Transient dynamics and food–web complexity in the Lotka–Volterra cascade model

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Abstract
How does the long–term behaviour near equilibrium of model food webs correlate with their short–term transient dynamics? Here, simulations of the Lotka–Volterra cascade model of food webs provide the first evidence to answer this question. Transient behaviour is measured by resilience, reactivity, the maximum amplification of a perturbation and the time at which the maximum amplification occurs. Model food webs with a higher probability of local asymptotic stability may be less resilient and may have a larger transient growth of perturbations. Given a fixed connectance, the sizes and durations of transient responses to perturbations increase with the number of species. Given a fixed number of species, as connectance increases, the sizes and durations of transient responses to perturbations may increase or decrease depending on the type of link that is varied. Reactivity is more sensitive to changes in the number of donor–controlled links than to changes in the number of recipient–controlled links, while resilience is more sensitive to changes in the number of recipient–controlled links than to changes in the number of donor–controlled links. Transient behaviour is likely to be one of the important factors affecting the persistence of ecological communities.

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