Quantifying resilience to recurrent ecosystem disturbances using flow–kick dynamics

Katherine Meyer (), Alanna Hoyer-Leitzel, Sarah Iams, Ian Klasky, Victoria Lee, Stephen Ligtenberg, Erika Bussmann and Mary Lou Zeeman
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Katherine Meyer: University of Minnesota
Alanna Hoyer-Leitzel: Mount Holyoke College
Sarah Iams: Harvard University
Ian Klasky: University of Colorado
Victoria Lee: Bowdoin College
Stephen Ligtenberg: Bowdoin College
Erika Bussmann: Minnetonka High School
Mary Lou Zeeman: Bowdoin College

Nature Sustainability, 2018, vol. 1, issue 11, 671-678

Abstract: Abstract Shifting ecosystem disturbance patterns due to climate change (for example, storms, droughts and wildfires) or direct human interference (for example, harvests and 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 continual noise, quantifying resilience to repeated, discrete disturbance events requires different analytical tools. Here, we introduce a mathematical flow–kick framework that uses dynamical systems tools to quantify resilience to disturbances explicitly in terms of their magnitude and frequency. We identify a boundary between disturbance regimes that cause either escape from, or stabilization within, a basin of attraction. We use the boundary to define resilience metrics tailored to repeated, discrete perturbations. The flow–kick model suggests that the distance-to-threshold resilience metric overestimates resilience in the context of repeated perturbations. It also reveals counterintuitive triggers for regime shifts. These include increasing the periods between disturbance events in proportion to increases to disturbance magnitude, and—in systems with multiple dynamic variables—increasing time periods between disturbances of constant magnitude.

Date: 2018
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DOI: 10.1038/s41893-018-0168-z

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