Calculating the uncertainty associated with log response ratios in plant–soil feedback studies

  • Sarah E. BatesEmail author
  • Elizabeth M. Wandrag
  • Richard P. Duncan


The strength and direction of plant–soil feedbacks are commonly estimated using log response ratios. Ratios have the benefit of being readily comparable across taxa and studies, but calculating the uncertainty associated with a ratio is not always straightforward. Many studies do not report estimates of uncertainty for feedback ratios despite this being central to interpreting the findings. We describe three ways to calculate the uncertainty associated with the mean log response ratio in plant–soil feedback studies (an analytical formula, bootstrapping, and model fitting), and show how these approaches produce comparable estimates for 95% confidence intervals around the mean. While the choice of method will depend on the experimental design of the study, we suggest that model fitting may be the most reliable and flexible approach. Presenting feedback ratios and their associated uncertainty in a consistent manner will allow clearer assessment of the findings of individual studies and facilitate cross-study comparisons, such as meta-analysis.


Plant–soil feedback Log response ratio Uncertainty Bootstrapping Modelling uncertainty 



This work was funded by Australian Research Council Grant DP150101839 to Richard Duncan and funding from the University of Canberra to Richard Duncan.

Supplementary material

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Supplementary file1 (DOCX 22 kb)
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Supplementary file2 (XLSX 21 kb)
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Supplementary file3 (XLSX 10 kb) Appendix 3. Eragrotis curvula growth data: used to compare three methods of calculating a feedback estimate and uncertainty associated.
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Supplementary file4 (DOCX 16 kb)


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Sarah E. Bates
    • 1
    Email author
  • Elizabeth M. Wandrag
    • 1
    • 2
  • Richard P. Duncan
    • 1
  1. 1.Institute for Applied EcologyUniversity of CanberraBruceAustralia
  2. 2.School of Environmental and Rural ScienceUniversity of New EnglandArmidaleAustralia

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