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International Journal of Ecology
Volume 2012 (2012), Article ID 947103, 12 pages
http://dx.doi.org/10.1155/2012/947103
Research Article

Trait-Environment Relationships and Tiered Forward Model Selection in Linear Mixed Models

1Biometris, Wageningen University and Research Centre, P.O. Box 100, 6700 AC Wageningen, The Netherlands
2Ecosystem Management Research Group, Department of Biology, University of Antwerp, Universiteitsplein 1c, 2610 Antwerpen, Belgium

Received 23 December 2011; Revised 1 April 2012; Accepted 2 April 2012

Academic Editor: Jean Clobert

Copyright © 2012 Tahira Jamil et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. M. Diamond, “Assembly of species communities,” in Massachusetts, Harvard University Press, Cambridge, Mass, USA, 1975.
  2. E. Weiher and P. A. Keddy, “The assembly of experimental wetland plant communities,” Oikos, vol. 73, no. 3, pp. 323–335, 1995. View at Scopus
  3. W. Kotowski, O. Beauchard, W. Opdekamp, P. Meire, and R. van Diggelen, “Waterlogging and canopy interact to control species recruitment in floodplains,” Functional Ecology, vol. 24, no. 4, pp. 918–926, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Menezes, D. J. Baird, and A. Soares, “Beyond taxonomy: a review of macroinvertebrate trait-based community descriptors as tools for freshwater biomonitoring,” Journal of Applied Ecology, vol. 47, no. 4, pp. 711–719, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Díaz, I. Noy-Meir, and M. Cabido, “Can grazing response of herbaceous plants be predicted from simple vegetative traits?” Journal of Applied Ecology, vol. 38, no. 3, pp. 497–508, 2001. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Lavorel and E. Garnier, “Predicting changes in community composition and ecosystem functioning from plant traits: revisiting the Holy Grail,” Functional Ecology, vol. 16, no. 5, pp. 545–556, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. S. Kahmen and P. Poschlod, “Effects of grassland management on plant functional trait composition,” Agriculture, Ecosystems & Environment, vol. 128, no. 3, pp. 137–145, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Kahmen and P. Poschlod, “Plant functional trait responses to grassland succession over 25 years,” Journal of Vegetation Science, vol. 15, no. 1, pp. 21–32, 2004. View at Scopus
  9. E. Weiher, A. V. D. Werf, K. Thompson, M. Roderick, E. Garnier, and O. Eriksson, “Challenging theophrastus: a common core list of plant traits for functional ecology,” Journal of Vegetation Science, vol. 10, no. 5, pp. 609–620, 1999. View at Scopus
  10. C. Violle, M.-L. Navas, D. Vile et al., “Let the concept of trait be functional!,” Oikos, vol. 116, no. 5, pp. 882–892, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Dray and P. Legendre, “Testing the species traits environment relationships: the fourth-corner problem revisited,” Ecology, vol. 89, no. 12, pp. 3400–3412, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. B. J. McGill, B. J. Enquist, E. Weiher, and M. Westoby, “Rebuilding community ecology from functional traits,” Trends in Ecology and Evolution, vol. 21, no. 4, pp. 178–185, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. D. Vile, B. Shipley, and E. Garnier, “Ecosystem productivity can be predicted from potential relative growth rate and species abundance,” Ecology Letters, vol. 9, no. 9, pp. 1061–1067, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. S. Greven and T. Kneib, “On the behaviour of marginal and conditional AIC in linear mixed models,” Biometrika, vol. 97, no. 4, pp. 773–789, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. R. Wolfinger, “Covariance structure selection in general mixed models,” Communications in Statistics, vol. 22, no. 4, pp. 1079–1106, 1993.
  16. R. D. Wolfinger, “Heterogeneous variance-covariance structures for repeated measures,” Journal of Agricultural, Biological, and Environmental Statistics, vol. 1, no. 2, pp. 205–230, 1996. View at Scopus
  17. J. A. Hoeting, R. A. Davis, A. A. Merton, and S. E. Thompson, “Model selection for geostatistical models,” Ecological Applications, vol. 16, no. 1, pp. 87–98, 2006. View at Publisher · View at Google Scholar · View at Scopus
  18. W. D. Hosmer and S. Lemeshow, Applied Logistic Regression, Wiley, New York, NY, USA, 2nd edition, 2000.
