Perils of correlating CUSUM-transformed variables to infer ecological relationships

a U.S. Geological Survey, Menlo Park, California bDepartment of Environmental Science and Policy, University of California, Davis, California c National Environmental Research Institute, Aarhus University, Roskilde, Denmark dCenter for Watershed Sciences, and Bodega Marine Laboratory, University of California, Davis, Bodega Bay, California e Romberg Tiburon Center, San Francisco State University, Tiburon, California f Australian Centre for Biodiversity, School of Biological Sciences, Monash University, Victoria, Australia g U.S. Geological Survey, Sacramento, California hJohn Muir Institute of the Environment, Tahoe Environmental Research Center, Watershed Sciences Center, University of California, Davis, California i Leibniz-Institute of Marine Sciences at Kiel University (IFM-GEOMAR), Kiel, Germany