Progress in the mathematical modelling of developmental processes in biological systems, since publication of <i>On Growth and Form</i> by D’Arcy W. Thompson

In his renowned book On Growth and Form, first published in 1917, D’Arcy Wentworth Thompson stressed the significance of physical laws and mechanisms in determining the development of form and pattern in living organisms. This was at variance with the view held by the majority of his contemporaries in Biology, that natural selection and evolution were the primary factors involved in driving these processes. This disparity of views was understandable in Thompson’s day, given that most biologists of the time were (at least implicitly) vitalists.Now, given a general acceptance that the phenomena of life are subject to the laws of physics and chemistry, Thompson’s ideas are seen as complementary to the processes of evolution by natural selection. Yet, Thompson’s viewpoint still finds itself marginal to present day thinking in developmental biology, in that his ideas emphasise the significance of physical, more than biochemical and genetic processes. In particular On Growth and Form highlights the role of minimisation principles, and of formal symmetries of one type or another in developmental phenomena. Although these are manifestly of great significance to a full understanding of developmental systems, such principles are still not central to the attention of experimentalists in mainstream research.I conclude that Thompson, in the early 20th Century, could not quantify biology, because neither enough biology, nor enough of the underlying physics and chemistry, were yet understood. Even if they had been, the mathematical tools available at the time were inadequate. The real revolution has come with the advent of high performance computing, enabling the complexities with which Thompson aspired to grapple, to be studied meaningfully