Figure 1.

Examples of quantitative definitions of resistance and resilience from ecology (Westman, 1978; Orwin and Wardle, 2004; Suding et al., 2004). A microbial community parameter of interest has a mean value of y₀ and temporal variance, illustrated here by a 95% confidence interval around the mean (though other quantifications of variance, such as standard deviation or variance ratios may be used). A pulse disturbance ends (or a press disturbance begins) at time t₀ and the parameter changes by |y₀ − y_L| after a time lag t_L − t₀. Resistance (RS) is an index of the magnitude of this change.

$$RS=1-\frac{2\left|y_0-y_L\right|}{y_0+\left|y_0-y_L\right|}$$ (1)

Resilience (RL) is an index of the rate of return to y₀ after the lag period,

$$RL=\left[\frac{2\left|y_0-y_L\right|}{\left|y_0-y_L\right|+\left|y_0-y_n\right|}-1\right]÷\left(t_n-t_L\right)$$ (2)

where y_n is the parameter value at measurement time t_n. A parameter is “recovered” when it is statistically indistinguishable from the pre-disturbance mean. Alternatively, the parameter may not recover and instead may stabilize at a new mean value representing an alternative stable state. This possibility is more likely in response to a press disturbance. Further, RS and RL could be related to normalized parameters describing the disturbance (e.g., intensity, duration, frequency of the stressor in relation to the pre-disturbance mean and variance), which is useful for cross-system comparisons.