**Preface to "Partial Differential Equations in Ecology: 80 Years and Counting"**

Application of partial differential equations (PDEs) in ecology has a long history dating back to 1937. It was at this time that Ronald Fisher and Andrey Kolmogorov et al., through their research on the spread of an advantageous gene, discovered the travelling wave solution of a scalar diffusion-reaction equation. Fifteen years later, Alan Turing's work on chemical morphogenesis demonstrated that, due to diffusive instability, a system of two coupled PDEs gives rise to pattern formation: an interesting result that was later shown to have a variety of ecological applications. These seminal papers led to an outbreak of research on all aspects of the population dynamics in space and time using PDEs of the diffusion-reaction type. Nowadays, on appropriate spatial and temporal scales, PDEs remain a fully relevant and powerful modelling framework; they are widely used both to bring new light to old problems and to gain insight into new ones. This volume, originally published as a Special Issue of *Mathematics*, presents a small collection of specially selected papers and aims to highlight the current role of PDE-based models in ecology and population dynamics. A variety of models is used, including traditional reaction-diffusion equations, cross-diffusion, the Cahn–Hilliard equation, among others, and a broad range of problems is addressed.

> **Sergei Petrovski** *Editor*
