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).