Traditional theoretical ecology describes low-dimensional patterns (few species, few traits...) used as archetypes for intuition. Network models combine many such patterns into more complex systems, but this comes with hard empirical challenges: predictions are sensitive to the whole structure of species interactions, and this structure is difficult to measure precisely and exhaustively.

New approaches, inspired by statistical mechanics, try to make more general predictions on these high-dimensional systems. The underlying assumption is that large systems that have emerged through many concurrent processes, rather than being precisely designed (or co-evolved), tend to exhibit only properties that are most robust to changes in structure. Such robust properties can easily be captured in null models such as random interactions, stochastic dynamics, etc. Hence a different, collective kind of simplicity appears at the other end of complexity.

Our questions are:

• Under which conditions is this sort of emergent simplicity found in theoretical and empirical ecosystems?
  
• Can we probe such high-dimensional properties, measure them, see them reflected in ecosystem stability?
  
• In which ways must we deviate from this simple limit to better understand real systems? How can we combine low-dimensional structures and high-dimensional robustness?