  Shifting ecosystem disturbance patterns due to climate change (e.g. storms,
droughts, wildfires) or direct human interference (e.g. harvests, nutrient
loading) highlight the importance of quantifying and strengthening the
resilience of desired ecological regimes. Although existing metrics capture
resilience to isolated shocks, gradual parameter changes, and continuous noise,
quantifying resilience to repeated, discrete disturbances requires novel
analytical tools. Here we introduce a flow-kick framework that quantifies
resilience to disturbances explicitly in terms of their magnitude and
frequency. We present a resilience boundary between disturbances that cause
either escape from a basin of attraction or stabilization within it, and use
the resilience boundary to build resilience metrics tailored to repeated,
discrete disturbances. The flow-kick model suggests that the
distance-to-threshold resilience metric overestimates resilience in the context
of repeated disturbances. It also reveals counterintuitive triggers for regime
shifts, such as increasing recovery times between disturbances, or increasing
disturbance magnitude and recovery times proportionately.
