Spatial complementarity in tree crowns explains overyielding in species mixtures

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1 VOLUME: 1 ARTICLE NUMBER: 0063 In the format provided by the authors and unedited. Spatial complementarity in tree crowns explains overyielding in species mixtures Laura J. Williams, Alain Paquette, Jeannine Cavender-Bares, Christian Messier and Peter B. Reich NATURE ECOLOGY & EVOLUTION DOI: /s

2 Supplementary Note Relationships between crown complementarity, complementarity effects and selection effects. Stem biomass overyielding (also known as the net biodiversity effect, NE) can be statistically separated into additive parts that represent the selection effect (SE) and the complementarity effect (CE) 1. Statistically, SE is defined as the covariance between yields in monocultures and the change in yields from monoculture to mixture, and CE is defined as the mean change in yield from monoculture to mixture 1. SE and CE both contribute to the net overyielding in stem biomass observed across this experiment with SEs tending to be stronger (Supplementary Fig. 4) 2. The observed crown complementarity (CCI obs ) relates most strongly to the net biodiversity effect (r 2 = 0.61, P < 0.001) that is, the sum of SE and CE but also shows a significant positive relationship with SEs (r 2 = 0.48, P < 0.001) and a weak positive relationship with CE (r 2 = 0.13, P = 0.081; Supplementary Fig. 4a). While the net shift from monocultures to mixture in crown complementarity (CCI obs - CCCCCC!"#" ) mirrors these trends (Supplementary Fig. 4b), the portion of crown complementarity attributable to species differences in crowns (CCI pred - CCCCCC!"#" ) was more strongly associated with SE (Supplementary Fig. 4c) and the portion of crown complementarity attributable to plasticity (CCI obs - CCCCCC!"#" ) was most strongly associated with CE (Supplementary Fig. 4d). However, the latter two relationships were strongly influenced by a single species mixture. Both SE and CE are underlain by real biological interactions competition, facilitation and/or niche partitioning 1,3.The tendency for stronger SEs in this experiment indicates that stem biomass overyielding tends to be more attributable to the enhanced growth of single species within mixtures. The number of individuals is fixed within our experiment (cf. many grassland biodiversity experiments). As a result, the only way that a species that was more productive in monoculture could increase overall stem biomass overyielding (net effects) in a mixture via SE is by the species overyielding per capita as well as per plot. This suggests that either some form of facilitation or reduced competition from neighbours increased its performance in mixture. Overall, these results suggest that crown complementarity provides a biological mechanism to explain net patterns of stem biomass overyielding across mixtures, combining components of stem biomass overyielding that are statistically attributable to selection effects and to complementarity effects. NATURE ECOLOGY & EVOLUTION DOI: /s

3 Supplementary Methods Characterising crown shape with the beta distribution. To characterise shape, we fit the beta distribution to tree profiles, as follows:!!!!!(!)!(!) xx!!! (1 xx)!!! (S1) where a and b are the two shape parameters that describe the distribution. The beta distribution was chosen for its flexibility; it can represent a curve with a single peak at any point from left to right and with the peak being more or less pronounced 4. To fit the distribution, the crown s radius was assumed to be zero at ground level and zero at the top of the tree, and heights were modelled as the midpoint of each height stratum (e.g., 15 cm for the 0 to 30 cm height stratum). The height of each tree was scaled from 0 to 1, which separates shape from height, and radii were scaled to approximate an integral of one. For each tree profile, the Nelder-Mead optimisation method, implemented in the optim function 5, was used to estimate the two shape parameters using R 2 goodness of fit 6. The mean R 2 for trees (excluding the uppermost and lowermost points of the tree, which were fixed at one and defined as perfect fits) was 0.88 and ranged from 0.28 to 1; 11 of 328 trees had fits of R 2 < 0.6 and were excluded from analyses. Characterising variation in size and shape. For each species (i), the variation in each shape and size measurement was characterised using a phenotypic plasticity index (PI) 7 : PI i = (maximum i - minimum i )/maximum i (S2) PI was used in two ways for each species and measurement. First, to characterise variation among plots (PI among plots ), the mean measurement value was calculated for each plot (i.e. monoculture and mixture) and the highest and lowest mean values were used for the maximum and minimum, respectively. Second, to characterise species variation within plots (PI within plots ), PI was calculated for each plot using the highest and lowest value measured for conspecific trees, and these PIs were averaged to give the mean PI within plots. Variation within plots was calculated to provide additional context for the among-plot variation. Effect of vertical distributions of leaf area and mass on crown complementarity. To assess how the vertical distribution of leaves within a tree crown might influence crown complementarity, we calculated CCI (see Methods Eqns 1,2) by weighting crown volumes with estimates of leaf area and leaf mass. The volume of non-overlapping crowns was simply multiplied by estimates of the leaf area or leaf mass for the given tree and stratum, and expressed as a proportion of the total leaf area or mass of the two crowns. To estimate leaf area and leaf mass, we made a coarse visual categorisation of leaf density (very low-, low-, medium-, high-density) for each stratum of each focal tree. These categories were calibrated with a line-intercept method 8 for each species, so that we could approximate the leaf area per crown volume represented by each leaf-density category. For each tree, specific leaf area (SLA) was also measured for a leaf sample taken from the second highest and second lowest stratum; standard trait protocols were followed 9. These SLA values allow estimates of leaf area to be translated into coarse estimates of leaf mass. In these calculations, we assigned the SLA values from the high and low samples to the top and bottom half of the crown, respectively. NATURE ECOLOGY & EVOLUTION DOI: /s

