Ecological Archives E096-018-A1

Ecological Archives E096-018-A1

Jiajia Liu, Xinxin Zhang, Feifan Song, Shurong Zhou, Marc W. Cadotte, and Corey J. A. Bradshaw. 2015. Explaining maximum variation in productivity requires phylogenetic diversity and single functional traits. Ecology 96:176–183. http://dx.doi.org/10.1890/14-1034.1

Appendix A. Species list (Table A1), measures of diversity (Table A2) and their correlations (Table A3, Fig. A3)，full GLM results (Tables A4and A5), phylogenetic trees (Fig. A1), the removal treatment test (Fig. A2), and correlation between two PDs (Fig. A4).

Table A1. Species list categorized by taxonomic group (TG) and family.

TG	Family	Genus species
Asteraceae	Asteraceae	Ligularia virgaurea
Asteraceae	Asteraceae	Saussurea pulchra
Asteraceae	Asteraceae	Artemisia mongolica
Asteraceae	Asteraceae	Taraxacum mongolicum
Asteraceae	Asteraceae	Anaphalis lactea
Asteraceae	Asteraceae	Saussurea nigrescens
Asteraceae	Asteraceae	Saussurea leontodontoides
Asteraceae	Asteraceae	Ajania tenuifolia
Asteraceae	Asteraceae	Leontopodium haplophylloides
Asteraceae	Asteraceae	Saussurea stella
Asteraceae	Asteraceae	Aster diplostephioides
Fabaceae	Fabaceae	Astragalus polycladus
Fabaceae	Fabaceae	Oxytropis kansuensis
Fabaceae	Fabaceae	Tibetia himalaica
Fabaceae	Fabaceae	Thermopsis lanceolala
Fabaceae	Fabaceae	Medicago lupulina
others	Apiaceae	Chamaesium paradoxum
others	Caryophyllaceae	Cerastium fontanum
others	Scrophulariaceae	Euphrasia regelii
others	Rosaceae	Potentilla anserina
others	Rosaceae	Potentilla bifurca
others	Geraniaceae	Geranium pylzowianum
others	Lamiaceae	Scutellaria rehderiana
others	Alliaceae	Allium sikkimense
others	Ranunculaceae	Thalictrum alpinum
others	Ranunculaceae	Ranunculus tanguticus
others	Rosaceae	Potentilla potaninii
others	Orchidaceae	Herminium monorchis
others	Scrophulariaceae	Lancea tibetica
others	Gentianaceae	Lomatogonium carinthiacum
others	Scrophulariaceae	Veronica eriogyne
others	Plantaginaceae	Plantago depressa
others	Saxifragaceae	Parnassia trinervis
others	Caryophyllaceae	Stellaria uda
others	Gentianaceae	Gentianopsis paludosa
others	Ranunculaceae	Anemone obtusiloba
others	Scrophulariaceae	Pedicularis szetschuanica
others	Polygonaceae	Rumex acetosa
others	Ranunculaceae	Anemone trullifolia
others	Gentianaceae	Halenia elliptica
others	Gentianaceae	Gentiana farreri
others	Ranunculaceae	Anemone rivularis
others	Polygonaceae	Polygonum macrophyllum
others	Euphorbiaceae	Euphorbia helioscopia
others	Ranunculaceae	Delphinium kamaonense
Poaceae and Cyperaceae	Cyperaceae	Scirpus distigmaticus
Poaceae and Cyperaceae	Cyperaceae	Kobresia capillifolia
Poaceae and Cyperaceae	Cyperaceae	Kobresia myosuroides
Poaceae and Cyperaceae	Poaceae	Poa pratensis
Poaceae and Cyperaceae	Poaceae	Elymus nutans
Poaceae and Cyperaceae	Poaceae	Agrostis hugoniana
Poaceae and Cyperaceae	Poaceae	Koeleria litvinowii
Poaceae and Cyperaceae	Poaceae	Stipa aliena
Poaceae and Cyperaceae	Poaceae	Festuca sinensis

Table A2. Measures of diversity considered in the analysis. Variables selected for model construction in boldface.

