, Volume 156, Issue 3, pp 657–669 | Cite as

Beals smoothing revisited

  • Miquel De CáceresEmail author
  • Pierre Legendre
Community Ecology - Original Paper


Beals smoothing is a multivariate transformation specially designed for species presence/absence community data containing noise and/or a lot of zeros. This transformation replaces the observed values of the target species by predictions of occurrence on the basis of its co-occurrences with the remaining species. In many applications, the transformed values are used as input for multivariate analyses. As Beals smoothing values provide a sense of “probability of occurrence”, they have also been used for inference. However, this transformation can produce spurious results, and it must be used with caution. Here we study the statistical and ecological bases underlying the Beals smoothing function, and the factors that may affect the reliability of transformed values are explored using simulated data sets. Our simulations demonstrate that Beals predictions are unreliable for target species that are not related to the overall ecological structure. Furthermore, the presence of these “random” species may diminish the quality of Beals smoothing values for the remaining species. A statistical test is proposed to determine when observed values can be replaced with Beals smoothing predictions. Two real-data example applications are presented to illustrate the potentially false predictions of Beals smoothing and the necessary checking step performed by the new test.


Barro Colorado Island Beals smoothing Binary data Community ecology Randomization model 



This work benefitted from comments by Pedro-Peres Neto on randomization methods and by Daniel Borcard and Artur Lluent on the ecological interpretation of the Beals smoothing function. The authors are especially grateful to Jari Oksanen, who suggested interesting real-data applications and provided several suggestions, and to Bruce McCune and David Roberts for their comments on previous versions of the manuscript. This research was funded by NSERC grant no. OGP0007738 to P. Legendre. The BCI forest dynamics research project is part the Center for Tropical Forest Science, a global network of large-scale demographic tree plots. All experiments comply with the current laws of the country in which the experiments were performed.

Supplementary material

442_2008_1017_MOESM1_ESM.doc (54 kb)
S1. Expected value of Beals smoothing for a “random” species (doc 54 kb)


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Département de Sciences BiologiquesUniversité de MontréalMontréalCanada
  2. 2.Departament d’EstadísticaUniversitat de BarcelonaBarcelonaSpain

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