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The way in which climate change research funds are managed is shifting dramatically toward investments in large collaborative research networks. This poses significant challenges for researchers, and requires changes from the institutions and funders that support them.

The reality of global climate change demands novel approaches to science that are reflective of the scales at which changes are likely to occur, and of the new forms of knowledge required to positively influence policy to support vulnerable populations. We examine some of the opportunities and challenges presented by a collaborative, transdisciplinary research project on climate change adaptation in Africa and Asia that utilised a hotspot approach. A large scale effort to develop appropriate baselines was a key challenge at the outset of the program, as was the need to develop innovative methodologies to enable researchers to work at appropriate spatial scales. Efforts to match research to the biophysical scales at which change occurs need to be aware of the mismatch that can develop between these regional scales and the governance scales at which decisions are made.

In this paper we generalize to the case of diluted spin models and random combinatorial optimization problems a technique recently introduced by Guerra (cond-mat/0205123) to prove that the replica method generates variational bounds for disordered systems. We analyze a family of models that includes the Viana–Bray model, the diluted p-spin model or random XOR-SAT problem, and the random K-SAT problem, showing that the replica/cavity method, at the various levels of approximation, provides systematic schemes to obtain lower bounds of the free-energy at all temperatures and of the ground state energy. In the case of K-SAT and XOR-SAT it thus gives upper bounds of the satisfiability threshold. Our analysis underlines deep connections with the cavity method which are not evident in the long range case.