Variation cascades: resource pulses and top-down effects across time scales.

Top-down and bottom-up theories of trophic control have been fundamental to our understanding of community dynamics and structure. However, most ecological theories have focused on equilibrium dynamics and do not provide predictions for communities' responses in temporally fluctuating environments. By deriving the frequency response of populations in different trophic communities, we extend the top-down and bottom-up theories of ecology to include how temporal fluctuations in potential primary productivity percolate up the food chain and are re-expressed as population variability. Moreover, by switching from a time-based representation into the frequency domain, we provide a unified method to compare how the time scale of perturbations determines communities' responses. At low frequencies, primary producers and secondary consumers have the highest temporal variability, while the primary consumers are relatively stable. Similar to the Exploitation Ecosystem Hypothesis, top-down effects drive this alternating pattern of variability. We define the top-down effect of consumers on the variability of lower trophic levels as a variation cascade. However, at intermediate frequencies, variation cascades can amplify temporal variation up the food chain. At high frequencies, variation cascades weaken, and fluctuations are attenuated up the food chain. In summary, we provide a novel theory for how communities will respond to fluctuations in productivity, and we show that indirect species interactions play a crucial role in determining community dynamics across the frequency spectrum.