (at least to me) that no universal law has been stated for the process of evolution. The components of a possible model are clearly known. Organisms inherit genes and resulting phenotypes from their parents. There is a diversity of such phenotypes due to mutation, recombination, and other factors. Some phenotypes increase the probability for survival and reproduction, and others don’t. These simple statements should, one would imagine, allow for some form of mathematical treatment that could be simply (and perhaps elegantly) stated as a law (or more likely laws) of evolutionary biology.

The problem, of course, is in the details. And biologists are quite keen to drill down as far as they can to uncover more and more details about how life works. Most of these details cannot be accounted for in any general law or theory. So the argument goes that any simple law would fail to incorporate various modes of genetic variation, or neutral drift, or some other aspect of how evolution actually happens. The hard part therefore is come up with such laws that are general enough to be fairly simple and universal, but at the same time, are able to at least acknowledge, if not account for, the unending complexity of living creatures, how they live, and how they evolve.

But while the task is hard, the reward for success is quite tangible. With  good theoretical laws, certain doubts about evolution as the central basis for biological science might be laid to rest, and hopefully a good deal of disparate and confusing information could be integrated into a unified context. And biology would become another of the sciences governed by the rule of law.