Abstract
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.
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References
Austin MP (1976) On non-linear species response models in ordination. Vegetatio 33:33–41
Beals EW (1984) Bray–Curtis ordination: an effective strategy for analysis of multivariate ecological data. Adv Ecol Res 14:1–55
Beauchamp VB, Stromberg JC, Stutz JC (2006) Arbuscular mycorrhizal fungi associated with Populus–Salix stands in a semiarid riparian ecosystem. New Phytol 170:369
Bouxin G (2005) Ginkgo, a multivariate analysis package. J Veg Sci 16:355–359
Brisse H, Grandjouan G, Hoff M, de Ruffray P (1980) Utilisation d’un critère statistique de l’écologie en phytosociologie–exemple des forêts alluviales en Alsace. Coll Phytosociol 9:543–590
Brodeur RD, Fisher JP, Emmett RL, Morgan CA, Casillas E (2005) Species composition and community structure of pelagic nekton off Oregon and Washington under variable oceanographic conditions. Mar Ecol Prog Ser 298:41–57
De Cáceres M, Oliva F, Font X, Vives S (2007) GINKGO, a program for non-standard multivariate fuzzy analysis. Adv Fuzzy Sets Syst 2:41–56
Ellyson WJT, Sillett SC (2003) Epiphyte Communities on Sitka Spruce in an old-growth Redwood Forest. Bryologist 106:197–211
Ewald J (2002) A probabilistic approach to estimating species pools from large compositional matrices. J Veg Sci 13:191–198
Fortin MJ, Dale MRT (2005) Spatial analysis: a guide for ecologists. Cambridge University Press, Cambridge
Gotelli NJ (2000) Null model analysis of species co-occurrence patterns. Ecology 81:2606–2621
Harms KE, Condit R, Hubbell SP, Foster RB (2001) Habitat associations of trees and shrubs in a 50-ha neotropical forest plot. J Ecol 89:947–959
Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6:1979
Holz I, Gradstein RS (2005) Cryptogamic epiphytes in primary and recovering upper montane oak forests of Costa Rica–species richness, community composition and ecology. Plant Ecol 178:89–109
Hope ACA (1968) A simplified Monte Carlo test procedure. J R Stat Soc B 50:35–45
Hubbell SP, Condit R, Foster RB (2005) Barro colorado forest census plot data. Available at http://ctfs.si/edu/datasets/bci
Hutchinson GE (1957) Concluding remarks. Cold Spring Harb Symp Quant Biol 22:415–427
Joy MK, Death RG (2000) Development and application of a predictive model of riverine fish community assemblages in the Taranaki region of the North Island, New Zealand. NZ J Mar Freshw Res 34:241–252
Kimball S, Wilson P, Crowther J (2004) Local ecology and geographic ranges of plants in the Bishop Creek watershed of the eastern Sierra Nevada, California, USA. J Biogeogr 31:1637–1657
Lee P (2004) The impact of burn intensity from wildfires on seed and vegetative banks, and emergent understory in aspen-dominated boreal forests. Can J Bot/Rev Can Bot 82:1468–1480
Legendre P (2005) Species associations: the Kendall coefficient of concordance revisited. J Agric Biol Environ Stat 10:226–245
Legendre P, Legendre L (1998) Numerical ecology, 2nd English edn. Elsevier, Amsterdam
Marra JL, Edmonds RL (2005) Soil arthropod responses to different patch types in a mixed-conifer forest of the Sierra Nevada. For Sci 51:255
McCune B (1994) Improving community analysis with the Beals smoothing function. Ecoscience 1:82–86
McCune B, Grace JB (2002) Analysis of ecological communities. MjM Software Design, Gleneden Beach
McCune B, Mefford MJ (1999) PC-ORD. Multivariate analysis of ecological data, Version 4. MjM Software Design, Gleneden Beach
Minchin PR (1987) Simulation of multidimensional community patterns towards a comprehensive model. Vegetatio 71:145–156
Münzbergová Z, Herben T (2004) Identification of suitable unoccupied habitats in metapopulation studies using co-occurrence of species. Oikos 105:408–414
North M, Oakley B, Fiegener R, Gray A, Barbour M (2005) Influence of light and soil moisture on Sierran mixed-conifer understory communities. Plant Ecol 177:13–24
Oksanen J, Kindt R, Legendre P, O’Hara B, Simpson GL, Stevens MHH (2008) Vegan: community ecology package. R package version 1.11-0. http://cran.r-project.org/, http://vegan.r-forge.r-project.org/
Peres-Neto PR, Olden JD, Jackson DA (2001) Environmentally constrained null models: site suitability as occupancy criterion. Oikos 93:110
R Development Core Team (2007) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available at http://www.R-project.org
Roberts DW, Wight D (1988) Plant community distribution and dynamics in Bryce Canyon National Park. United States Department of Interior National Park Service
Roberts DW (2006) labdsv: Laboratory for Dynamic Synthetic Vegephenomenology. R package version 1.2–2. Available at http://cran.r-project.org/
Schnittler M, Unterseher M, Tesmer J (2006) Species richness and ecological characterization of myxomycetes and myxomycete-like organisms in the canopy of a temperate deciduous forest. Mycologia 98:223
Sidak Z (1967) Rectangular confidence regions for the means of multivariate normal distributions. J Am Stat Assoc 62:626–633
Swan JMA (1970) An examination of some ordination problems by use of simulated vegetational data. Ecology 51:89–102
Whitehouse HE, Bayley SE (2005) Vegetation patterns and biodiversity of peatland plant communities surrounding mid-boreal wetland ponds in Alberta, Canada. Can J Bot 83:621–637
Acknowledgments
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.
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Communicated by Scott Collins.
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De Cáceres, M., Legendre, P. Beals smoothing revisited. Oecologia 156, 657–669 (2008). https://doi.org/10.1007/s00442-008-1017-y
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DOI: https://doi.org/10.1007/s00442-008-1017-y