Assessing the relationship between biodiversity and stability of ecosystem function--is the coefficient of variation always the best metric?

Abstract

The role of biodiversity in regulating the stability of ecosystem functioning has importance for the reliable delivery of ecosystem services. To date, ecological studies that aim to measure stability in ecosystem function across a range in diversity have almost universally used the coefficient of variation (CV, the ratio of standard deviation (SD) of functional response to its mean), or its inverse 1/CV, in reaching conclusions. We argue that the use of CV for this purpose can lead to misleading conclusions on stability. We consider that defining the stability of ecosystem functioning solely in terms of the CV confines the term stability to a usage and context that is not natural or intuitive to many who wish to address questions about the reliability with which ecosystems deliver services. We use illustrative scenarios to show that an assessment of stability based on the CV is not as effective in many cases as one based on joint consideration of mean and standard deviation, and may be completely misleading, especially where low values of functional response are a desirable outcome. Faced with similar questions, agronomic studies that aim to assess the stability of ecosystem function (comparison of yield of different varieties within and across different sites) take both the average response and variability within-and between-sites into consideration. We argue that the way stability is measured should be appropriate for the questions about the delivery of ecosystem services that are being addressed. We suggest approaches based on the joint modelling of the mean and standard deviation as a basis for addressing questions of biodiversity and stability of ecosystem function. Assessment of the importance of diversity in providing ecosystem services for society is more likely to be made on socioeconomic evaluation of trade-offs between mean and variability of the function rather than its stability as measured by the coefficient of variation.

The relative importance of pollinator abundance and species richness for the temporal variance of pollination services

“…), the CV is not always a good indicator of stability because it conflates how mean ES and temporal variance of ES respond to the same environmental changes (Carnus et al. ). In addition, the CV of ES cannot be expressed as a sum of independent species‐level contributions and thus a broadly applicable Price equation partition is not possible, although versions can be developed for particular cases (see Fox : Supplementary Material for details).…”

Stability of grassland production is robust to changes in the consumer food web

“…The changes in the mean and variability of aboveground production observed in the current study also may impact a host of other ecosystem processes, such as secondary production, carbon sequestration and material cycling. More generally, this work highlights the unique insights arising from separately examining the responses of mean and variability of ecosystem functions to changes in environmental conditions in addition to scaled indices of stability (Hector et al 2010;Carnus et al 2014;Hautier et al 2014).…”

“…Yet both the amount of and temporal fluctuation in functions such as total carbon captured, nutrients cycled, secondary production, and biomass can be vastly different, leading to completely different functioning of the communities (Carnus et al . ). Furthermore, some ecosystem functions are highly variable (e.g.…”

“…In biodiversity research, stability of a function is often measured as the inverse coefficient of variation (or CV À1 , the square root of the variance of the function scaled by its mean over time) to indicate the function's temporal constancy. While such a scaled response makes it easier to compare different communities (Cottingham et al 2001), its sole use to examine effects of environmental variation on stability of ecosystem functions can conflate the separate responses of mean and variability to various drivers (Hector et al 2010;Gross et al 2013;Carnus et al 2014;Hautier et al 2014). For instance, two plant communities with vastly different primary production can have very similar stability (or CV) if the variability scales with the mean.…”

“…For instance, two plant communities with vastly different primary production can have very similar stability (or CV) if the variability scales with the mean. Yet both the amount of and temporal fluctuation in functions such as total carbon captured, nutrients cycled, secondary production, and biomass can be vastly different, leading to completely different functioning of the communities (Carnus et al 2014). Furthermore, some ecosystem functions are highly variable (e.g.…”