Some guidance on using mathematical notation in ecology

Abstract

Mathematical modelling is playing an increasing role in studies of ecological systems. This requires the communication of the details of a mathematical model, including the use of mathematical notation to represent ecological variables, parameters and processes. In our experience, the clarity of mathematical notation varies between papers and can often be inconsistent with general conventions. Poor notation can impede communication and understanding of ideas, and make models appear more complicated than necessary. Here, we present some guidelines, including: (a) define every term in an equation, (b) use fonts appropriately (italicise mathematical symbols, use bold lower case for vectors and bold upper case for matrices), (c) use subscripts appropriately (to index quantities, for example, by year), (d) use superscripts appropriately (to indicate a power, the transpose of a matrix or the steady-state value of a quantity), (e) avoid multiletter variable names, and (f) revisit notation early on in a project to see if it should be refined. Although we focus mainly on ecology, our guidelines should be of interest to researchers applying models in evolutionary biology and broader areas of biology.