Table 1:

Representative overview of current quantitative analyses of the core aspects of panarchy and the goal and context in which they have been applied. Examples are supported with references.

Panarchy aspect	Methods	Goal	Application	References
Adaptive cycle (single scale)
	Analysis of variance	Detecting adaptive cycle phases	Assessing shifting systems controls	Angeler et al., 2015a
	QtAC framework	Quantifying the adaptive cycle	Assessing system potential, connectedness and resilience	Schrenk et al., 2022
	Early warning signals	Detecting erosion of resilience	Regime shift detection	Dakos et al., 2015
Scaling patterns (multiple scales)
	Discontinuity analysis	Snapshot or time/space-implicit detection of scale-variant system structure	Regime shift detection Assessing dynamic system structure Spatial regime detection and regime migration	Spanbauer et al., 2016 Garmestani et al., 2009 Roberts et al., 2019
	Time series and spatial analysis based on canonical ordination	Detection of time-explicit dynamic scaling structure and spatial scaling patterns	Regime shift detection Ecosystem vulnerability assessment Detecting “parallel dimensions” in time and space	Spanbauer et al., 2014 Angeler et al., 2015b Angeler and Hur, 2023 Angeler et al., 2015c
	Fisher information	Detection of spatial/temporal transitions	Regime shift detection	Sundstrom et al., 2017 Eason et al., 2016
	Wombling	Spatial scale transitions	Regime shift detection	Roberts et al., 2022
	Fractal dimension analysis	Detection of scale and scale invariance	Detecting shifts of system control and feedbacks	Gunderson, 2008
Information flow
	Correlation analysis	Implicit, patterns-based inference of information flow	Ecosystem restoration and mitigation	Angeler and Hur, 2023
	Network analyses	Assessing cross-scale contributions of individual habitats to overall system connectivity	Landscape planning, management and measurement	Cumming et al., 2022
	Network causal loop diagrams	Information flow as “domino effects”	Cascading regime shifts	Rocha et al., 2019
	Multi-model analysis	Information flow inferred based on connectivity (static)	Teleconnection of spatial regimes	Heino et al., 2020
	Stoichiometric analyses	Assessing fluxes and metabolism	Matter flow in food webs	Welti et al., 2017
	Multi-state modeling	Dynamic information flow	Organism dispersal	Calvert et al., 2009