Resilience assessment in complex natural systems

Ecological resilience is the capability of an ecosystem to maintain the
same structure and function and to avoid crossing catastrophic tipping
points (i.e. irreversible regime shifts). While fundamental for
management, concrete ways to estimate and interpret resilience in real
ecosystems are still lacking. Here, we develop an empirical approach to
estimate resilience based on the stochastic cusp model derived from
catastrophe theory. The cusp model models tipping points derived from a
cusp bifurcation. We extend cusp in order to identify the presence of
stable and unstable states in complex natural systems. Our Cusp Resilience
Assessment (CUSPRA) has three characteristics: i) it provides estimates on
how likely a system is to cross a tipping point (in the form of a cusp
bifurcation) characterized by hysteresis, ii) it assesses resilience in
relation to multiple external drivers, and iii) it produces
straightforward results for ecosystem-based management. We validate our
approach using simulated data and demonstrate its application using
empirical time-series of an Atlantic cod population and of marine
ecosystems in the North Sea and the Mediterranean Sea. We show that CUSPRA
is a powerful method to empirically estimate resilience in support of a
sustainable management of our adapting ecosystems under global climate
change.

生态韧性（Ecological resilience）指生态系统维持自身结构与功能、避免跨越灾难性临界点（即不可逆生态状态转变）的能力。尽管其对生态管理至关重要，但目前仍缺乏可用于实际生态系统中估算与解读韧性的具体方法。本研究基于突变理论衍生的随机尖点模型，开发了一种估算生态韧性的实证方法。该尖点模型针对由尖点分岔（cusp bifurcation）得到的临界点进行建模，我们对尖点模型进行拓展，以识别复杂自然系统中的稳定与不稳定状态。我们提出的尖点韧性评估模型（Cusp Resilience Assessment, CUSPRA）具备三大特征：其一，可针对以滞后效应为特征的尖点分岔型临界点，估算系统跨越临界点的概率；其二，能够结合多重外部驱动因子评估生态韧性；其三，可为基于生态系统的管理提供直观易懂的分析结果。本研究通过模拟数据对该方法进行验证，并利用大西洋鳕鱼种群、北海及地中海海洋生态系统的实证时间序列数据展示其应用场景。研究结果表明，CUSPRA是一种有效的实证韧性估算方法，可为全球气候变化背景下动态适应中的生态系统可持续管理提供支撑。