An anatomy of interactions among species in a seasonal world

species in a seasonal world. – Oikos 99: 260–271. Mathematical models merging biological and predictable seasonal dynamics were used to simulate four types of organism interactions: competition, prey-predation, mutualism and facilitation. By analysing trajectories for biomass in phase portraits (i.e. species 1 biomass plotted against species 2 biomass) graphically and numerically, we found that each of the four interaction types showed characteristic patterns (‘‘fingerprints’’) in phase space. All the four interaction types could be distinguished, even though their time trajectories were strongly modified by seasonal forces. For each of the interaction types, we were able to identify characteristics of the interac-tion that most strongly distinguished it from the others. We could also assess the relative effect of species characteristics and seasonality on each of the four interac-tions. The simulations indicate that prey-predation is strongly influenced by seasonal forces and by the characteristics of the predator and its prey. A system variability index got a high value (SVI)=0.167 relative to those of the other interaction types (competition 0.01, mutualism 0.007 and facilitation 0.005). The result was obtained by calculating angles between successive vectors linking pairs of samples and the positive x-axis and arranging these as frequency histograms for each of the four quadrants of the phase portrait. In an effort to capture circular motions and other characteristics of the trajectories sampled, angle frequencies were analysed using multivariate statistics (PCA), yielding ‘‘characteristic directions’ ’ in phase space. We believe that the characteristic patterns identified also will be found in real time series