Table 1.

Comparison of methods available for assessing cross-scale structures necessary for studying systemic vulnerabilities to global change

Method	Data sets	Advantages	Limitations
Discontinuity analyses (GRI, CA, CART, BCART, KDE)	Univariate, rank-ordered, log-transformed data (e.g., body size or mass)	Data easy to obtain either from available sources or through measurement	Species dominance patterns not explicitly accounted for
		Simple assessment of non-linear (scale-specific) structures in data	Resilience assessment limited to the evaluation of cross-scale patterns
			Limiting assessment of ultimate factors causing discontinuities
Time series and spatial modeling (Canonical ordinationsa,b; wavelet analysesc)	Multivariate; species abundance, biomass and/or presence–absence data	Species abundances accounted for	Data acquisition labor intensive, high resource demand
		Separating the role of dominant and rare species	Higher analytical complexity relative to discontinuity analysis
		Evaluation of complementary aspects of resilience and adaptive capacity	Scales and patterns of structure contingent on sampling frequency and length
		Relating patterns to dynamic environmental change	Limited availability of adequate long-term data

GRI gap rarity index, CA cluster analysis, CART classification and regression trees, BCART Bayesian CART, KDE Kernel density estimates (see text)

^aAngeler et al. (2009), an example for time series modeling

^bDray et al. (2006), showing the modeling framework for assessing spatial resilience

^cKeitt and Fischer (2006), time series modeling