Data from: Functional traits and community composition: a comparison among community-weighted means, weighted correlations, and multilevel models

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.