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The Lambert W function in ecological and evolutionary models
Author(s) -
Lehtonen Jussi
Publication year - 2016
Publication title -
methods in ecology and evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.425
H-Index - 105
ISSN - 2041-210X
DOI - 10.1111/2041-210x.12568
Subject(s) - lambert w function , function (biology) , range (aeronautics) , mathematical model , computer science , ecology , mathematics , statistics , biology , mathematical analysis , materials science , evolutionary biology , composite material
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.