GoKawiilHere we develop an approach for predicting temporal stability and resilience from their resistance and recovery components. We began by considering a common measure of temporal stability, the inverse of the coefficient of variation, and defined similar measures of resistance, recovery and resilience that are also the inverse of a deviation. Given that the predicted relationships between integrated measures of stability (that is, temporal stability and resilience) and their component measures of stability (that is, resistance and recovery) will depend on the measures used, we also defined a second set of stability measures as the complement, rather than the inverse, of a deviation. We then showed how temporal stability and resilience can be predicted from their resistance and recovery components, and how resistance can be forecasted from monitoring temporal stability. After generating these new theoretical predictions, we empirically tested them with data from the world’s longest-running biodiversity experiment, allowing us to consider stability at both the ecosystem and the species levels.
Defining two sets of stability measures
We defined temporal stability (also known as invariability) with a common measure, the inverse of the coefficient of variation (CV; D1 in Table 1):
$${I}_{1}\equiv \frac{\mu }{\sigma }=\frac{1}{\mathrm{CV}},$$
and we similarly defined resistance (D2 in Table 1):
$${\Omega }_{1}\equiv \frac{\bar{{Y}_{n}}}{|\bar{{Y}_{n}}-{Y}_{e}|},$$
and recovery (D3 in Table 1):
$${\Delta }_{1}\equiv |\frac{\bar{{Y}_{n}}-{Y}_{e}}{\bar{{Y}_{n}}-{Y}_{e+1}}|,$$
with measures from our previous related work3. We similarly defined resilience (sensu proximity to unperturbed levels after a perturbation5,6,7,8,9,10) as (D4 in Table 1):
$${\Phi }_{1,x}\equiv \frac{\bar{{Y}_{n}}}{|\bar{{Y}_{n}}-{Y}_{e+x}|}.$$
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