Mathematical Perspectives on Rewilding

Achieving sustainable human-wildlife coexistence in well-functioning ecosystems is a vitally important and major challenge under global change. In response, rewilding is an emerging paradigm in ecosystem service provision through the re-establishment of natural ecological processes in self-sustaining ecosystems. Effective prediction of ecological changes in rewilding projects requires tools integrating quantitative methods with social-economic dimensions and thinking. We consider the current state of such quantitative treatments, highlighting opportunities for harnessing mathematics and statistics. We present an emerging quantitative framework, encompassing four key areas of the rewilding process: design and planning, ecological modelling, metrics for assessment, and coupled social-ecological systems, informed by recent progress in mathematical, statistical, and ecological modelling. The adaptive cycle concept is used to integrate these four key areas. Dynamical systems modelling informed by empirical knowledge allows us to address trans-disciplinary feedbacks, nonlinearities, and anticipate the potential for emerging properties and critical transitions/regime shifts during rewilding, predicting the range and likelihood of alternative scenarios. Our framework provides a possible foundation and new opportunities for a more robust quantitative and predictive methodology for rewilding. We argue that a project is more likely to achieve its goals, and in a more cost-effective way, if mathematical scientists are included from the beginning.