Quantifying temporal variability in population abundances

Understanding variability of population abundances is of central concern to theoretical and applied evolutionary ecology, yet quantifying the conceptually simple idea has been substantially problematic. Standard statistical measures of variability are particularly biassed by rare events, zero counts and other ‘non-Gaussian’ behaviour, which are often inappropriately weighted or excluded from analysis. I conjecture that these problems are primarily a function of calculating variation as deviation from an average abundance, while the average may not be static, nor actually reflect abundance at any point in the time series. Here I describe a simple metric (population variability PV) that quantifies variability as the average percent difference between all combinations of observed abundances. Zero counts can be included if desired. Similar to standard metrics, variability is measured on a proportional scale, facilitating comparative applications. Standard metrics are based on Gaussian distributions, are over-sensitive to rare events and heavy tailed behaviour, and can inappropriately indicate ‘more time-more variation’ effects (reddened spectrum). Here I demonstrate that, while PV behaves similarly for ‘normal’ time series, it is independent of deviation from mean abundance for heavy tailed distributions, its robustness to non-Gaussian behaviour resolves artificial reddened spectrum issues, and variability calculated using PV from short time series is substantially more accurate at estimating known long term variability than standard metrics. PV therefore provides common ground for evaluating the variability of populations undergoing different dynamics, and with different statistical distributions of abundance, and can be easily generalized to a variety of contexts and disciplines.