The consecutive Disparity index, D: a measure of temporal variability in ecological studies

Abstract

Temporal variability in ecological processes has attracted the attention of many disciplines inecology, which has resulted in the development of several quantitative indices. The coefficient of variation(CV=standard deviation9mean 1) is still one of the most commonly used indices to assess temporalvariability, despite being known to present several problems on its assessment (e.g., mean dependence orhigh sensitivity to rare events). The proportional variability (PV) index was developed to solve some of theCV's drawbacks, but, so far, no variability index takes into account the chronological order of the values intime series. In this paper, we introduce the consecutive disparity index (D), a temporal variability indexthat takes into account the chronological order of the values, assessing the average rate of change betweenconsecutive values. We used computer simulations and empirical data for fruit production in trees, birdcounts, and rodent captures to compare the behavior ofD, PV, and CV under different scenarios.Dwassensitive to changes in temporal autocorrelation in the negative autocorrelation range, and CV and PVwere sensitive in the positive autocorrelation range despite not considering the chronological order of thevalues. The CV, however, was highly dependent on the mean of the time series, whileDand PV were not.Our results demonstrate that, like PV,Dsolves many of the problems of the CV index while taking intoaccount the chronological order of values in time series. The mathematical and statistical features ofDmake it a suitable index for analyzing temporal variability in a wide range of ecological studies.