Logarithmic scales in ecological data presentation may cause misinterpretation

Menge, Duncan N. L.; MacPherson, Anna; Bytnerowicz, Thomas A.; Quebbeman, Andrew W.; Schwartz, Naomi B.; Taylor, Benton N.; Wolf, Amelia A.

doi:10.1038/s41559-018-0610-7

Cited by 38 publications

(32 citation statements)

References 46 publications

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“…Trait-trait relationships between each bi-variate trait set were first analyzed using the Pearson correlation (Pearson’s r ). Statistical results are discussed based on transformed data, though non-transformed data are also presented for clarity and interpretation (Menge et al, 2018). Following assessments of bi-variate correlation, we considered the correlation structure among all traits using principal components analysis (PCA).…”

Section: Methodsmentioning

confidence: 99%

Physical and Functional Constraints on Viable Belowground Acquisition Strategies

2019

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Since their emergence onto land, terrestrial plants have developed diverse strategies to acquire soil resources. However, we lack a framework that adequately captures how these strategies vary among species. Observations from around the world now allow us to quantify the variation observed in commonly-measured fine-root traits but it is unclear how root traits are interrelated and whether they fall along an “economic” spectrum of acquisitive to conservative strategies. We assessed root trait variation and mycorrhizal colonization rates by leveraging the largest global database of fine-root traits (the Fine-Root Ecology Database; FRED). We also developed a heuristic model to explore the role of mycorrhizal fungi in defining belowground exploration efficiency across a gradient of thin- to thick-diameter roots. In support of the expectations of the “root economic spectrum,” we found that root diameter was negatively related to specific root length (Pearson’s r=-0.76). However, we found an unexpected negative relationship between root diameter and root tissue density (Pearson’s r = -0.40), and we further observed that root nitrogen content was largely unrelated to other economic traits. Mycorrhizal colonization was most closely associated with root diameter (Pearson’s r = 0.62) and was unrelated to root tissue density and root nitrogen. The heuristic model demonstrated that while thinner roots have inherently greater capacity to encounter soil resources based on higher surface area per unit mass, the potential for increased associations with mycorrhizal fungi in thicker roots, combined with greater hyphal growth, can result in equally acquisitive strategies for both thin- and thick roots. Taken together, our assessments of root trait variation, trade-offs with mycorrhizal fungi, and broader connections to root longevity allowed us to propose a series of fundamental constraints on belowground resource acquisition strategies. Physical tradeoffs based on root construction (i.e., economic traits) and functional limitations related to the capacity of a root to encounter and acquire soil resources combine to limit the two-dimensional belowground trait space. Within this trait space there remains a diversity of additional variation in root traits that facilitates a wide range of belowground resource acquisition strategies.

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Section: Methodsmentioning

confidence: 99%

Physical and Functional Constraints on Viable Belowground Acquisition Strategies

2019

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“…Log transformations have recently fallen out of favor with many scientists as techniques, such as generalized linear models, that model non‐normal probability distributions have become more widespread and accessible (O’Hara and Kotze 2010). Arguments against log transformation typically rest on the assumption that the primary justification for log transformation is to normalize error distributions and improve estimates of statistical significance, and on the perception that log transformation makes results more difficult to interpret (Menge et al 2018). While normalization of residuals may be a desirable property in some cases, it is not the primary motivation behind log‐transforming ratio data.…”

Section: Introductionmentioning

confidence: 99%

The misuse of ratios in ecological stoichiometry

Isles¹

2020

Ecology

134

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Ecological stoichiometry is concerned with the ratios of different elements, particularly carbon, nitrogen, and phosphorus. Ratios by their nature do not respond symmetrically to changes in the numerator and denominator and do not follow normal distributions; however, researchers frequently fail to consider these properties in their analyses, which has biased reported results. Calculating means, variance, or linear slopes based on untransformed ratios results in biased results. I demonstrate the consequences of these errors for inferences from stoichiometric analyses using simple examples and several large monitoring data sets. I then review 100 studies in ecological stoichiometry and find that misuse of ratio data is common, with 93% of studies containing at least one error. These errors may be problematic, particularly in large‐scale meta‐analyses summarizing data over large ranges. Fortunately, most of these mistakes can be easily avoided by first log transforming elemental ratios. I therefore recommend that, to ensure robust and reproducible results, researchers in ecological stoichiometry should adopt a convention of presenting stoichiometric ratio data as the logarithm of molar ratios in the future. The widespread use of untransformed nitrogen to phosphorus ratio as an indicator of nutrient limitation has likely exaggerated the importance of phosphorus limitation, particularly in freshwater systems.

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“…The proposed plots are tools that may facilitate the understanding of epidemic outbreaks or communication about outbreaks, but their utility is not established at this point. Logarithm transformations of data may cause interpretation difficulties for some readers, including scientists [9]; we would expect that many policy makers or members of the general public would appreciate that the proposed graphs be accompanied by a commentary and explanation (such as the video posted on Covid Trends website [7]). We have not conducted any tests of usability or impact.…”

Section: Limitationsmentioning

confidence: 99%

Alternative graphical displays for the monitoring of epidemic outbreaks, with application to COVID-19 mortality

Perneger

Kevorkian

Grenet

et al. 2020

BMC Med Res Methodol

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Background Classic epidemic curves – counts of daily events or cumulative events over time –emphasise temporal changes in the growth or size of epidemic outbreaks. Like any graph, these curves have limitations: they are impractical for comparisons of large and small outbreaks or of asynchronous outbreaks, and they do not display the relative growth rate of the epidemic. Our aim was to propose two additional graphical displays for the monitoring of epidemic outbreaks that overcome these limitations. Methods The first graph shows the growth of the epidemic as a function of its size; specifically, the logarithm of new cases on a given day, N(t), is plotted against the logarithm of cumulative cases C(t). Logarithm transformations facilitate comparisons of outbreaks of different sizes, and the lack of a time scale overcomes the need to establish a starting time for each outbreak. Notably, on this graph, exponential growth corresponds to a straight line with a slope equal to one. The second graph represents the logarithm of the relative rate of growth of the epidemic over time; specifically, log10(N(t)/C(t-1)) is plotted against time (t) since the 25th event. We applied these methods to daily death counts attributed to COVID-19 in selected countries, reported up to June 5, 2020. Results In most countries, the log(N) over log(C) plots showed initially a near-linear increase in COVID-19 deaths, followed by a sharp downturn. They enabled comparisons of small and large outbreaks (e.g., Switzerland vs UK), and identified outbreaks that were still growing at near-exponential rates (e.g., Brazil or India). The plots of log10(N(t)/C(t-1)) over time showed a near-linear decrease (on a log scale) of the relative growth rate of most COVID-19 epidemics, and identified countries in which this decrease failed to set in in the early weeks (e.g., USA) or abated late in the outbreak (e.g., Portugal or Russia). Conclusions The plot of log(N) over log(C) displays simultaneously the growth and size of an epidemic, and allows easy identification of exponential growth. The plot of the logarithm of the relative growth rate over time highlights an essential parameter of epidemic outbreaks.

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Logarithmic scales in ecological data presentation may cause misinterpretation

Cited by 38 publications

References 46 publications

Physical and Functional Constraints on Viable Belowground Acquisition Strategies

Physical and Functional Constraints on Viable Belowground Acquisition Strategies

The misuse of ratios in ecological stoichiometry

Alternative graphical displays for the monitoring of epidemic outbreaks, with application to COVID-19 mortality

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