The world is losing species at an increasing pace. It is therefore extremely important to be able to forecast how extinctions will impact ecosystems services. Conservation and restoration efforts are well underway. The main problem is to decide how to allocate resources, which species to conserve, and how to proceed with the restoration plans. These problems have been attacked with a variety of tools. Species, however, are not isolated entities, but rather they are embedded in a complex network of relations with other species and non-living components of the ecosystem. A network approach -- that takes into account species in their context-- is required.
Molecular biologists study how a gene works in an organism by switching it off; engineers try to replicate the functioning of a device by taking it apart and studying how its components are wired together; archaeologists reconstruct ancient machinery by examining fragments buried for centuries. These are all examples of reverse engineering. This approach is usually precluded to ecologists given the potentially dramatic consequences of disturbing ecosystems, except in mathematical models and `in silico' (performed on computer) simulations of scenarios.
I intend to study the patterns of extinctions in ecological networks using mathematical and simulation models. The ultimate goal is to detect which are the important characteristics for the robustness of ecological networks by taking them apart. This would help us associate an "extinction risk" not only to species, but to ecosystems as well and help us understand how to restore ecological networks so that they are robust to extinctions.
An example of such an approach is represented in the figure below. It shows the special importance of particular species in maintaining a connected and working food web. On the left is the food web of the Chesapeake Bay ecosystem. This network describes who eats whom in the system. On the right is the corresponding dominators tree. This simple network maps who depends on whom for survival. In fact, the extinction of any species cascades in the extinction of all the species that depend on it. The dominators tree representation makes this dynamic evident. If species 9 goes extinct, so do 21 and 22.
Project Page 
Interview with Stefano Allesina  November 11, 2009, Jai Ranganathan's Voyage of the Beagle podcasts - Using Google to Understand Complex Ecosystems