Quantifying Proportional Variability

Heath, Joel P.; Borowski, Peter

doi:10.1371/journal.pone.0084074

Cited by 19 publications

(21 citation statements)

References 15 publications

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“…differs from the original one written in Heath () because there was a mistake calculating the number of combinations (an unnecessary factorial), further corrected in Rouyer et al. () and Heath and Borowski (). It is, therefore, an index restricted to values between 0 (minimum) and 1 (maximum variability, only achieved when time series are of length 2 and one of its values is 0).…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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

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Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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“… Properties of the indices are based on (Fernández‐Martínez et al., 2018; Heath, 2006; Heath & Borowski, 2013) and our results. …”

Section: Temporal Variability: Why We Need Alternative Measures To CVmentioning

confidence: 51%

“…The use of CV as a measure of temporal variability has been debated for decades in various fields of science and even in masting literature itself (Crone et al., 2011; Fernández‐Martínez et al., 2018; Heath, 2006; Martín‐Vide, 1986; McArdle & Gaston, 1995; Mcardle et al., 1990). Computer simulations and heterogeneous data sets have recently been used to test the response of CV under different conditions (Fernández‐Martínez et al., 2018; Heath, 2006; Heath & Borowski, 2013). The results supported previous concerns about the adequacy of using CVs to assess differences in temporal variability across data sets, because estimates of CV (a) depend strongly on the mean of the time series, (b) increase with the length of the time series, (c) are biased when non‐normally distributed data sets are used, and (d) present a pathological behavior when rare events occur in a time series.…”

Section: Temporal Variability: Why We Need Alternative Measures To CVmentioning

confidence: 99%

“…To summarize, PV assesses the proportional difference between all pairs of values within a time series, while D assesses the proportional differences between consecutive values. Both PV and D overcome the mathematical problems of CV (Fernández‐Martínez et al., 2018; Heath, 2006; Heath & Borowski, 2013) and provide clear advantages over the traditional CV for comparing data sets with different statistical properties. The main benefits of PV and D over CV are summarized in Table 1.…”

Section: Temporal Variability: Why We Need Alternative Measures To CVmentioning

confidence: 99%

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Measuring temporal patterns in ecology: The case of mast seeding

Fernández‐Martínez

Peñuelas

2021

Ecology and Evolution

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How to accurately describe temporal patterns in ecological processes has been a long-standing question in ecology (McCann, 2000).Metrics to estimate stability, temporal variability, and resilience are, actually, still under intense debate (Arnoldi et al., 2016). The field of masting, for which assessing temporal patterns of seed production is crucial, is not an exception. Mast seeding, or masting, has traditionally been described as a reproductive phenomenon consisting of the highly variable and synchronized production of seeds at the population scale (Kelly, 1994;Pearse et al., 2016;Silvertown, 1980). The use of the term "masting," or describing a species or population as following a masting behavior, however, is sometimes confusing, arbitrary, or insufficiently accurate in the scientific literature to be

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“…A smaller proportion of indicators measure the spread of a quantity such as the degree of difference in GDP rates across different regions of New Zealand. In those instances, the proportional variability was used instead of the standard deviation due to the non-normality of the indicators [28]. Custom measures such as the Gini coefficient were used for quantifying the inequality of incomes, while the house affordability measure (HAM) was used to determine the accessibility of the housing market.…”

Section: Indicator Valuesmentioning

confidence: 99%

Towards a global index of shared prosperity: a case study on New Zealand

Sušnjak¹,

Schumacher²,

Ali³

et al. 2019

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Global prosperity has been rising over the last decade, along with public debate about growing inequality and its potentially negative social and economic consequences. The purpose of our research is to create an annually updated composite index, The Shared Prosperity Index (SPI), to quantify and visualise how effectively prosperity has been shared in New Zealand over time as well as near-future predictions. Past measures of inequality have tended to focus on a single factor such as income distribution, but in recent years a number of composite indices have emerged internationally which have attempted to provide a multi-dimensional perspective regarding prosperity and collective wellbeing. The SPI is differentiated from the existing measures by emphasising on the idea of shared rather than absolute prosperity and with a particular focus on the New Zealand context. The SPI employs eight multivariate dimensions identified as drivers of shared prosperity: income and wealth, employment, housing, health, socio-economic wellbeing, education, safety and security, and general equality, and incorporates national and international data sources to compute a composite index. Results show that the level of sharing was at its peak in New Zealand during the early to mid-1980s, before dropping sharply between 1987 and 1994, coinciding with cuts to government services and a move to a more open and less-regulated economy. Shared prosperity began slowly rising again until 2007 when it flattened out and trended downwards. In terms of individual SPI dimensions, we find a steep fall in recent years in the Safety and Security, and the General Equality dimensions, with the lowest level of sharing in the Income and Wealth dimension. The highest levels of sharing are evident in the Employment dimension, mainly due to falls in New Zealand's unemployment levels.

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Quantifying Proportional Variability

Cited by 19 publications

References 15 publications

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

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

Measuring temporal patterns in ecology: The case of mast seeding

Towards a global index of shared prosperity: a case study on New Zealand

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