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Theoretical biology is a relatively new, vigorously growing field of research and understanding. Its role in biology is similar to that of theoretical (mathematical) approaches in physics. On the one side, we have the observations, experiments and field studies, and on the other side we have theoretical concepts, mathematical models and deductive structures. Mathematical models can describe biological phenomena in a way that would otherwise be impossible. For example, one cannot normally follow the fate of populations of biological objects (molecules, cells, individual organisms, etc.) for millions of generations without an adequate mathematical model.
According to John von Neumann's definition, models are mathematical structures that, with verbal interpretation, describe the biological phenomena. They are a formalised way of passing from the concrete to the abstract. Theoretical biology has been growing since its golden age in the 1920s and 1930s, when Lotka, Volterra, Kostitzin and Kolmogorov began to formalise ecology and Wright, Fisher and Haldane laid the foundations of population genetics to study evolution through models.
It must be emphasised that theoretical biology differs from theoretical physics in that (i) it puts emphasis on a rational treatment of diversity and complexity; (ii) it tries to combine holistic ideas with the modelling approach; (iii) the number of relevant facts to take into account is very large. Its main role can be summarised by the words of the Nobel laureate Sir Peter Medawar: no new principle will declare itself from beneath a heap of facts. (A recent good example is the need for interpretation of the results to be expected from the Human Genome Project.) It is timely to distil from the avalanche of observations whatever general principles can be discerned.