4 Crown complementarity using LAI. We examined whether the relationship between the crown complementarity index (CCI) and stem biomass overyielding held when using an independent dataset of leaf area in place of crown volume. To do this, the leaf area index (LAI) for each species and vertical stratum was measured for two- and four-species mixtures using a modified line intercept method 8. For each species mixture, fifteen lines were measured and averaged. Using these data, we calculated CCI (see Methods Eqns 1, 2) by substituting LAI for crown volume. NATURE ECOLOGY & EVOLUTION DOI: /s

5 Bp Ll Qr Ba Ar As Pre Ps To Pg Pru Ab Supplementary Figure 1 Growth rate and shade tolerance. The shade tolerance ranking 10 (0-5, least to most tolerant) was significantly associated with maximum growth rate (log 10 transformed, see Methods) both among the angiosperm species (grey circles, n = 5; SMA regression: r 2 = 0.97, P < 0.001) and gymnosperm species (black triangles, n = 7; SMA regression: r 2 = 0.79, P = 0.003) in this study. The slope of the relationship does not significantly differ between angiosperms and gymnosperms (SMA regression, P = 0.47), but the intercept does (P < 0.001). Species codes: Ab = Abies balsamea, Ar = Acer rubrum, As = Acer saccharum, Ba = Betula alleghaniensis, Bp = Betula papyrifera, Ll = Larix laricina, Pg = Picea glauca, Pre = Pinus resinosa, Pru = Picea rubens, Ps = Pinus strobus, Qr = Quercus rubra, To = Thuja occidentalis. NATURE ECOLOGY & EVOLUTION DOI: /s

6 Supplementary Figure 2 Three indices of crown complementarity. Three crown complementarity indices (CCI) were calculated for each species mixture, and differ in the pool of focal trees (left) from which pairs of trees were drawn to assess crown complementarity (middle; see Methods and Fig. 1b,c): (a) Observed crown complementarity (CCI obs ) used trees measured in the mixture; (b) Predicted crown complementarity (CCI pred ) used trees of the constituent species measured in monoculture; (c) Mean monoculture crown complementarity (CCCCCC!"#" ) used trees of the constituent species measured in monoculture, but only calculates crown complementarity for tree pairs of the same species (i.e. CCCCCC!"#" is identical to the mean crown complementarity observed in the monocultures of constituent species). Crown complementarity was averaged across all possible tree pairs within a pool of focal trees to give the crown complementarity index (CCI, see Methods Eqns 1, 2). The net change in complementarity from monoculture-grown to mixture-grown trees is calculated as the difference between CCCCCC!"#" and CCI obs, differences between CCI pred and CCI obs are attributed to plasticity (defined here as any shifts in crown shape or size from monoculture- to mixture-grown trees), and differences between CCCCCC!"#" and CCI pred are attributed to inherent differences among species. NATURE ECOLOGY & EVOLUTION DOI: /s

