Manuscript Topics

Mathematical ecology is a wide-ranging field of research that uses mathematical models, computational methodologies, and various other approaches (e.g. methods of data science where relevant) to tackle ecological challenges encountered in the real world. Mathematical modelling allows the creation of a virtual laboratory where hypotheses about population dynamics on various spatial and temporal scales can be tested comprehensively, safely, and cost-effectively. Originating in the seminal works by Lotka, Volterra, and Gause, mathematical ecology as a science has reached the stage of maturity over the last two decades. Mathematical modelling has become a standard part of the theoretical ecologist’s toolbox. It is widely used in highly theoretical studies (“blue-sky” research) and in more specific studies aiming to inform ecosystem management. Mathematical modeling approaches were particularly successful in studies on critical transitions in ecosystems, vegetation spatial patterns, biological invasions, and food webs, to name just a few.

Modern times have brought new challenges. Global environmental change has placed ecosystems under increasing stress, affecting all aspects of population dynamics. Progress in methods of collecting ecological data (e.g., based on relevant technological advances) has brought vast amounts of new data of better quality and higher resolution. It has also been increasingly recognized that classical modelling approaches and standard mathematical tools, although still efficient in many cases, are not always sufficient, as they cannot capture the true complexity of the system’s properties and dynamics. Correspondingly, the focus of research has been shifting towards more advanced mathematical approaches; examples are given by weakly nonlinear analysis, methods of time scale separation, nonlocal/fractal models, non-autonomous systems, etc.

The primary objective of this special issue is to offer a comprehensive overview of the forefronts in mathematical ecology. It aims to cover classical modelling methodologies alongside newer and/or more advanced approaches to confront emerging challenges within the field. We encourage submissions of studies concentrating on specific ecosystems or specific phenomena as well as more abstract theoretical papers. Articles based on rigorous mathematical analysis, as well as those primarily reliant on simulations, will be given full consideration. The primary criteria for evaluation depend on the novelty and significance of the ecological issue being addressed.

Topics covered include but not limited to:
• population dynamics under climate change
• extinctions, especially those resulting from environmental change
• nature conservation and rewilding
• multiscale models of ecosystems and population dynamics
• slow-fast systems
• non-autonomous models of population dynamics
• critical transitions, tipping points, and long transients
• biological invasions
• coupled social-ecological systems
• spatiotemporal complexity and pattern formation

Keywords:
Population dynamics, extinctions, climate change, biological conservation, rewilding, slow-fast systems, multiscale systems, complexity, tipping points, critical transitions, long transients, non-autonomous systems, socio-ecological systems, biological invasions, ecological pattern formation

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