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Logarithmic scales in ecological data presentation may cause misinterpretation


Scientific communication relies on clear presentation of data. Logarithmic scales are used frequently for data presentation in many scientific disciplines, including ecology, but the degree to which they are correctly interpreted by readers is unclear. Analysing the extent of log scales in the literature, we show that 22% of papers published in the journal Ecology in 2015 included at least one log-scaled axis, of which 21% were log–log displays. We conducted a survey that asked members of the Ecological Society of America (988 responses, and 623 completed surveys) to interpret graphs that were randomly displayed with linear–linear or log–log axes. Many more respondents interpreted graphs correctly when the graphs had linear–linear axes than when they had log–log axes: 93% versus 56% for our all-around metric, although some of the individual item comparisons were even more skewed (for example, 86% versus 9% and 88% versus 12%). These results suggest that misconceptions about log-scaled data are rampant. We recommend that ecology curricula include explicit instruction on how to interpret log-scaled axes and equations, and we also recommend that authors take the potential for misconceptions into account when deciding how to visualize data.

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Fig. 1: Logarithm usage in papers published in Ecology in 2015.
Fig. 2: Graphs viewed in our survey.
Fig. 3: Survey responses about which population changes more steeply with distance.
Fig. 4: Survey responses about each population level at the edge of the habitat.
Fig. 5: Survey responses about the manner in which each population changes with distance.


  1. Vitousek, P. M. Nutrient Cycling and Limitation: Hawai’i as a Model Ecosystem (Princeton Univ. Press, Princeton, 2004).

    Book  Google Scholar 

  2. Benton, T. G. & Grant, A. Elasticity analysis as an important tool in evolutionary and population ecology. Trends Ecol. Evol. 14, 467–471 (1999).

    Article  CAS  PubMed  Google Scholar 

  3. Taubert, F. et al. Global patterns of tropical forest fragmentation. Nature 554, 519–522 (2018).

    Article  CAS  PubMed  Google Scholar 

  4. Covington, A. K., Bates, R. G. & Durst, R. A. Definition of pH scales, standard reference values, measurement of pH and related terminology. Pure Appl. Chem. 57, 531–542 (1985).

    Article  Google Scholar 

  5. Richter, C. F. An instrumental earthquake magnitude scale. Bull. Seismol. Soc. Am. 25, 1–32 (1935).

    Google Scholar 

  6. Pogson, N. Magnitudes of thirty-six of the minor planets for the first day of each month of the year 1857. Mon. Not. R. Astron. Soc. 17, 12–15 (1856).

    Article  Google Scholar 

  7. Cowell, F. A. Measuring Inequality (Oxford Univ. Press, New York, 2011).

    Book  Google Scholar 

  8. Hastings, A. Population Biology: Concepts and Models (Springer, New York, 1997).

  9. Krane, K. S. & Halliday, D. Introductory Nuclear Physics (Wiley, New York, 1988).

    Google Scholar 

  10. Bolker, B. M. Ecological Models and Data in R (Princeton Univ. Press, Princeton, 2008).

    Book  Google Scholar 

  11. Sokal, R. R. & Rohlf, F. J. Biometry 3rd edn (W. H. Freeman, New York, 1995).

    Google Scholar 

  12. Matz, M. Towards a computational theory of algebraic competence. J. Math. Behav. 3, 93–166 (1980).

    Google Scholar 

  13. Kaur, B. & Boey, H. P. S. Algebraic misconceptions of first year college students. Focus Learn. Probl. Math. 16, 43–58 (1994).

    Google Scholar 

  14. Yen, R. Reflections on higher school certificate examinations: learning from their mistakes, High School Certificate 1998. Reflections 24, 3–8 (1999).

    Google Scholar 

  15. Liang, C. B. & Wood, E. Working with logarithms: students’ misconceptions and errors. Math. Educ. 8, 53–70 (2005).

    Google Scholar 

  16. Preston, F. W. The canonical distribution of commonness and rarity: part I. Ecology 43, 185–215 (1962).

    Article  Google Scholar 

  17. Peters, R. H. The Ecological Implications of Body Size (Cambridge Univ. Press, Cambridge, 1986).

    Google Scholar 

  18. Rizzuto, M., Carbone, C. & Pawar, S. Foraging constraints reverse the scaling of activity time in carnivores. Nat. Ecol. Evol. 2, 247–253 (2018).

