Beals smoothing revisited.

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.