The Lambert W function in ecological and evolutionary models

Summary The Lambert W function is a mathematical function with a long history, but which was named and rigorously defined relatively recently. It is closely related to the logarithmic function and arises from many models in the natural sciences, including a surprising number of problems in ecology and evolution. I describe the basic properties of the function and present examples of its application to models of ecological and evolutionary processes. The Lambert W function makes it possible to solve explicitly several models where this is not possible with elementary functions. I present examples of such models from existing literature, as well as novel models. Solving models explicitly with the Lambert W function can provide deeper insight and a new point of view on a biological problem. Explicit solutions with the Lambert W function are easily amenable to further mathematical operations, such as differentiation and integration. These advantages apply to a wide range of models, from the marginal value theorem to population growth rates and disease epidemics.