Using the angle frequency method to detect signals of competition and predation in experimental time series

Gunnar Sandvik,* Christine M. Jessup, Knut L. Seip and Brendan J. M. Bohannan Department of Environmental Technology, Høgskolen i Telemark, Porsgrunn, Norway Department of Biological Sciences, Stanford University, Stanford, CA, USA *Correspondence: E-mail: [email protected]; [email protected] Abstract Identifying interactions among organisms is central to the study of ecology. The Angle Frequency Method (AFM) allows the detection of interactions in time series data. The AFM takes pairwise data plotted in phase diagrams and identifies signals (vector directions in phase diagrams) associated with particular interactions. Using microbial experimental systems consisting of predators (bacteriophage T4) and prey/competitors (strains of Escherichia coli), we demonstrate that the AFM can identify predator–prey and competitive interactions. The level of control afforded by such microbial experimental systems allows direct tests of the utility and robustness of the AFM. Signals of predation were distinct from signals of competition, with the strongest signal of predation corresponding to the collapse of the predator population at low prey densities. Signals of competition reflected the difference in competitive strength between the superior and the inferior competitors. In addition, the effects of invasion and resource enrichment on interactions in the laboratory communities were detectable using the AFM. Our analyses support results from model simulations and analyses of lake time series by identifying similar sets of signals characteristic of predation and competition, and demonstrate that the AFM is an effective tool in rigorous studies of time series.