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Quantifying the uncertainty of variance partitioning estimates of ecological datasets

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.

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Data availability

The source code of all simulations, as well as all generated raw data are available in this repository: https://github.com/Matthias-M-Fischer/Variance-Partitioning-Paper. The two re-analysed datasets have already been published and are readily available.

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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.

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Correspondence to Matthias M. Fischer.

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Handling Editor: Bryan F. J. Manly.

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Fig. S1

Effect 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)

Fig. S2

Influence 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)

Fig. S3

Effects 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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Fischer, M.M. Quantifying the uncertainty of variance partitioning estimates of ecological datasets. Environ Ecol Stat 26, 351–366 (2019). https://doi.org/10.1007/s10651-019-00431-6

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Keywords

  • Canonical correspondence analysis
  • Effect size
  • Multivariate statistics
  • Resampling
  • Variance partitioning