Diversity measure	Description	References
S	Realized species richness of plot	Tilman, Wedin and Knops 1996
H'	Shannon's diversity index	Tilman, Wedin and Knops 1996
D	Simpson's diversity	Tilman, Wedin and Knops 1996
PD	Phylogenetic diversity (the sum of all hylogentic branch lengths connecting species together)	Cardinale et al. 2006
MNND	Mean nearest-neighbor distance (the mean of the shortest distances connecting each species to any other species in the assemblage)	Webb et al. 2002
MPD	Mean pairwise distance (the mean of all the distances connecting species in an assemblage)	Webb et al. 2002
MNND_ab	Abundance-weighted MNND	Webb et al. 2002
MPD_ab	Abundance-weighted MPD	Webb et al. 2002
H_ed	Entropic measure of the distribution of evolutionary distinctiveness in an assemblage	Gamfeldt, Hillebrand and Jonsson 2008
H_aed	Abundance-weighted H_ed	Gamfeldt, Hillebrand and Jonsson 2008
H_eed	Equitability of H_aed	Gamfeldt, Hillebrand and Jonsson 2008
PAE	Phylogenetic abundance evenness: measures the skew in abundances along terminal branches	Gamfeldt, Hillebrand and Jonsson 2008
IAC	Imbalance of abundances among clades: measures the deviation in abundance distribution among internal splits from a null	Gamfeldt, Hillebrand and Jonsson 2008
FD	Functional diversity: the sum of all branch lengths connecting species together in a hierarchical clustering dendrogram based on a multivariate distance matrix	Petchey and Gaston 2002
FAD	Functional attribute diversity: the sum of all pairwise species distances calculated as the Euclidean distance between species	Walker, Kinzig and Langridge 1999

FEve	Functional Evenness: abundance-weighted pairwise functional distances	Villéger, Mason and Mouillot 2008
FDis	Functional dispersion: weighted distances from a weighted centroid in multi trait space	Villéger, Mason and Mouillot 2008
FDiv	Functional divergence: mean abundance-weighted deviance from an absolute abundance-weighted deviance	Villéger, Mason and Mouillot 2008
FRic	Functional richness: convex hull volume of the trait space	Cornwell et al. 2006, Villéger et al. 2008
RaoQ	Quadratic entropy	Botta-Dukát 2005

Table A3. Spearman's r correlation matrix for raw input variables. Shown are species richness (S), Shannon's evenness (H'), phylogenetic diversity (PD), mean pairwise distance (MPD), distribution of evolutionary distinctiveness (H_ed), functional diversity (FD), functional attribute diversity (FAD), maximum plant height (H_max), leaf phosphorus (P) and nitrogen (N) content, mean seed mass (SM) and specific leaf area (SLA). ρ > 0.3 in boldface.

	S	H	PD	H_ed	MPD	FD	FAD	H_max	SM	N	P
H	0.938
PD	0.975	0.924
H_ed	0.997	0.937	0.971
MPD	0.858	0.864	0.908	0.857
FD	0.848	0.767	0.775	0.843	0.634
FAD	0.973	0.903	0.925	0.969	0.807	0.933
H_max	0.143	0.152	0.099	0.133	0.140	0.473	0.278
SM	0.091	0.196	0.144	0.094	0.291	0.204	0.148	0.607
N	0.087	0.116	0.129	0.101	0.159	-0.043	0.039	-0.411	-0.005
P	0.207	0.190	0.154	0.197	0.066	0.451	0.284	0.449	0.000	-0.387
SLA	-0.224	-0.169	-0.268	-0.227	-0.208	-0.030	-0.158	0.319	0.182	-0.258	0.412

Table A4. Generalized linear model (GLM) results for biomass production as a function of number of species (S), Shannon's evenness (H'), phylogenetic diversity (PD = phylogenetic diversity, MPD = mean pairwise distance and Hed = evolutionary distinctiveness), and various community-level means of single functional traits (H_max = maximum plant height, P = leaf phosphorus content, N = leaf nitrogen content, SM = mean seed mass and SLA = specific leaf area) or multivariate functional trait indices (FD = functional diversity, FAD = functional attribute diversity). Shown are the estimated number of model parameters (k), maximum log-likelihood (LL), the information-theoretic Akaike's information criterion corrected for small samples (AICc), change in AICc relative to the top-ranked model (ΔAICc), AICc weight (wAICc = model probability) and the percent deviance explained (%DE) as a measure of the model's goodness-of-fit.

