Simple parametric tests for trait–environment association

Cajo J.F. ter Braak*, Pedro R. Peres-Neto, Stéphane Dray

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)

Abstract

Question: The CWM approach is an easy way of analysing trait–environment association by regressing (or correlating) the mean trait per plot against an environmental variable and assessing the statistical significance of the slope or the associated correlation coefficient. However, the CWM approach does not yield valid tests, as random traits (or random indicator values) are far too often judged significantly related to the environmental variable, even when the trait and environmental variable are extrinsic to (not derived from) the community data. Existing solutions are the ZS-modified test (Zelený & Schaffers,) and the max (or sequential) test based on the fourth-corner correlation. Both tests are based on permutations which become cumbersome when many tests need to be carried out and many permutations are required, as in methods that correct for multiple testing. The main goal of this study was to compare these existing permutation-based solutions and to develop a quick and easy parametric test that can replace them. Methods: This study decomposes the fourth-corner correlation in two ways, which suggests a simple parametric approach consisting of assessing the significances of two linear regressions, one plot-level test as in the CWM approach and one species-level test, the reverse of the CWM approach, that regresses the environmental mean per species (i.e. the species niche centroid) on to the trait. The tests are combined by taking the maximum p-value. The type I error rates and power of this parametric max test are examined by simulation of one- and two-dimensional Gaussian models and log-linear models. Results: The ZS-modified test and the fourth-corner max test are conservative in different scenarios, the ZS-modified test being even more conservative than the fourth-corner. The new parametric max test is shown to control the type I error and has equal or even higher power than permutation tests based on the fourth-corner, the ZS-modified test and variants thereof. A weighted version of the new test showed inflated type I error. Conclusion: The combination of two simple regressions is a good alternative to the fourth-corner and the ZS-modified test. This combination is also applicable when multiple trait measurements are made per plot.

Original languageEnglish
Pages (from-to)801-811
JournalJournal of Vegetation Science
Volume29
Issue number5
Early online date10 Jul 2018
DOIs
Publication statusPublished - Sep 2018

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testing
test
environmental factors
niche
niches
linear models
methodology
simulation

Keywords

  • community ecology
  • community-level test
  • CWM of traits
  • environmental gradients
  • fourth-corner
  • functional traits
  • modified test
  • species niche centroid
  • species-level test
  • statistical ecology
  • trait–environment relationship

Cite this

ter Braak, Cajo J.F. ; Peres-Neto, Pedro R. ; Dray, Stéphane. / Simple parametric tests for trait–environment association. In: Journal of Vegetation Science. 2018 ; Vol. 29, No. 5. pp. 801-811.
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abstract = "Question: The CWM approach is an easy way of analysing trait–environment association by regressing (or correlating) the mean trait per plot against an environmental variable and assessing the statistical significance of the slope or the associated correlation coefficient. However, the CWM approach does not yield valid tests, as random traits (or random indicator values) are far too often judged significantly related to the environmental variable, even when the trait and environmental variable are extrinsic to (not derived from) the community data. Existing solutions are the ZS-modified test (Zelen{\'y} & Schaffers,) and the max (or sequential) test based on the fourth-corner correlation. Both tests are based on permutations which become cumbersome when many tests need to be carried out and many permutations are required, as in methods that correct for multiple testing. The main goal of this study was to compare these existing permutation-based solutions and to develop a quick and easy parametric test that can replace them. Methods: This study decomposes the fourth-corner correlation in two ways, which suggests a simple parametric approach consisting of assessing the significances of two linear regressions, one plot-level test as in the CWM approach and one species-level test, the reverse of the CWM approach, that regresses the environmental mean per species (i.e. the species niche centroid) on to the trait. The tests are combined by taking the maximum p-value. The type I error rates and power of this parametric max test are examined by simulation of one- and two-dimensional Gaussian models and log-linear models. Results: The ZS-modified test and the fourth-corner max test are conservative in different scenarios, the ZS-modified test being even more conservative than the fourth-corner. The new parametric max test is shown to control the type I error and has equal or even higher power than permutation tests based on the fourth-corner, the ZS-modified test and variants thereof. A weighted version of the new test showed inflated type I error. Conclusion: The combination of two simple regressions is a good alternative to the fourth-corner and the ZS-modified test. This combination is also applicable when multiple trait measurements are made per plot.",
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Simple parametric tests for trait–environment association. / ter Braak, Cajo J.F.; Peres-Neto, Pedro R.; Dray, Stéphane.