    Article  PubMed  Google Scholar 

  19. Smith, B. & Wilson, J. B. A consumer’s guide to evenness indices. Oikos 76, 70–82 (1996).

    Article  Google Scholar 

  20. Wright, I. J. et al. The worldwide leaf economics spectrum. Nature 428, 821–827 (2004).

    Article  CAS  PubMed  Google Scholar 

  21. Zhou, X. H. & Tu, W. Confidence intervals for the mean of diagnostic test charge data containing zeros. Biometrics 56, 1118–1125 (2000).

    Article  CAS  PubMed  Google Scholar 

  22. Tian, L. & Wu, J. Confidence intervals for the mean of lognormal data with excess zeros. Biom. J. 48, 149–156 (2006).

    Article  PubMed  Google Scholar 

  23. Goodale, C. L. et al. Soil processes drive seasonal variation in retention of 15N tracers in a deciduous forest catchment. Ecology 96, 2653–2668 (2015).

    Article  PubMed  Google Scholar 

  24. Atwater, D. Z. & Callaway, R. M. Testing the mechanisms of diversity-dependent overyielding in a grass species. Ecology 96, 3332–3342 (2015).

    Article  PubMed  Google Scholar 

  25. Taylor, P. G. et al. Organic forms dominate hydrologic nitrogen export from a lowland tropical watershed. Ecology 96, 1229–1241 (2015).

    Article  PubMed  Google Scholar 

  26. McConkey, K. R., Brockelman, W. Y., Saralamba, C., & Nathalang, A. Effectiveness of primate seed dispersers for an “oversized” fruit Garcinia benthamii. Ecology 96, 2737–2747 (2015).

    Article  PubMed  Google Scholar 

  27. Wallace, J. B., Eggert, S. L., Meyer, J. L. & Webster, J. R. Stream invertebrate productivity linked to forest subsidies: 37 stream-years of reference and experimental data. Ecology 96, 1213–1228 (2015).

    Article  PubMed  Google Scholar 

  28. Albertson, L. K. & Allen, D. C. Meta-analysis: abundance, behavior, and hydraulic energy shape biotic effects on sediment transport in streams. Ecology 96, 1329–1339 (2015).

    Article  CAS  PubMed  Google Scholar 

  29. Carey, J. C. et al. Temperature responses of soil respiration largely unaltered with experimental warming. Proc. Natl Acad. Sci. USA 113, 13797–13802 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Gorham, E. & Kelly, J. A history of ecological research derived from titles of articles in the journal “Ecology,” 1925–2015. Bull. Ecol. Soc. Am. 99, 61–72 (2018).

    Article  Google Scholar 

  31. Krosnick, J. A. & Presser, S. in Handbook of Survey Research 2nd edn (eds Marsden, P. V. & Wright, J. D.) 263–314 (Emerald Group, Bingley, 2010).

  32. Lange, A., Vogt, C. & Ziegler, A. On the importance of equity in international climate policy: an empirical analysis. Energy Econ. 29, 545–562 (2007).

    Article  Google Scholar 

  33. Dannenberg, A., Sturm, B. & Vogt, C. Do equity preferences matter for climate negotiators? An experimental investigation. Environ. Resour. Econ. 47, 91–109 (2010).

    Article  Google Scholar 

  34. Lange, A., Löschel, A., Vogt, C. & Ziegler, A. On the self-interested use of equity in international climate negotiations. Eur. Econ. Rev. 54, 359–375 (2010).

    Article  Google Scholar 

  35. Kesternich, M. Minimum participation rules in international environmental agreements: empirical evidence from a survey among delegates in international climate negotiations. Appl. Econ. 48, 1047–1065 (2016).

    Article  Google Scholar 

  36. Dannenberg, A., Zitzelsberger, S. & Tavoni, A. Climate negotiators’ and scientists’ assessments of the climate negotiations. Nat. Clim. Change 7, 437–443 (2017).

    Article  Google Scholar 

  37. Ortega, S. et al. Women and Minorities in Ecology II (Ecological Society of America, 2006);

  38. R Development Core Team R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, 2013).

  39. van Someren, M. W., Barnard, Y. F. & Sandberg, J. A. C. The Think Aloud Method: A Practical Approach to Modelling Cognitive Processes (Academic, London, 1994).

    Google Scholar 

  40. Tippett, C. D. Refutation text in science education: a review of two decades of research. Int. J. Sci. Math. Educ. 8, 951–970 (2010).

    Article  Google Scholar 

  41. Sinatra, G. M. & Broughton, S. H. Bridging reading comprehension and conceptual change in science education: the promise of refutation text. Read. Res. Q. 46, 374–393 (2011).

