Systems approaches have great potential for application in predictive ecology. In this paper, we present a range of examples, where systems approaches are being developed and applied at a range of scales in the field of global change and biogeochemical cycling. Systems approaches range from Bayesian calibration techniques at plot scale, through data assimilation methods at regional to continental scales, to multi-disciplinary numerical model applications at country to global scales. We provide examples from a range of studies and show how these approaches are being used to address current topics in global change and biogeochemical research, such as the interaction between carbon and nitrogen cycles, terrestrial carbon feedbacks to climate change and the attribution of observed global changes to various drivers of change. We examine how transferable the methods and techniques might be to other areas of ecosystem science and ecology.

We show that the geometric phase between any two states, including orthogonal states, can be computed and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase change in an infinitesimal loop near an orthogonal state. Also, the Pancharatnam phase change during the passage through an orthogonal state is shown to be either π or zero (mod 2π). All the off-diagonal geometric phases can be obtained from the projective geometric phase calculated with our generalized connection.