Percent Beats Scales: Study Finds Ordinal Cover Estimates Double the Error in Vegetation Data

For nearly a century, vegetation scientists around the world have stepped into meadows, forests, and grasslands with a peculiar habit: instead of writing down the percentage of ground a plant species covers, they assign it to a category on an ordinal scale. The most famous of these, the Braun-Blanquet scale, sorts species into classes such as 1, 2, 3, 4, and 5, each spanning a broad range of cover values. The practice dates back to the Swiss phytosociologist Josias Braun-Blanquet, whose textbooks in 1932 and 1964 codified a system designed for the pre-computer era, when plant communities were described by hand and classified by manually sorting paper tables of vegetation relevés. A new simulation study published in Vegetation Classification and Survey now argues that this tradition comes at a steep and largely unnecessary price: a substantial inflation of the very errors researchers try to control when they measure nature.

The study, conducted by Jürgen Dengler and Idoia Biurrun, set out to test a claim often repeated in the field: that estimating an ordinal category is less error-prone and more reproducible than directly estimating percent cover. The authors simulated 121 virtual plant species whose true covers ranged from 0.001 percent to about 92.7 percent, increasing by a factor of 1.1 between consecutive species so that the entire logarithmic range of possible covers was evenly represented. Ten virtual observers with identical skills then estimated the cover of each species thirteen times under different assumptions about estimation precision, and each sampling was repeated ten times. Crucially, the simulation assumed that the observer’s estimation error was the same whether they worked in percent or with an ordinal scale, so that any difference in the final numbers could only come from the transformation steps themselves.

Those transformation steps are the heart of the problem. When a researcher estimates percent cover directly, the single estimation error of the observer is the only imperfection entering the dataset. When the same observer instead assigns a species to a category on the seven-step Braun-Blanquet scale or the five-step Hult-Sernander-Du Rietz scale, two additional translation steps are inserted: the perceived cover is snapped into a category, and the category is later back-transformed into a percentage, typically by replacing it with the arithmetic mean of its class borders. Each step discards information. A species truly covering 26 percent, for example, might be estimated by one observer as 25 percent and by another as 27 percent; those numbers look different on paper but are both close to reality. If both observers instead record category 3, their notes appear perfectly consistent, yet the standard back-transformation of that category is roughly 38 percent, far from the truth.

To model estimation precision realistically, the authors drew on an empirical study from 1986 in which Hatton and colleagues asked 24 graduate students to estimate the fractional areas of artificial paper shapes within a sampling plot. That work revealed a scale-dependent coefficient of variation following a power law, meaning that small covers are estimated proportionally far less precisely than large ones. The simulation implemented this empirical relationship, along with variants 50 percent better and 50 percent worse, and additionally explored ten constant coefficients of variation ranging from 0.1 to 1.0. The authors then compared the mean relative and absolute errors of the final numbers produced by each recording method, expressing the disadvantage of the ordinal scales as an error inflation factor.

The results were strikingly one-sided. In nearly all settings, the ordinal scales produced larger errors in the final data than direct percent estimation. Under the setting the authors consider most realistic, based on the empirical Hatton data and considering species with more than 1 percent cover, the mean relative estimation error in the field was 32.3 percent, corresponding to an average absolute deviation of 2.9 percentage points. Applying the seven-step Braun-Blanquet scale inflated the mean relative error to 60.2 percent, nearly a twofold increase, while the five-step Hult-Sernander-Du Rietz scale raised it to 44.1 percent, about a 1.4-fold increase. In absolute terms, the true cover was missed by 5.1 percentage points with the Braun-Blanquet approach and 4.7 points with the Hult-Sernander-Du Rietz scale, compared with 2.9 points for direct estimation. Statistical tests on the simulated errors confirmed highly significant differences among the three methods, with percent estimation performing best in every comparison.

