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Environmental and Ecological Statistics

, Volume 26, Issue 4, pp 351–366 | Cite as

Quantifying the uncertainty of variance partitioning estimates of ecological datasets

  • Matthias M. FischerEmail author
Article

Abstract

An important objective of experimental biology is the quantification of the relationship between sets of predictor and response variables, a statistical analysis often termed variance partitioning (VP). In this paper, a series of simulations is presented, aiming to generate quantitative estimates of the expected statistical uncertainty of VP analyses. We demonstrate scenarios with considerable uncertainty in VP estimates, which can significantly reduce the statistical reliability of the obtained results. Especially when a predictor variable of a dataset shows a low variance between the sampled sites, VP estimates may show a high margin of error. This becomes particularly important when the respective predictor variable only explains a small fraction of the overall variance, or the number of replicates is particularly small. Moreover, it is demonstrated that the expected error of VP estimates of a dataset can be approximated, and that accurate confidence intervals of the estimates can be obtained by bootstrap resampling, giving researchers a tool for the quantification of the uncertainty associated with an arbitrary VP analysis. The applicability of this method is demonstrated by a re-analysis of the Oribatid mite dataset introduced by Borcard and Legendre in 1994 and the Barro Colorado Island tree count dataset by Condit and colleagues. We believe that this study may encourage biologists to approach routine statistical analyses such as VP more critically, and report the error associated with them more frequently.

Keywords

Canonical correspondence analysis Effect size Multivariate statistics Resampling Variance partitioning 

Notes

Acknowledgements

I would like to thank M.Sc. Joscha Reichert for his extensive and extremely helpful comments on an earlier version of the manuscript. I also would like to thank Dr. Stavros D. Veresoglou for providing the initial research question and his guidance and assistance throughout this research project. Finally, I am indebted to three anonymous peer reviewers who provided thoughtful and constructive feedback to an earlier version of this manuscript and greatly helped improving its quality.

Supplementary material

10651_2019_431_MOESM1_ESM.pdf (219 kb)
Fig. S1Effect of the sample size n on the bias of the obtained VP estimates. Error bars represent the standard error of the mean across all simulated ten replicate analyses (PDF 218 KB)
10651_2019_431_MOESM2_ESM.pdf (189 kb)
Fig. S2Influence of the sampling range width on the bias of the obtained VP estimates. Error bars represent the standard error of the mean across all ten simulated replicates (PDF 189 KB)
10651_2019_431_MOESM3_ESM.pdf (219 kb)
Fig. S3Effects of the difference in optimal values in species response curves on the bias of the obtained VP estimates. Error bars represent the standard error of the mean across all ten simulated replicates (PDF 218 KB)

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Freie Universität Berlin, Institut für Biologie, MikrobiologieBerlinGermany

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