The right stuff : appropriate mathematics for evolution and development biology

We are looking for the ‘right stuff’, i.e. appropriate mathematical and computational tools/ models for describing, studying, building or understanding fundamental aspects of natural living systems or living systems as-they-could-be (whether carbon-based, digital or otherwise) as opposed to inanimate systems. Classical mathematical methods of population genetics tend to set out a fixed space of possibilities for the evolution of gene frequencies within a population. Unfortunately, by circumscribing the state-space at the outset, such an approach excludes the possibility of expressing change in developmental mechanisms or new evolutionary innovations such as body plans. While differential equation descriptions have proved crucial for understanding physics and chemistry and aspects of evolution, they seem to have largely failed as an appropriate language for some key aspects of biological systems.