  19. T. Jamil and C. J. F. ter Braak, “Selection properties of type II maximum likelihood (empirical Bayes) in linear models with individual variance components for predictors,” Pattern Recognition Letters, vol. 33, no. 9, pp. 1205–1212, 2012. View at Publisher · View at Google Scholar
  20. A. Klimkowska, R. van Diggelen, S. den Held, R. Brienen, S. Verbeek, and K. Vegelin, “Seed production in fens and fen meadows along a disturbance gradient,” Applied Vegetation Science, vol. 12, no. 3, pp. 304–315, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. J. A. Nelder, “Letter to the editors: what is the mixed-models controversy?” International Statistical Review, vol. 76, no. 1, pp. 134–135, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Klimešová and L. Klimeš, “CLO-PLA3. a database of clonal growth architecture of Central European plants,” 2006, http://clopla.butbn.cas.cz/.
  23. M. Kleyer, R. M. Bekker, I. C. Knevel et al., “The LEDA traitbase: a database of life-history traits of the Northwest European flora,” Journal of Ecology, vol. 96, no. 6, pp. 1266–1274, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. H. Ellenberg, H. E. Weber, R. Düll, V. Wirth, W. Werner, and D. Paulissen, Zeigerwerte von Pflanzen in Mitteleuropa, vol. 18, Scripta Geobotanica, 2nd edition, 1992.
  25. T. G. Tutin, V. H. Heywood, N. A. Burges, D. H. Valentine, S. M. Walters, and D. A. Webb, Flora Europaea, vol. 5 of Set and CD-ROM Pack, Cambridge University Press, Cambridge, UK, 2nd edition, 2001.
  26. I. Kühn, W. Durka, and S. Klotz, “BiolFlor—A new plant—trait database as a tool for plant invasion ecology,” Diversity and Distributions, vol. 10, no. 5-6, pp. 363–365, 2004. View at Publisher · View at Google Scholar · View at Scopus
  27. M. Kuhn, “Building predictive models in R using the caret package,” Journal of Statistical Software, vol. 28, no. 5, pp. 1–26, 2008. View at Scopus
  28. M. Kuhn, “caret: Classification and Regression Training. R package version 4.98,” 2011, http://CRAN.R-project.org/package=caret.
  29. T. Jamil, W. Ozinga, and C. J. F. ter Braak, “Selecting traits that explain species-environment relationships: a generalized linear mixed model approach,” submitted.
  30. N. L. Poff, J. D. Olden, N. K. M. Vieira, D. S. Finn, M. P. Simmons, and B. C. Kondratieff, “Functional trait niches of North American lotic insects: traits-based ecological applications in light of phylogenetic relationships,” Journal of the North American Benthological Society, vol. 25, no. 4, pp. 730–755, 2006. View at Publisher · View at Google Scholar · View at Scopus
  31. G. C. Fernandez, “Model selection in PROC MIXED—a user—friendly SAS® macro application,” in Proceedings of the SAS Global forum, Orlando, Fla, USA, April 2007.
  32. R. C. Littell, G. A. Milliken, W. W. Stroup, R. D. Wolfinger, and O. Schabenberger, SAS for Mixed Models, SAS Institute, Cary, NC, USA, 2006.
  33. M. Yuan and Y. Lin, “Efficient empirical bayes variable selection and estimation in linear models,” Journal of the American Statistical Association, vol. 100, no. 472, pp. 1215–1225, 2005. View at Publisher · View at Google Scholar · View at Scopus
  34. B. T. West, K. B. Welch, and A. T. Galecki, Linear Mixed Models: A Practical Guide Using Statistical Software, Chapman & Hall/CRC, 2006.
  35. P. J. Diggle, P. Heagerty, K. Y. Liang, and S. L. Zeger, Analysis of Longitudinal Data, Oxford University Press, Oxford, UK, 2002.
  36. H. Akaike, “Information theory and an extension of the maximum likelihood principle,” in 2nd International Symposium on Information Theory, Tsahkadsor, Armenian SSR, 1973.
  37. C. M. Hurvich and C. Tsai, Regression and Time Series Model Selection in Small Samples, Oxford University Press, 1989.
  38. H. Bozdogan, “Model selection and akaike's information criterion (AIC): the general theory and its analytical extensions,” Psychometrika, vol. 52, no. 3, pp. 345–370, 1987. View at Publisher · View at Google Scholar · View at Scopus
  39. S. Gideon, “Estimating the Dimension of a Model,” The Annals of Statistics, vol. 6, no. 2, pp. 461–464, 1978.
  40. M. J. Gurka, “Selecting the best linear mixed model under REML,” The American Statistician, vol. 60, no. 1, pp. 19–26, 2006. View at Publisher · View at Google Scholar · View at Scopus
  41. K. P. Burnham and D. R. Anderson, Model Selection and Multimodel Inference : A Practical Information-Theoretic Approach, Springer, New York, NY, USA, 2002.
