  We discuss the role and merits of symmetry methods for the analysis of
biological systems. In particular, we consider systems of first order ordinary
differential equations and provide a comprehensive review of the geometrical
foundations pertinent to symmetries of such systems. Subsequently, we present
an algorithm for finding infinitesimal generators of symmetries for systems
with rational reaction terms, and an open-source implementation of the
algorithm using symbolic computations. We discuss two complementary
perspectives on symmetries in mechanistic modelling; as tools for the analysis
of a given model or as a geometrical principle for incorporating biological
properties in the construction of new models. Through numerous examples of
relevance to modelling in biology we demonstrate the different uses of symmetry
methods, and also discuss how to infer symmetries from experimental data.