In: Journal of Vegetation Science, Vol. 29, No. 5, 09.2018, p. 801-811.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Simple parametric tests for trait–environment association

AU - ter Braak, Cajo J.F.

AU - Peres-Neto, Pedro R.

AU - Dray, Stéphane

PY - 2018/9

Y1 - 2018/9

N2 - Question: The CWM approach is an easy way of analysing trait–environment association by regressing (or correlating) the mean trait per plot against an environmental variable and assessing the statistical significance of the slope or the associated correlation coefficient. However, the CWM approach does not yield valid tests, as random traits (or random indicator values) are far too often judged significantly related to the environmental variable, even when the trait and environmental variable are extrinsic to (not derived from) the community data. Existing solutions are the ZS-modified test (Zelený & Schaffers,) and the max (or sequential) test based on the fourth-corner correlation. Both tests are based on permutations which become cumbersome when many tests need to be carried out and many permutations are required, as in methods that correct for multiple testing. The main goal of this study was to compare these existing permutation-based solutions and to develop a quick and easy parametric test that can replace them. Methods: This study decomposes the fourth-corner correlation in two ways, which suggests a simple parametric approach consisting of assessing the significances of two linear regressions, one plot-level test as in the CWM approach and one species-level test, the reverse of the CWM approach, that regresses the environmental mean per species (i.e. the species niche centroid) on to the trait. The tests are combined by taking the maximum p-value. The type I error rates and power of this parametric max test are examined by simulation of one- and two-dimensional Gaussian models and log-linear models. Results: The ZS-modified test and the fourth-corner max test are conservative in different scenarios, the ZS-modified test being even more conservative than the fourth-corner. The new parametric max test is shown to control the type I error and has equal or even higher power than permutation tests based on the fourth-corner, the ZS-modified test and variants thereof. A weighted version of the new test showed inflated type I error. Conclusion: The combination of two simple regressions is a good alternative to the fourth-corner and the ZS-modified test. This combination is also applicable when multiple trait measurements are made per plot.

AB - Question: The CWM approach is an easy way of analysing trait–environment association by regressing (or correlating) the mean trait per plot against an environmental variable and assessing the statistical significance of the slope or the associated correlation coefficient. However, the CWM approach does not yield valid tests, as random traits (or random indicator values) are far too often judged significantly related to the environmental variable, even when the trait and environmental variable are extrinsic to (not derived from) the community data. Existing solutions are the ZS-modified test (Zelený & Schaffers,) and the max (or sequential) test based on the fourth-corner correlation. Both tests are based on permutations which become cumbersome when many tests need to be carried out and many permutations are required, as in methods that correct for multiple testing. The main goal of this study was to compare these existing permutation-based solutions and to develop a quick and easy parametric test that can replace them. Methods: This study decomposes the fourth-corner correlation in two ways, which suggests a simple parametric approach consisting of assessing the significances of two linear regressions, one plot-level test as in the CWM approach and one species-level test, the reverse of the CWM approach, that regresses the environmental mean per species (i.e. the species niche centroid) on to the trait. The tests are combined by taking the maximum p-value. The type I error rates and power of this parametric max test are examined by simulation of one- and two-dimensional Gaussian models and log-linear models. Results: The ZS-modified test and the fourth-corner max test are conservative in different scenarios, the ZS-modified test being even more conservative than the fourth-corner. The new parametric max test is shown to control the type I error and has equal or even higher power than permutation tests based on the fourth-corner, the ZS-modified test and variants thereof. A weighted version of the new test showed inflated type I error. Conclusion: The combination of two simple regressions is a good alternative to the fourth-corner and the ZS-modified test. This combination is also applicable when multiple trait measurements are made per plot.

KW - community ecology

KW - community-level test

KW - CWM of traits

KW - environmental gradients

KW - fourth-corner

KW - functional traits

KW - modified test

KW - species niche centroid

KW - species-level test

KW - statistical ecology

KW - trait–environment relationship

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DO - 10.1111/jvs.12666

M3 - Article

VL - 29

SP - 801

EP - 811

JO - Journal of Vegetation Science

JF - Journal of Vegetation Science

SN - 1100-9233

IS - 5

ER -