Material and Methods
Data
collection
We conducted a survey of suitable studies using ISI Web of Science and
Google Scholar, and cited references in relevant publications, up to
September 01, 2019. We identified relevant studies using the research
terms: ”(tree OR forest) AND (tree diversity OR tree richness OR stand
mixture OR mixed stand OR mixed plantation OR tree mixture OR mixed
forest plantations OR mix tree) AND (experiment) AND (productivity OR
biomass OR growth OR volume OR stem OR overyielding) NOT (permanent
forest) NOT (grass OR grassland)”. We included studies for the
meta-analyses when they met the following criteria: (1) studies
contained at least one mixture treatment with corresponding
monocultures, (2) all productivity and names of the species in each
mixture and corresponding monocultures could be extracted directly from
the text, tables, and/or figures, (3) the proportion of constituent
species in each mixtures could be extracted or be calculated, (4)
studies were specifically implemented to isolate the effects of tree
diversity from other factors, such as soil conditions and topographic
features.
When the productivity of stand mixtures and corresponding monocultures
were measured across multiple years, we extracted data from the latest
year. We used GetData Graph Digitizer (v. 2.26.0.20) to extract data
from the figures. In total, 59 published papers with 210 paired
observations of aboveground productivity for tree mixtures and
corresponding monocultures were selected. We extracted the data of tree
species identities and the relative proportions of stem density from the
constituent species of each species mixture.
We also obtained the plant
functional traits, including leaf nitrogen content (LNC), specific leaf
area (SLA), and wood density (WD) for each tree species from each study.
When the plant functional traits were not available in the original
publication, they were extracted from the TRY Plant Trait Database
(Kattge et al. 2011) and other published
datasets and literature. The LNC and SLA represent the leaf economics
functions, whereas the WD represents the wood economics function (see
Fig. S1 in Supporting Information).
Furthermore, we obtained the experimental duration, mean annual
temperature (MAT) and mean annual precipitation (MAP) for each study. In
cases where the MAT and MAP were not reported, they were extracted from
a global climate database (http://www.worldclim.org/) using the
geographical coordinates of the study sites. Overall, the species
richness ranged from two to 24, and the experimental duration ranged
from 0.5 to 120 years (Table S1). We performed a principal component
analysis (PCA) of the MAT and MAP and extracted the first principal
component (representing 82.69% of total inertia) to represent the
climate condition of each study (Fig. S2).
Functional dispersion and
functional identity of species
mixtures.
We used functional dispersion (FDis) to represent the functional
dissimilarities between the co-occurring species of each mixture. FDis
opens possibilities for formal statistical tests for comparing
differences in functional diversity between groups of communities
through a distance-based test for homogeneity of multivariate dispersion
(Anderson 2006;
Laliberte & Legendre 2010). FDis was
unaffected by species richness and could handle any number of traits
(Laliberte & Legendre 2010). Most of the
mixtures included in this study contained only two tree species.
Multidimensional FDis, as well as
the FDis for each individual trait of each species mixture were
calculated weighted by the relative abundances of each
species. The relative abundance of
constituent species of each mixture was calculated by stem density or
basal area. For most studies, the proportion of each species in the
mixtures was equal (Table S1).The Gower dissimilarity matrix and
species-species Euclidean distance matrix were employed to compute the
multidimensional FDis and FDis of every single trait, respectively
(Laliberté et al. 2014).
The functional identity of each species mixture was represented by the
community-weighted mean (CWM) of the SLA, LNC, and WD, which was
calculated as the averaged trait value of each species mixture (see
details in Table S2). The FDis and CWM calculations were conducted using
the FD package (Laliberte &
Legendre 2010).
Data
analysis
The effects of tree mixtures on productivity were calculated as the
natural log-transformed response ratio (lnRR )
(Hedges et al. 1999):
lnRR = ln(X t / X c)
(1)
where X t and X c are the
observed productivity of species mixture and the mean productivity of
all monocultures corresponding to the mixture, respectively.
The effect size and subsequent inferences were dependant on how
individual observations were weighted in a particular meta-analysis
(Chen et al. 2019). Weightings that are
based on sampling variances might assign extreme importance to a few
individual observations (which consequently caused the average
lnRR to be determined by a small number of studies), we employed
the number of replications, as similar to previous studies
(Pittelkow et al. 2014;
Ma & Chen 2016), for weighting in this
study:
W r = (N c ×N t) / (N c +N t) (2)
where W r is the weight of each observation, andN c and N t are the numbers
of replications of monocultures and mixtures, respectively.
We examined how the FDis and CWM in tree mixtures were associated with
the species richness in mixtures using Model II regression with thelmodel2 package (Legendre 2015).
We initially tested the extent to which the FDis and CWM impacted the
mixture effect on productivity across the species richness levels.
Subsequently, we tested how they determined the tree mixture effect
within two-, three- and four-species mixtures, respectively. These three
species richness levels contained the largest number of mixtures in this
meta-analysis. The linear-mixed effect model was constructed using Eqn.
(3):
\(\mathrm{\text{ln\ RR}}\mathrm{\ \sim\ }\mathrm{\beta}_{\mathrm{0}}\mathrm{+}\mathrm{\beta}_{\mathrm{1}}\mathrm{\bullet}x_{i}\mathrm{+}\mathrm{\pi}_{\mathrm{\text{study}}}\mathrm{+\ }\mathrm{\varepsilon}_{\mathrm{\text{ij}}}\)(3)
where xi are the species richness in mixtures,
multidimensional FDis, FDis and CWM of each individual trait,
respectively; β, πspecies and εij are
regression coefficients, the random effect of ”study”, and sampling
error, respectively. The random effect accounts for autocorrelation
between observations within the same study. We conducted the analysis
using maximum likelihood estimation with the lme4 package
(Bates et al. 2015). All analyses were
performed in R 3.6.1 (Team 2019).