Theoretical biology is a branch of biology that uses mathematical and computational tools to model and represent biological processes.

The complexity of real biological systems comes from the number of interacting parts and heterogeneity. These interactions can span times scales of picoseconds for electron transfer in photochemical reactions to billions of years in the case of evolution. Length scales range from molecules to cells and from organisms to ecosystems. This complexity requires sophisticated mathematics, which being not easily accessible to empirical biologists has led to the existence of a divide between theoretical and empirical biologists. Theoretical biologists may trade-off between abstraction and realism or between the qualitative and the quantitative. Theoretical biology as a term if often used together with the term mathematical biology.

## History

The first example of a mathematical law for a biological event was in 1896 when British professor K. Person applied statistical techniques of probability curves and regression lines to genetic data. Communication between experimental biologists and applied mathematicians in the 1930s began the field of population genetics.

In the 1960s the International Union of Biological Sciences began to form a skeleton of concepts and methods from which the theoretical biology could grow. Discussions at symposia were intended to discover and formulate concepts and logical relations characteristics of living organisms in contrast to inorganic systems. The implications of these concepts to philosophy were also sought.

The best known example of theory in biology is the theory of evolution by natural selection by Charles Darwin. While he was a hands-on naturalist and geologist, his main contribution to science was theoretical. However Darwin never formalized his theory in mathematical terms. Darwin once wrote, “I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics; for men thus endowed seem to have an extra sense”. Mathematical foundation for the theory of evolution was developed by population geneticists such as Pearson, Fisher, Wright and Haldane the end of the 1960s. The gradualist Darwinian view of natural selection was unified with a Mendelian understanding of genetics and observations by naturalists, experimental geneticists and paleontologists.

### Applications

Lotka-Volterra models of competition and prey-predation initiated the field of theoretical ecology. A clonal selection theory by Burnet which is a central part of what is understood of the adaptive immune system. Important roles for theoretical biology in neuroscience include the Hodgkin-Huxley model of action potentials and cable theory used by Rall as a framework for neuron dendritic structures. It has been argued that theoretical biology is needed to make sense of an abundance of data about genes, proteins and biological processes, that has come from increased computational power.