Model	LL	k	AICc	DAICc	*wAICc*	%DE
~H_ed+H_max	-271.463	3	551.497	0.000	0.574	77.7
~PD+H_max	-271.856	3	552.283	0.786	0.388	77.5
~S+H_max	-274.217	3	557.006	5.509	0.037	76.0
~MPD+H_max	-277.387	3	563.345	11.848	0.002	74.0
~H'+H_max	-280.501	3	569.574	18.077	<0.001	71.7
~H_ed+N+SM	-285.986	4	582.841	31.344	<0.001	67.4
~S+N+SM	-286.326	4	583.521	32.024	<0.001	67.1
~H_ed+N+SM+SLA	-285.980	5	585.195	33.698	<0.001	67.4
~S+N+SM+SLA	-286.273	5	585.782	34.285	<0.001	67.1
~H'+N+SM	-289.698	4	590.266	38.770	<0.001	64.0
~H'+N+SM+SLA	-289.467	5	592.169	40.672	<0.001	64.2
~MPD+N+SM	-291.528	4	593.927	42.430	<0.001	62.3
~PD+N+SM	-291.803	4	594.476	42.979	<0.001	62.0
~MPD+N+SM+SLA	-291.528	5	596.292	44.795	<0.001	62.3
~PD+N+SM+SLA	-291.791	5	596.818	45.321	<0.001	62.0
~H_ed+P+SM	-293.852	4	598.574	47.078	<0.001	59.9
~H_ed+N	-295.878	3	600.327	48.830	<0.001	57.7
~H_ed+SM	-296.253	3	601.078	49.581	<0.001	57.3
~H'+N	-296.959	3	602.489	50.993	<0.001	56.5
~H_ed+N+SLA	-295.832	4	602.534	51.037	<0.001	57.8
~H_ed+SM+SLA	-295.835	4	602.540	51.044	<0.001	57.8
~S+P+SM	-296.104	4	603.077	51.581	<0.001	57.5
~H'+N+SLA	-296.940	4	604.750	53.253	<0.001	56.6
~H'+P+SM	-297.194	4	605.259	53.762	<0.001	56.3
~S+SM	-298.644	3	605.860	54.363	<0.001	54.6
~H'+SM	-298.702	3	605.975	54.478	<0.001	54.5
~MPD+N	-298.832	3	606.235	54.738	<0.001	54.4
~S+SM+SLA	-298.354	4	607.578	56.081	<0.001	54.9
~H'+SM+SLA	-298.664	4	608.198	56.701	<0.001	54.6
~MPD+N+SLA	-298.736	4	608.342	56.845	<0.001	54.5
~MPD+P+SM	-298.901	4	608.671	57.175	<0.001	54.3
~H_ed+P	-300.239	3	609.049	57.552	<0.001	52.7
~FD	-302.065	2	610.467	58.971	<0.001	50.4
~S+N	-301.423	3	611.417	59.921	<0.001	51.2
~H'+P	-301.483	3	611.538	60.041	<0.001	51.1
~PD+P+SM	-300.715	4	612.299	60.802	<0.001	52.1
~H_ed	-303.261	2	612.861	61.364	<0.001	48.8
~H'	-303.488	2	613.314	61.817	<0.001	48.5
~MPD+P	-302.496	3	613.563	62.066	<0.001	49.8
~S+N+SLA	-301.415	4	613.700	62.203	<0.001	51.2
~H_ed+SLA	-302.577	3	613.725	62.228	<0.001	49.7
~H'+SLA	-303.323	3	615.218	63.721	<0.001	48.7
~PD+N	-304.420	3	617.411	65.915	<0.001	47.2
~PD+SM	-304.707	3	617.985	66.488	<0.001	46.9
~PD+SM+SLA	-304.280	4	619.429	67.933	<0.001	47.4
~PD+N+SLA	-304.369	4	619.607	68.110	<0.001	47.3
~MPD+SM	-305.589	3	619.750	68.253	<0.001	45.6
~MPD+SM+SLA	-304.947	4	620.764	69.267	<0.001	46.5
~S+P	-306.727	3	622.026	70.530	<0.001	44.0
~S	-309.802	2	625.942	74.445	<0.001	39.4
~S+SLA	-309.248	3	627.068	75.572	<0.001	40.2
~PD+P	-309.484	3	627.539	76.042	<0.001	39.9
~MPD+SLA	-309.968	3	628.506	77.010	<0.001	39.1
~MPD	-311.139	2	628.617	77.120	<0.001	37.3
~FAD	-312.941	2	632.220	80.723	<0.001	34.3
~PD	-314.134	2	634.606	83.110	<0.001	32.2
~PD+SLA	-313.311	3	635.193	83.696	<0.001	33.6
~N+SM+SLA	-314.022	4	638.914	87.418	<0.001	32.4
~N+SM	-316.040	3	640.652	89.155	<0.001	28.8
~H_max	-318.529	2	643.396	91.899	<0.001	24.2
~SM	-322.101	2	650.540	99.043	<0.001	16.9
~P+SM	-321.426	3	651.424	99.927	<0.001	18.3
~SM+SLA	-321.584	3	651.740	100.243	<0.001	18.0
~N+SLA	-323.393	3	655.357	103.860	<0.001	14.1
~N	-324.636	2	655.610	104.113	<0.001	11.4
~1	-329.409	1	662.985	111.488	<0.001	0.0
~P	-328.601	2	663.540	112.043	<0.001	2.0
~SLA	-329.159	2	664.656	113.159	<0.001	0.6

