Dynamically generated variability in plant-pathogen systems with biological control

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Abstract
Using a combination of replicated microcosm experiments, simple nonlinear modelling and model fitting we show that unexpected levels of variability can be detected and described in the dynamics of plant disease. Temporal development of damping-off disease of radish seedlings caused by an economically important plant pathogen, Rhizoctonia solani, is quantified, with and without the addition of an antagonistic fungus, Trichoderma viride. The biological control agent reduces the average amount of disease but also greatly enhances the variability among replicates. The results are shown to be consistent with predictions from a nonlinear model that exhibits dynamically generated variability in which small differences in the initiation of infection associated with the antagonist are later amplified as the pathogen spreads from plant to plant. The effect of dynamically generated variability is mediated by the interruption of transient disease progress curves for separate replicates by an exponential decrease in susceptibility of the host over time. The decay term essentially 'freezes' the dynamics of the transient behaviour so that the solutions for different replicates settle on asymptotes that depend on initial conditions and parameter values. The effect is further magnified by nonlinear terms in the infection force in the models. A generalization of the Lyapunov exponent is introduced to quantify the amplification. The observed behaviour has profound consequences for the design and interpretation of ecological experiments, and can also account for the notorious failure of many biological control strategies through the creation of `hot spots', created by the amplification of plant to plant infection, where the control by the antagonist is locally unsuccessful.

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