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


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.


Canonical correspondence analysis Effect size Multivariate statistics Resampling Variance partitioning 



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)


  1. Allouche O, Steinitz O, Rotem D, Rosenfeld A, Kadmon R (2008) Incorporating distance constraints into species distribution models. J Appl Ecol 45(2):599–609CrossRefGoogle Scholar
  2. Amici V, Santi E, Filibeck G, Diekmann M, Geri F, Landi S, Scoppola A, Chiarucci A (2013) Influence of secondary forest succession on plant diversity patterns in a mediterranean landscape. J Biogeogr 40(12):2335–2347CrossRefGoogle Scholar
  3. Austin M (1976) On non-linear species response models in ordination. Vegetatio 33(1):33–41CrossRefGoogle Scholar
  4. Bojková J, Schenková J, Horsák M, Hájek M (2011) Species richness and composition patterns of clitellate (Annelida) assemblages in the treeless spring fens: the effect of water chemistry and substrate. Hydrobiologia 667(1):159–171CrossRefGoogle Scholar
  5. Borcard D, Legendre P (1994) Environmental control and spatial structure in ecological communities: an example using oribatid mites (acari, oribatei). Environ Ecol Stat 1(1):37–61CrossRefGoogle Scholar
  6. Borcard D, Legendre P, Drapeau P (1992) Partialling out the spatial component of ecological variation. Ecology 73(3):1045–1055CrossRefGoogle Scholar
  7. Burrascano S, Sabatini F, Blasi C (2011) Testing indicators of sustainable forest management on understorey composition and diversity in southern Italy through variation partitioning. Plant Ecol 212(5):829–841CrossRefGoogle Scholar
  8. Chen Y (2013) A comparison of synonymous codon usage bias patterns in dna and rna virus genomes: quantifying the relative importance of mutational pressure and natural selection. BioMed Res Int. CrossRefPubMedPubMedCentralGoogle Scholar
  9. Condit R, Pitman N, Leigh EG, Chave J, Terborgh J, Foster RB, Núnez P, Aguilar S, Valencia R, Villa G et al (2002) Beta-diversity in tropical forest trees. Science 295(5555):666–669CrossRefGoogle Scholar
  10. Cottenie K (2005) Integrating environmental and spatial processes in ecological community dynamics. Ecol Lett 8(11):1175–1182CrossRefGoogle Scholar
  11. Dong X, Li B, He F, Gu Y, Sun M, Zhang H, Tan L, Xiao W, Liu S, Cai Q (2016) Flow directionality, mountain barriers and functional traits determine diatom metacommunity structuring of high mountain streams. Sci Rep 6:24711CrossRefGoogle Scholar
  12. Dou P, Cui B, Xie T, Dong D, Gu B (2016) Macrobenthos diversity response to hydrological connectivity gradient. Wetlands 36(1):45–55CrossRefGoogle Scholar
  13. Dray S, Pélissier R, Couteron P, Fortin M-J, Legendre P, Peres-Neto PR, Bellier E, Bivand R, Blanchet FG, De Cáceres M et al (2012) Community ecology in the age of multivariate multiscale spatial analysis. Ecol Monogr 82(3):257–275CrossRefGoogle Scholar
  14. Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7(1):1–26CrossRefGoogle Scholar
  15. Efron B, Tibshirani R (1986) Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Stat Sci 1(1):54–75CrossRefGoogle Scholar
  16. Fried G, Kazakou E, Gaba S (2012) Trajectories of weed communities explained by traits associated with species’ response to management practices. Agric Ecosyst Environ 158:147–155CrossRefGoogle Scholar
  17. Fyllas NM, Patino S, Baker T, Bielefeld Nardoto G, Martinelli L, Quesada C, Paiva R, Schwarz M, Horna V, Mercado L et al (2009) Basin-wide variations in foliar properties of amazonian forest: phylogeny, soils and climate. Biogeosciences 6:2677–2708CrossRefGoogle Scholar
  18. Gilbert B, Bennett JR (2010) Partitioning variation in ecological communities: do the numbers add up? J Appl Ecol 47(5):1071–1082CrossRefGoogle Scholar
  19. Gobet A, Böer SI, Huse SM, Van Beusekom JE, Quince C, Sogin ML, Boetius A, Ramette A (2012) Diversity and dynamics of rare and of resident bacterial populations in coastal sands. ISME J 6(3):542CrossRefGoogle Scholar
  20. Heikkinen RK, Luoto M, Virkkala R, Rainio K (2004) Effects of habitat cover, landscape structure and spatial variables on the abundance of birds in an agricultural-forest mosaic. J Appl Ecol 41(5):824–835CrossRefGoogle Scholar