The inflation was worst for rare species. When all cover values were included, error inflation factors reached as high as 103.6 in some settings, because the coarsest categories of the ordinal scales lump together everything from a trace of cover to several percent, obliterating differences that matter greatly on a logarithmic scale. Error inflation was generally higher when observers were more precise, higher for relative than for absolute errors, and higher when small species were included. Only in a few unrealistic combinations, with very high estimation error and analyses restricted to species covering more than 10 percent, did the ordinal scales perform marginally better. The authors also found that the particular weakness of their Braun-Blanquet variant stemmed from category 2, which spans a fivefold range of cover values from 5 to 25 percent, whereas the Hult-Sernander-Du Rietz classes each span only a twofold range, illustrating a general principle identified by earlier methodological work: the so-called partition error of an ordinal scale decreases as the number of categories increases.

Why, then, do ordinal scales persist? The authors, who between them have recorded thousands of relevés with the Braun-Blanquet system before switching, identify three main reasons. First, many researchers simply learned the method and never questioned it. Second, many believe that assigning a category involves a smaller estimation error than writing a percentage, a misconception the simulation directly refutes: apparent consistency between two observers who both write 3 masks estimates that are far from reality. Third, some argue that ordinal categories are faster to record. The authors report from their own experience that switching to percent cover required only a short adjustment period and did not reduce the number of relevés completed per day; indeed, many students taught to use the Braun-Blanquet scale report that they first estimate percent cover mentally before translating it into a category, making the ordinal step an added burden rather than a shortcut. The authors acknowledge that a rigorous experimental test of speed would be difficult, since observers asked to use an ordinal scale might work less carefully, which would only worsen the error inflation beyond what the simulation assumed.

The consequences ripple through virtually every numerical analysis that modern vegetation ecology performs. Ordination and classification may be relatively robust, as earlier studies have suggested similar outcomes with ordinal and percent data. But methods that rely on the logarithm of cover, such as Shannon diversity and evenness indices, are acutely sensitive: covers of 0.1 percent and 0.001 percent, easily distinguished in the field, are equalised by any of the common ordinal scales. Parametric statistical tests, justified for directly estimated percent values, become dubious when applied to back-transformed categories with only a few steps. And some approaches, such as the analysis of species-abundance distributions, are simply impossible when cover is recorded in a handful of classes. The problem is compounded by the sheer weight of legacy data: in sPlot, the most comprehensive vegetation-plot database on Earth, 66 percent of all plots were recorded with some variant of the Braun-Blanquet scale, only 15 percent with direct percent cover, and 19 percent with one of 55 other measures.

The authors also note a historical irony: most researchers today use versions of the Braun-Blanquet scale that differ from what Braun-Blanquet actually defined. His 1964 textbook contains four inconsistent definition tables, all of which place the border between categories 1 and 2 at 10 percent rather than the frequently cited 5 percent, and he never formally endorsed the seven-step scale now embedded in the widely used TURBOVEG software, whose built-in replacement value for category 4 is 68 percent rather than the 63 percent claimed in recent literature. Combined cover-abundance scales, which mix percent cover with counts of individuals, introduce further mathematical problems beyond those quantified here. The authors’ recommendation is therefore straightforward: vegetation ecologists should abandon ordinal importance scales and estimate cover directly in percent. The method made sense in a pre-computer era of manual table sorting, they argue, but in an age when essentially all analyses require numeric cover values, accepting a nearly twofold inflation of error for no gain in speed or reproducibility is a tradition the discipline can no longer afford.

Subject of Research: Error comparison of direct percent cover estimation versus ordinal cover scales in vegetation plot sampling

Article Title: Should we estimate plant cover in percent or on ordinal scales?

Article References: Dengler, J., & Dembicz, I. (2023). Should we estimate plant cover in percent or on ordinal scales?. Vegetation Classification and Survey, 4, 131-138. https://doi.org/10.3897/vcs.98379

Image Credits: AI Generated

DOI: 10.3897/VCS.98379

Keywords: vegetation ecology, Braun-Blanquet scale, percent cover, ordinal scales, phytosociology, estimation error, vegetation plots, biodiversity monitoring, simulation study, Hult-Sernander-Du Rietz scale, sPlot database, cover-abundance scales