We develop new mathematical, statistical and computational methods for theoretical ecology. The main areas we cover are:
- Ecological networks: species in ecological communities form tangled networks of ecological interactions. These networks differ from other social and technological networks in that the nodes are all different (i.e., they represent different species), rather than being of the same “type”.
- Spectral methods: we want to characterize ecological networks using the eigenvalues and eigenvectors associated with their adjacency and Laplacian matrices. In this way, we can study very large food webs and other ecological networks.
- Models for food web structure: given a series of balls and arrows, can we construct a network that resembles empirical ones? What are the “rules” we should follow? How can we evaluate the “goodness” of these models?
- Stability of large ecological systems: using Random Matrix Theory, we can study the large-scale behavior of ecological communities.
- Response to extinctions: when species go extinct, what happens to the other species in the community?
- Science of science: can we study the scientific endeavor using the same tools we develop for other complex systems? How shall we evaluate the impact of researchers? How shall we fix the peer-review algorithm?