DOI: 10.5061/dryad.7gj0s3b
title: Data from: Functional traits and community composition: a comparison among community-weighted means, weighted correlations, and multilevel models

description: 1. Of the several approaches that are used to analyze functional
 trait-environment relationships, the most popular is community-weighted
 mean regressions (CWMr) in which species trait values are averaged at the
 site level and then regressed against environmental variables. Other
 approaches include model-based methods and weighted correlations of
 different metrics of trait-environment associations, the best known of
 which is the fourth-corner correlation method. 2. We investigated these
 three general statistical approaches for trait-environment associations:
 CWMr, five weighted correlation metrics (Peres-Neto et al. 2017), and two
 multilevel models (MLM) using four different methods for computing
 p-values. We first compared the methods applied to a plant community
 dataset. To determine the validity of the statistical conclusions, we then
 performed a simulation study. 3. CWMr gave highly significant associations
 for both traits, while the other methods gave a mix of support. CWMr had
 inflated type I errors for some simulation scenarios, implying that the
 significant results for the data could be spurious. The weighted
 correlation methods had generally good type I error control but had low
 power. One of the multilevel models, that from Jamil et al. (2013), had
 both good type I error control and high power when an appropriate method
 was used to obtain p-values. In particular, if there was no correlation
 among species in their abundances among sites, a parametric bootstrap
 likelihood ratio test (LRT) gave the best power. When there was
 correlation among species in their abundances, a conditional parametric
 LRT had correct type I errors but had lower power. 4. There is no overall
 best method for identifying trait-environment associations. For the simple
 task of testing, one-by-one, associations between single environmental
 variables and single traits, the weighted correlations with permutation
 tests all had good type I error control, and their ease of implementation
 is an advantage. For the more complex task of multivariate analyses and
 model fitting, and when high statistical power is needed, we recommend
 MLM2 (Jamil et al. 2013); however, care must be taken to ensure against
 inflated type I errors. Because CWMr exhibited highly inflated type I
 error rates, it should always be avoided. 2. We investigated these three
 general statistical approaches for trait-environment associations: CWMr,
 five weighted correlation metrics (Peres-Neto et al. 2017), and two
 multilevel models (MLM) using five different methods for computing
 p-values. We first compared the methods applied to a plant community
 dataset. To determine the validity of the statistical conclusions, we then
 performed a simulation study. 3. CWMr gave highly significant associations
 for both traits, while the other methods gave a mix of support. CWMr had
 inflated type I errors for some simulation scenarios. The weighted
 correlation methods had generally good type I error control but had low
 power. One of the multilevel models, that from Jamil et al. (2013), had
 both good type I error control and high power when an appropriate method
 was used to obtain p-values. In particular, if there was no correlation
 among species in their abundances among sites, a parametric bootstrap
 likelihood ratio test (LRT) gave the best power. When there was
 correlation among species in their abundances, a conditional parametric
 LRT had correct type I errors but suffered from low power. 4. There is no
 overall best method for identifying trait-environment associations. For
 the simple task of testing, one-by-one, associations between single
 environmental variables and single traits, the weighted correlations with
 permutation tests all had good type I error control, and their ease of
 implementation is an advantage. For the more complex task of multivariate
 analyses and model fitting, and when high statistical power is needed, we
 recommend MLM2 (Jamil et al. 2013); however, care must be taken to ensure
 against inflated type I errors. Because CWMr exhibited highly inflated
 type I error rates, it should be avoided.
description: Whittaker plant
 community plot revisit dataData on plant
 occurrences documented in revisits to a low-elevation, non-serpentine
 subset of Robert Whittaker's historic vegetation plots in the
 Siskiyou Mountains.whittaker revisit
 data.csv