Table A5. After substituting the five original control quadrats with 10 quadrats where rare species were removed (see Methods), generalized linear model (GLM) results for biomass production as a function of number of species (S), Shannon's evenness (H') and phylogenetic diversity (PD = phylogenetic diversity, MPD = mean pairwise distance and H_ed = evolutionary distinctiveness), and various community-level means of single functional traits (H_max = maximum plant height, P = leaf phosphorus content, N = leaf nitrogen content, SM = mean seed mass and SLA = specific leaf area) or multivariate functional trait indices (FD = functional diversity, FAD = functional attribute diversity). Shown are the estimated number of model parameters (k), maximum log-likelihood (LL), the information-theoretic Akaike's information criterion corrected for small samples (AICc), change in AICc relative to the top-ranked model (ΔAICc), AICc weight (wAICc = model probability) and the percent deviance explained (%DE) as a measure of the model's goodness-of-fit.

Model	LL	k	AICc	ΔAICc	wAICc	%DE
~H_ed+H_max	-290.438	3	589.410	0.000	0.665	77.7
~PD+H_max	-291.421	3	591.375	1.965	0.249	77.1
~S+H_max	-292.509	3	593.552	4.143	0.084	76.5
~MPD+H_max	-296.914	3	602.362	12.952	0.001	73.8
~H'+H_max	-297.543	3	603.619	14.210	0.001	73.4
~H_ed+N+SM	-303.915	4	618.642	29.232	<0.001	68.9
~S+N+SM	-304.273	4	619.357	29.948	<0.001	68.6
~H_ed+N+SM+SLA	-303.904	5	620.959	31.549	<0.001	68.9
~S+N+SM+SLA	-304.258	5	621.666	32.257	<0.001	68.6
~H'+N+SM	-307.244	4	625.299	35.890	<0.001	66.2
~H'+N+SM+SLA	-307.170	5	627.490	38.081	<0.001	66.3
~PD+N+SM	-310.341	4	631.494	42.084	<0.001	63.6
~PD+N+SM+SLA	-310.335	5	633.820	44.410	<0.001	63.6
~H_ed+P+SM	-313.346	4	637.503	48.093	<0.001	60.8
~H_ed+SM	-315.403	3	639.340	49.931	<0.001	58.8
~H_ed+SM+SLA	-314.760	4	640.331	50.921	<0.001	59.4
~H_ed+N	-316.028	3	640.589	51.179	<0.001	58.1
~H'+N	-316.407	3	641.347	51.938	<0.001	57.8
~S+P+SM	-315.629	4	642.070	52.660	<0.001	58.5