  42. K. W. Broman and T. P. Speed, “A model selection approach for the identification of quantitative trait loci in experimental crosses,” Journal of the Royal Statistical Society, vol. 64, no. 4, pp. 641–656, 2002. View at Publisher · View at Google Scholar · View at Scopus
  43. D. Bates, M. Maechler, B. Bolker, et al., “lme4: Linear mixed-effects models using S4 classes. R package version 0.999375-39,” 2011, http://CRAN.R-project.org/package=lme4.
  44. G. Verbeke and G. Molenberghs, Linear Mixed Models for Longitudinal Data, Springer, New York, NY, USA, 2000.
  45. S. Xu, “An empirical bayes method for estimating epistatic effects of quantitative trait loci,” Biometrics, vol. 63, no. 2, pp. 513–637, 2007. View at Publisher · View at Google Scholar · View at Scopus
  46. C. Bishop, Pattern recognition and machine learning (information science and statistics), Springer, New York, NY, USA, 2006.
  47. M. E. Tipping, “Sparse bayesian learning and the relevance vector machine,” Journal of Machine Learning Research, vol. 1, pp. 211–244, 2001.
  48. J. Berger, Statistical Decision Theory and Bayesian Analysis, Springer, 1985.
  49. P. Legendre, R. G. Galzin, and M. L. Harmelin-Vivien, “Relating behavior to habitat: solutions to the fourth-corner problem,” Ecology, vol. 78, no. 2, pp. 547–562, 1997. View at Scopus
  50. D. Chessel, A. B. Dufour, and S. Dray, “ade4: Analysis of Ecological Data : Exploratory and Euclidean methods in Environmental sciences. R package version 1.4-17,” 2011, http://CRAN.R-project.org/package=ade4.
  51. A. Cormont, C. C. Vos, C. A. M. van Turnhout, R. P. B. Foppen, and C. J. F. Ter Braak, “Using life-history traits to explain bird population responses to changing weather variability,” Climate Research, vol. 49, no. 1, pp. 59–71, 2011. View at Publisher · View at Google Scholar
  52. B. Shipley, P. A. Keddy, D. R. J. Moore, and K. Lemky, “Regeneration and establishment strategies of emergent macrophytes,” Journal of Ecology, vol. 77, no. 4, pp. 1093–1110, 1989. View at Scopus
  53. C. J. F. ter Braak, A. Cormont, and S. Dray, “Improved testing of species traits-environment relationships in the fourth corner problem,” Ecology. In press.
  54. J. P. M. Lenssen, F. B. J. Menting, and W. H. V. D. Putten, “Plant responses to simultaneous stress of waterlogging and shade: amplified or hierarchical effects?” New Phytologist, vol. 157, no. 2, pp. 281–290, 2003. View at Publisher · View at Google Scholar · View at Scopus
  55. S. Dolédec, B. Statzner, and M. Bournard, “Species traits for future biomonitoring across ecoregions: Patterns along a human-impacted river,” Freshwater Biology, vol. 42, no. 4, pp. 737–758, 1999. View at Publisher · View at Google Scholar · View at Scopus
  56. M. Westqby, E. Jurado, and M. Leishman, “Comparative evolutionary ecology of seed size,” Trends in Ecology & Evolution, vol. 7, no. 11, pp. 368–372, 1992. View at Scopus
  57. J. P. Grime, Plant Strategies and Vegetation Processes, Wiley, Chichester, UK, 1979.
  58. N. C. Garwood, “Functional morphology of tropical tree seedlings,” in The Ecology of Tropical Forest Tree Seedlings, M. D. Swaine, Ed., pp. 59–129, UNESCO, Paris, France, 1996.
  59. P. T. Green and P. A. Juniper, “Seed mass, seedling herbivory and the reserve effect in tropical rainforest seedlings,” Functional Ecology, vol. 18, no. 4, pp. 539–547, 2004. View at Publisher · View at Google Scholar · View at Scopus
  60. P. A. Keddy, L. Twolan-Strutt, and I. C. Wisheu, “Competitive effect and response rankings in 20 wetland plants: are they consistent across three environments?” Journal of Ecology, vol. 82, no. 3, pp. 635–643, 1994. View at Scopus
  61. A. Stockey and R. Hunt, “Predicting secondary succession in wetland mesocosms on the basis of autecological information on seeds and seedlings,” Journal of Applied Ecology, vol. 31, no. 3, pp. 543–559, 1994. View at Scopus
  62. P. J. Grubb, “Control of forest growth and distribution on wet tropical mountains: with special reference to mineral nutrition,” Annual Review of Ecology and Systematics, vol. 8, pp. 83–107, 1977.
  63. M. Henry, H. Stevens, D. E. Bunker, S. A. Schnitzer, and W. P. Carson, “Establishment limitation reduces species recruitment and species richness as soil resources rise,” Journal of Ecology, vol. 92, no. 2, pp. 339–347, 2004. View at Publisher · View at Google Scholar · View at Scopus