Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
Department of Biology, Quebec Centre for Biodiversity Science, McGill University, Montreal, Quebec, Canada.
J Anim Ecol. 2021 Sep;90(9):2027-2040. doi: 10.1111/1365-2656.13421. Epub 2021 Feb 8.
Resilience is broadly understood as the ability of an ecological system to resist and recover from perturbations acting on species abundances and on the system's structure. However, one of the main problems in assessing resilience is to understand the extent to which measures of recovery and resistance provide complementary information about a system. While recovery from abundance perturbations has a strong tradition under the analysis of dynamical stability, it is unclear whether this same formalism can be used to measure resistance to structural perturbations (e.g. perturbations to model parameters). Here, we provide a framework grounded on dynamical and structural stability in Lotka-Volterra systems to link recovery from small perturbations on species abundances (i.e. dynamical indicators) with resistance to parameter perturbations of any magnitude (i.e. structural indicators). We use theoretical and experimental multispecies systems to show that the faster the recovery from abundance perturbations, the higher the resistance to parameter perturbations. We first use theoretical systems to show that the return rate along the slowest direction after a small random abundance perturbation (what we call full recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before losing any species (what we call full resistance). We also show that the return rate along the second fastest direction after a small random abundance perturbation (what we call partial recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before at most one species survives (what we call partial resistance). Then, we use a dataset of experimental microbial systems to confirm our theoretical expectations and to demonstrate that full and partial components of resilience are complementary. Our findings reveal that we can obtain the same level of information about resilience by measuring either a dynamical (i.e. recovery) or a structural (i.e. resistance) indicator. Irrespective of the chosen indicator (dynamical or structural), our results show that we can obtain additional information by separating the indicator into its full and partial components. We believe these results can motivate new theoretical approaches and empirical analyses to increase our understanding about risk in ecological systems.
弹性被广泛理解为生态系统抵抗和从对物种丰度和系统结构产生影响的扰动中恢复的能力。然而，评估弹性的主要问题之一是了解恢复和抵抗力的度量标准在多大程度上提供了关于系统的互补信息。虽然丰度扰动的恢复在动力稳定性分析下具有很强的传统，但尚不清楚同一形式主义是否可用于衡量对结构扰动（例如模型参数扰动）的抵抗力。在这里，我们提供了一个基于Lotka-Volterra 系统中的动力和结构稳定性的框架，将对物种丰度小扰动的恢复（即动力指标）与对任何幅度的参数扰动的抵抗力（即结构指标）联系起来。我们使用理论和实验多物种系统来表明，从丰度扰动中恢复的速度越快，对参数扰动的抵抗力就越高。我们首先使用理论系统表明，在小随机丰度扰动后沿着最慢方向的返回速率（我们称之为完全恢复）与系统在失去任何物种之前所能承受的最大随机参数扰动（我们称之为完全抵抗力）呈负相关。我们还表明，在小随机丰度扰动后沿着第二快方向的返回速率（我们称之为部分恢复）与系统在最多一个物种存活之前所能承受的最大随机参数扰动呈负相关（我们称之为部分抵抗力）。然后，我们使用实验微生物系统的数据集来验证我们的理论预期，并证明弹性的完全和部分组成部分是互补的。我们的研究结果表明，我们可以通过测量动力学（即恢复）或结构（即阻力）指标来获得关于弹性的相同信息量。无论选择的指标是动力学还是结构，我们的结果都表明，我们可以通过将指标分为完全和部分成分来获得更多信息。我们相信这些结果可以激发新的理论方法和经验分析，以提高我们对生态系统风险的认识。