    Article  Google Scholar 

  42. Lassonde, K. A., Kendeou, P. & O’Brien, E. J. Refutation texts: overcoming psychology misconceptions that are resistant to change. Scholarsh. Teach. Learn. Psychol. 2, 62–74 (2016).

    Article  Google Scholar 

  43. Kowalski, P. & Taylor, A. K. Reducing students’ misconceptions with refutational teaching: for long-term retention, comprehension matters. Scholarsh. Teach. Learn. Psychol. 3, 90–100 (2017).

    Article  Google Scholar 

  44. O’Hara, R. B. & Kotze, D. J. Do not log-transform count data. Methods Ecol. Evol. 1, 118–122 (2010).

    Article  Google Scholar 

  45. Wilson, J. B. Priorities in statistics, the sensitive feet of elephants, and don’t transform data. Folia Geobot. 42, 161–167 (2007).

    Article  Google Scholar 

  46. Feng, C. et al. log transformation: application and interpretation in biomedical research. Stat. Med. 32, 230–239 (2013).

    Article  PubMed  Google Scholar 

  47. Ives, A. R. For testing the significance of regression coefficients, go ahead and log-transform count data. Methods Ecol. Evol. 6, 828–835 (2015).

    Article  Google Scholar 

  48. Warton, D. I., Lyons, M., Stoklosa, J. & Ives, A. R. Three points to consider when choosing a LM or GLM test for count data. Methods Ecol. Evol. 7, 882–890 (2016).

    Article  Google Scholar 

  49. Neuheimer, A. B. et al. Adult and offspring size in the ocean over 17 orders of magnitude follows two life history strategies. Ecology 96, 3303–3311 (2015).

    Article  CAS  PubMed  Google Scholar 

  50. Luo, Z., Wang, E. & Smith, C. Fresh carbon input differentially impacts soil carbon decomposition across natural and managed systems. Ecology 96, 2806–2813 (2015).

    Article  PubMed  Google Scholar 

  51. Matta, C. F., Massa, L., Gubskaya, A. V. & Knoll, E. Can one take the logarithm or the sine of a dimensional quantity or a unit? Dimensional analysis involving transcendental functions. J. Chem. Educ. 88, 67–70 (2011).

    Article  CAS  Google Scholar 

  52. Deng, Q. et al. Down-regulation of tissue N:P ratios in terrestrial plants by elevated CO2. Ecology 96, 3354–3362 (2015).

    Article  PubMed  Google Scholar 

  53. Kempel, A. et al. Herbivore preference drives plant community composition. Ecology 96, 2923–2934 (2015).

    Article  PubMed  Google Scholar 

  54. LeBauer, D. S. & Treseder, K. K. Nitrogen limitation of net primary productivity in terrestrial ecosystems is globally distributed. Ecology 89, 371–379 (2008).

    Article  PubMed  Google Scholar 

  55. Yu, Q. et al. Stoichiometric homeostasis predicts plant species dominance, temporal stability, and responses to global change. Ecology 96, 2328–2335 (2015).

    Article  PubMed  Google Scholar 

  56. Yuan, Z. Y. & Chen, H. Y. H. Negative effects of fertilization on plant nutrient resorption. Ecology 96, 373–380 (2015).

    Article  CAS  PubMed  Google Scholar 

  57. Hedges, L. R., Gurevitch, J. & Curtis, P. S. The meta-analysis of response ratios in experimental ecology. Ecology 80, 1150–1156 (1999).

    Article  Google Scholar 

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We thank all the respondents whose efforts created these data, the volunteers who participated in pilot surveys and K. McCarter for helping to distribute the survey to the Ecological Society of America member list. Feedback from the Menge laboratory and J. Lubchenco improved this work.

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Authors and Affiliations



All authors conceived of the project. D.N.L.M. and A.C.M. designed the survey. T.A.B., A.W.Q., N.B.S., B.N.T. A.A.W. and D.N.L.M. conducted the bibliometric analysis. D.N.L.M. analysed data and wrote the paper. All authors edited the paper.

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Correspondence to Duncan N. L. Menge.

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Supplementary information

Supplementary Information 1

Supplementary Table 1

Reporting Summary

Supplementary Information 2

Supplementary Tables 2–6, Supplementary Figures 1–7

Supplementary Information 3

Online survey

Supplementary Data 1

Dataset from the bibliometric analysis

Supplementary Data 2

Survey data, with demographic information removed

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Menge, D.N.L., MacPherson, A.C., Bytnerowicz, T.A. et al. Logarithmic scales in ecological data presentation may cause misinterpretation. Nat Ecol Evol 2, 1393–1402 (2018).

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