7 Supplementary Figure 3 Three indices of crown complementarity for each species mixture. Three crown complementarity indices (CCI) were calculated for each species mixture: observed (CCI obs, black), predicted (CCI pred, grey), and mean monoculture (CCCCCC!"#", white). Rectangles surround CCI indices that do not significantly differ for a given mixture (P > 0.05, after Sequential Bonferroni correction). Mixtures ordered from low to high functional dispersion (FDis) in maximum growth rate. The five mixtures where observed CCI was lower than the predicted CCI are shaded in grey. The shapes of symbols represent the composition of mixtures: circles represent angiosperm only mixtures, triangles represent gymnosperm only mixtures, and squares represent gymnosperm-angiosperm mixtures. Species codes: Ab = Abies balsamea, Ar = Acer rubrum, As = Acer saccharum, Ba = Betula alleghaniensis, Bp = Betula papyrifera, Ll = Larix laricina, Pg = Picea glauca, Pre = Pinus resinosa, Pru = Picea rubens, Ps = Pinus strobus, Qr = Quercus rubra, To = Thuja occidentalis, All = 12 species mixture. NATURE ECOLOGY & EVOLUTION DOI: /s

8 Supplementary Figure 4 Crown complementarity and the selection effects and complementarity effects contributing to net stem biomass overyielding. Stem biomass overyielding (net effect, NE, light grey; see Figs. 3-4) can be statistically separated into two parts: a component attributable to the selection effect (SE, dark grey) and a component attributable to the complementarity effect (CE, open circles and black line) 1. (a) Observed crown complementarity was most strongly associated with SE (r 2 = 0.48, b = , t 23 = 4.585, P < 0.001), but also showed a weak positive association with CE (r 2 = 0.13, b = , t 23 = 1.828, P = 0.081). (b) The net change in crown complementarity from monoculture- to mixture-grown trees (CCI obs - CCCCCC!"#" ) was significantly positively associated with SE (r 2 = 0.62, b = 52.57, t 23 = 6.08, P < 0.001) and weakly associated with CE (r 2 = 0.11, b = 22.22, t 23 = 1.68, P = 0.107). (c) The contribution of species differences to complementarity (CCI pred - CCCCCC!"#" ) was significantly positively associated with SE (r 2 = 0.51, b = 61.54, t 23 = 4.90, P < 0.001) but not with CE (P = 0.897). (c) The contribution of plasticity to complementarity (CCI obs - CCI pred ) was significantly positively associated with CE (r 2 = 0.20, b = 43.78, t 23 = 2.40, P = 0.025) and weakly associated with SE (r 2 = 0.11, b = 32.33, t 23 = 1.69, P = 0.104); however, these relationships were strongly influenced by a single mixture with the highest CE and lowest SE, which was composed of Betula papyrifera and Quercus rubra. Relationships that are not statistically significant (α = 0.05) are shown with dashed lines. NATURE ECOLOGY & EVOLUTION DOI: /s

9 Supplementary Figure 5 Crown complementarity weighted by leaf area and mass and stem biomass overyielding. The observed crown complementarity (CCI obs ) explained similar proportions of variation in stem biomass overyielding across the 25 mixed-species plots when calculated using crown volume (black, as reported in the main text, r 2 = 0.61, b = 65.43, t 23 = 6.01, P < 0.001), crown volume weighted by leaf area (grey, r 2 = 0.59, b = 59.08, t 23 = 5.73, P < 0.001), or crown volume weighted by leaf mass (white symbols and dashed regression line, r 2 = 0.56, b = 58.41, t 23 = 5.41, P < 0.001). See Supplementary Methods. NATURE ECOLOGY & EVOLUTION DOI: /s

10 Supplementary Figure 6 Crown complementarity calculated using leaf area index and stem biomass overyielding. The crown complementarity index calculated using leaf area index (CCI LAI ) was positively associated with stem biomass overyielding across all two- and fourspecies mixtures (thick line, n = 24; r 2 = 0.31, b = 27.12, t 22 = 3.119, P = 0.005). Two-species mixtures shown in black and four-species mixtures shown in grey; there was no significant interaction with species richness (P = 0.650). See Supplementary Methods. NATURE ECOLOGY & EVOLUTION DOI: /s

