Trade-offs among the abilities of organisms to respond to different environmental factors are often assumed to play a major role in the coexistence of species. There has been extensive theoretical study of the role of such trade-offs in ecological communities but it has proven difficult to study such trade-offs experimentally. Microorganisms are ideal model systems with which to experimentally study the causes and consequences of ecological trade-offs. In model communities of E. coli B and T-type bacteriophage, a trade-off in E. coli between resistance to bacteriophage and competitive ability is often observed. This trade-off can allow the coexistence of different ecological types of E. coli. The magnitude of this trade-off affects, in predictable ways, the structure, dynamics and response to environmental change of these communities. Genetic factors, environmental factors, and gene-by-environment interactions determine the magnitude of this trade-off. Environmental control of the magnitude of trade-offs represents one avenue by which environmental change can alter community properties such as invasability, stability and coexistence.
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 interaction 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 interactions. 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.
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.
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