  21. Heikkinen RK, Luoto M, Kuussaari M, Pöyry J (2005) New insights into butterfly-environment relationships using partitioning methods. Proc R Soc Lond B Biol Sci 272(1577):2203–2210CrossRefGoogle Scholar
  22. Hill M, Tiedeman C (2006) Effective groundwater model calibration: with analysis of data, sensitivities, predictions, and uncertainty. Wiley, HobokenGoogle Scholar
  23. Hoffman GE, Schadt EE (2016) Variance partition: interpreting drivers of variation in complex gene expression studies. BMC Bioinform 17(1):483CrossRefGoogle Scholar
  24. Hutchinson G (1957) Population studies-animal ecology and demography-concluding remarks. In: Cold Spring Harbor symposia on quantitative biology, vol 22, pages 415–427. Cold Spring Harbor Lab Press, New YorkCrossRefGoogle Scholar
  25. Hyvönen T, Holopainen J, Tiainen J (2005) Detecting the spatial component of variation in the weed community at the farm scale with variation partitioning by canonical correspondence analysis. Weed Res 45(1):48–56CrossRefGoogle Scholar
  26. Legendre P, Mi X, Ren H, Ma K, Yu M, Sun I-F, He F (2009) Partitioning beta diversity in a subtropical broad-leaved forest of China. Ecology 90(3):663–674CrossRefGoogle Scholar
  27. Li J, Xu Q, Zheng Z, Lu H, Luo Y, Li Y, Li C, Seppä H (2015) Assessing the importance of climate variables for the spatial distribution of modern pollen data in China. Quat Res 83(2):287–297CrossRefGoogle Scholar
  28. Makarenkov V, Legendre P (2002) Nonlinear redundancy analysis and canonical correspondence analysis based on polynomial regression. Ecology 83(4):1146–1161CrossRefGoogle Scholar
  29. Minchin PR (1987) Simulation of multidimensional community patterns: towards a comprehensive model. Vegetatio 71(3):145–156Google Scholar
  30. Morelli F, Benedetti Y, Su T, Zhou B, Moravec D, Šímová P, Liang W (2017) Taxonomic diversity, functional diversity and evolutionary uniqueness in bird communities of beijing’s urban parks: effects of land use and vegetation structure. Urban For Urban Green 23:84–92CrossRefGoogle Scholar
  31. Mykrä H, Heino J, Muotka T (2007) Scale-related patterns in the spatial and environmental components of stream macroinvertebrate assemblage variation. Glob Ecol Biogeogr 16(2):149–159CrossRefGoogle Scholar
  32. Oksanen J, Blanchet FG, Friendly M, Kindt R, Legendre P, McGlinn D, Minchin PR, O’Hara RB, Simpson GL, Solymos P, Stevens MHH, Szoecs E, Wagner H (2016) Vegan: community ecology package. R package version 2.4-0Google Scholar
  33. Pelletier J, Codjia C, Potvin C (2012) Traditional shifting agriculture: tracking forest carbon stock and biodiversity through time in Western Panama. Glob Change Biol 18(12):3581–3595CrossRefGoogle Scholar
  34. Peres-Neto PR, Legendre P, Dray S, Borcard D (2006) Variation partitioning of species data matrices: estimation and comparison of fractions. Ecology 87(10):2614–2625CrossRefGoogle Scholar
  35. Sacchi R, Mangiacotti M, Scali S, Sannolo M, Zuffi MA, Pellitteri-Rosa D, Bellati A, Galeotti P, Fasola M (2015) Context-dependent expression of sexual dimorphism in island populations of the common wall lizard (Podarcis muralis). Biol J Linnean Soc 114(3):552–565CrossRefGoogle Scholar
  36. ter Braak C (1986) Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67(5):1167–1179CrossRefGoogle Scholar
  37. Wang Y, Yang J, Liu L, Yu Z (2015) Quantifying the effects of geographical and environmental factors on distribution of stream bacterioplankton within nature reserves of Fujian, China. Environ Sci Pollut Res 22(14):11010–11021CrossRefGoogle Scholar
  38. Wang X, Helgason B, Westbrook C, Bedard-Haughn A (2016) Effect of mineral sediments on carbon mineralization, organic matter composition and microbial community dynamics in a mountain Peatland. Soil Biol Biochem 103:16–27CrossRefGoogle Scholar
  39. Yang W, Zheng Y, Gao C, Duan J-C, Wang S-P, Guo L-D (2016) Arbuscular mycorrhizal fungal community composition affected by original elevation rather than translocation along an altitudinal gradient on the qinghai-tibet plateau. Sci Rep 6:36606CrossRefGoogle Scholar

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© 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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