Lynn Govaert, Emanuel A. Fronhofer, Sébastien Lion, Christophe Eizaguirre, Dries Bonte, Martijn Egas, Andrew P. Hendry, Ayana De Brito Martins, Carlos J. Melián, Joost A. M. Raeymaekers, Irja I. Ratikainen, Bernt-Erik Saether, Jennifer A. Schweitzer, Blake Matthews

1. Theoretical models pertaining to feedbacks between ecological and evolutionary processes are prevalent in multiple biological fields. An integrative overview is currently lacking, due to little crosstalk between the fields and the use of different methodological approaches. 2. Here we review a wide range of models of eco-evolutionary feedbacks and highlight their underlying assumptions. We discuss models where feedbacks occur both within and between hierarchical levels of ecosystems, including populations, communities, and abiotic environments, and consider feedbacks across spatial scales. 3. Identifying the commonalities among feedback models, and the underlying assumptions, helps us better understand the mechanistic basis of eco-evolutionary feedbacks. Eco-evolutionary feedbacks can be readily modelled by coupling demographic and evolutionary formalisms. We provide an overview of these approaches and suggest future integrative modelling avenues. 4. Our overview highlights that eco-evolutionary feedbacks have been incorporated in theoretical work for nearly a century. Yet, this work does not always include the notion of rapid evolution or concurrent ecological and evolutionary time scales. We discuss the importance of density- and frequency-dependent selection for feedbacks, as well as the importance of dispersal as a central linking trait between ecology and evolution in a spatial context.