11 Supplementary Table 1 Mean size and shape of trees SUPPLEMENTARY INFORMATION Species Angiosperms: Tree height (m) Crown volume (m 3 ) Size Max. crown radius (m) Crown depth (prop.) Acer rubrum 2.05 ± ± ± ± 0.12 Acer saccharum ± 0.28 ± 0.31 ± 0.11 ± 0.17 Betula alleghaniensis ± 0.34 ± 0.33 ± 0.06 ± 0.11 Betula papyrifera ± 0.62 ± 0.58 ± 0.08 ± 0.06 Quercus rubra ± 0.67 ± 0.78 ± 0.11 ± 0.06 Gymnosperms: Abies balsamea ± 0.23 ± 0.08 ± 0.03 ± 0.00 Larix laricina ± 0.69 ± 1.15 ± 0.15 ± 0.04 Picea glauca ± 0.12 ± 0.09 ± 0.04 ± 0.00 Picea rubens ± 0.15 ± 0.11 ± 0.06 ± 0.00 Pinus resinosa ± 0.28 ± 0.28 ± 0.08 ± 0.00 Pinus strobus ± 0.19 ± 0.18 ± 0.06 ± 0.00 Thuja occidentalis ± 0.19 ± 0.25 ± 0.09 ± 0.00 Crown depth expressed as a proportion of tree height. Crown shape Mean Mode Variance Skew 0.55 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.09 Shape Shape parameter parameter a b 2.31 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.26 Mean (± standard deviation) of the size and shape of monoculture-grown trees four years after the experiment was planted (n = 6 trees, except n = 5 trees for Larix laricina). Shape was characterised using the beta distribution (see Methods and Supplementary Methods). NATURE ECOLOGY & EVOLUTION DOI: /s

12 Supplementary Table 2 Plasticity in crown size and shape SUPPLEMENTARY INFORMATION Species Crown volume (m 3 ) Crown size Max. crown radius (m) Crown depth (prop.) Beta mean Crown shape Beta Beta mode variance Beta skew Angiosperms: Acer rubrum 0.74 (0.72) 0.36 (0.34) 0.22 (0.16) 0.13 (0.15) 0.35 (0.27) 0.32 (0.35) 0.24 (0.30) Acer saccharum 0.69 (0.48)** 0.32 (0.31) 0.21 (0.12) 0.25 (0.14)** 0.38 (0.25)* 0.39 (0.26)* 0.41 (0.24)** Betula alleghaniensis 0.50 (0.68) 0.25 (0.36) 0.18 (0.14) 0.18 (0.16) 0.34 (0.29) 0.28 (0.30) 0.25 (0.23) Betula papyrifera 0.73 (0.49)*** 0.41 (0.27)* 0.23 (0.15)* 0.16 (0.11) 0.21 (0.17) 0.34 (0.30) 0.26 (0.20) Quercus rubra 0.72 (0.60) 0.44 (0.32) (0.16) (0.16) (0.23) (0.29)* 0.37 (0.28) Gymnosperms: Abies balsamea 0.50 (0.56) 0.19 (0.28) 0 (0) 0.18 (0.18) 0.38 (0.34) 0.30 (0.31) 0.16 (0.16) Larix laricina 0.54 (0.52) 0.21 (0.32) 0.12 (0.07)* 0.14 (0.16) 0.31 (0.31) 0.26 (0.16)* 0.19 (0.24) Picea glauca 0.60 (0.41) 0.28 (0.20) 0 (0) 0.12 (0.16) 0.38 (0.39) 0.23 (0.26) 0.14 (0.17) Picea rubens 0.72 (0.49) 0.44 (0.24). 0 (0) 0.07 (0.13) 0.29 (0.39) 0.16 (0.22) 0.08 (0.13) Pinus resinosa 0.66 (0.42) 0.23 (0.26) 0 (0) 0.08 (0.10) 0.54 (0.63) 0.17 (0.18) 0.10 (0.11) Pinus strobus 0.51 (0.46) 0.23 (0.20) 0 (0) 0.14 (0.14) 0.44 (0.46) 0.20 (0.15) 0.15 (0.15) Thuja occidentalis 0.61 (0.43) 0.30 (0.19) 0 (0) 0.09 (0.10) 0.58 (0.63) 0.21 (0.19) 0.09 (0.09) Crown depth expressed as a proportion of tree height. Asterisks indicate a significant difference in a species mean trait value among one or more plots:. P <0.1, * P <0.05, ** P <0.01, *** P <0.001 Plasticity indices (PI) 7 for the crown size and shape of species four years after the experiment was planted (see Methods and Supplementary Methods). PI among plots (i.e. neighbourhoods) is shown along with the average PI within plots in parentheses. All species were present in seven plots except Acer saccharum 8 plots, Picea glauca 10 plots, and Pinus strobus 11 plots. Shape was characterised using the beta distribution (see Methods and Supplementary Methods). NATURE ECOLOGY & EVOLUTION DOI: /s

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