The workshop “Spatio-Temporal Dynamics in Ecology” was hosted by the Lorentz Center in the period December 8–12, 2014. It brought together leading scientists working on the interface of Ecology, Mathematics and Physics, who presented the state of the art in population and ecosystem dynamics, as well as in animal behavior. Through these talks and associated discussions, the organizers aimed to outline research areas where cross-fertilization is much needed.

The ecosystem dynamics theme benefited from the combined expertise of established ecologists, mathematical modelers and dynamicists present at the meeting. The presentations covered timely topics such as the prediction of critical transitions and catastrophic phenomena, the intertwining of biodiversity and complexity, the transformative role of data in mathematical practice, and the modeling and analysis of spatial processes across Ecology. The extensive discussions focused on the interplay between field and modeling reality, the integration of fieldwork into mathematical practice, the juxtaposition of universal mechanisms to idiosyncrasies of experimental models and, additionally, the importance of interdisciplinary training and practice for young and aspiring scientists. Many smaller groups also got the opportunity to discuss hands-on work and collaborative projects.

Broadly put, the workshop highlighted a number of trends, as well as of themes where synergy can be mutually beneficial.

1 There is a pressing need to develop mathematical tools that can deal with large ecosystems and vast modeling uncertainties. The coupling of Mathematical Analysis to Statistics and Algebra has major potential to make an impact in that direction.

2 Within the topic of pattern formation, an interesting discussion developed around the topic of wave length changes in regular patterns in a range of ecosystems, in particular around the question whether wave length changes could be used to indicate the decline of resilience in the face of (globally) changing environmental conditions.

3 Mathematical Ecology must account for socio-economic externalities and feedbacks even more than today. The link between Ecology and Climate Science must also be strengthened.

4 There is significant misunderstanding with regard of the use of the term Levy walks to describe animal movements and that there is a need for a paper that clearly outlines the different viewpoints in favor and against the Levy hypothesis, and that provides an overarching perspective that unites the field.

5 Modeling is being transformed by the emergence of agent-based models and computational upscaling. This trend is important, as models at the individual level reflect mechanisms and demographic heterogeneities more transparently.

6 Despite intensive efforts, spatial processes and multi-species interactions remain largely unexplored and poorly understood. Both continue to resonate well with the interests of the dynamic community.

7 Transdisciplinarity and knowledge transfer are necessary to deal with large-scale problems. This highlights the importance of emerging interdisciplinary training networks, as well as of outreach efforts of individual researchers.

The separate meetings held during the workshop were essential to putting together such a helicopter view, as well as to start giving shape to a unified theory. Currently, this breakout group is working on two papers, one of which has reached a first draft version.