~H_ed+N+SLA	-315.845	4	642.501	53.091	<0.001	58.3
~H'+P+SM	-316.208	4	643.228	53.818	<0.001	58.0
~H'+SM	-317.529	3	643.592	54.182	<0.001	56.6
~H'+N+SLA	-316.395	4	643.600	54.191	<0.001	57.8
~S+SM	-317.840	3	644.212	54.803	<0.001	56.2
~H'+SM+SLA	-317.389	4	645.590	56.180	<0.001	56.7
~MPD+N	-318.585	3	645.704	56.294	<0.001	55.4
~S+SM+SLA	-317.448	4	645.708	56.298	<0.001	56.7
~MPD+N+SLA	-318.146	4	647.103	57.693	<0.001	55.9
~H_ed+P	-321.392	3	651.318	61.908	<0.001	52.3
~H'+P	-321.822	3	652.178	62.769	<0.001	51.8
~S+N	-321.915	3	652.363	62.953	<0.001	51.7
~PD+P+SM	-320.845	4	652.502	63.092	<0.001	52.9
~H'	-323.513	2	653.342	63.932	<0.001	49.8
~FD	-323.729	2	653.774	64.364	<0.001	49.5
~H_ed	-323.873	2	654.063	64.653	<0.001	49.3
~H_ed+SLA	-322.886	3	654.305	64.895	<0.001	50.5
~S+N+SLA	-321.854	4	654.518	65.108	<0.001	51.7
~H'+SLA	-323.148	3	654.829	65.420	<0.001	50.2
~MPD+P	-323.869	3	656.271	66.862	<0.001	49.3
~PD+SM	-324.457	3	657.447	68.038	<0.001	48.6
~PD+SM+SLA	-323.775	4	658.361	68.952	<0.001	49.4
~PD+N	-325.344	3	659.222	69.812	<0.001	47.5
~PD+N+SLA	-325.117	4	661.045	71.635	<0.001	47.8
~S+P	-328.381	3	665.296	75.886	<0.001	43.5
~S	-330.864	2	668.044	78.635	<0.001	39.9
~MPD+SLA	-330.018	3	668.569	79.159	<0.001	41.2
~S+SLA	-330.114	3	668.761	79.351	<0.001	41.0
~MPD	-331.951	2	670.218	80.809	<0.001	38.3
~PD+P	-331.694	3	671.921	82.511	<0.001	38.7
~FAD	-334.467	2	675.249	85.840	<0.001	34.5
~N+SM	-334.052	3	676.637	87.228	<0.001	35.1
~N+SM+SLA	-332.952	4	676.714	87.305	<0.001	36.8
~PD+SLA	-334.443	3	677.419	88.010	<0.001	34.5
~PD	-335.723	2	677.762	88.353	<0.001	32.5
~H_max	-341.253	2	688.821	99.411	<0.001	22.9
~SM	-342.079	2	690.473	101.064	<0.001	21.3
~P+SM	-341.582	3	691.698	102.288	<0.001	22.3
~SM+SLA	-341.944	3	692.421	103.012	<0.001	21.6
~N	-345.920	2	698.156	108.747	<0.001	13.7
~N+SLA	-345.507	3	699.548	110.138	<0.001	14.6
~1	-352.136	1	708.428	119.018	<0.001	0.0
~P	-351.718	2	709.752	120.342	<0.001	1.0
~SLA	-352.131	2	710.577	121.167	<0.001	0.0

Fig. A1. (a) Maximum-likelihood and (b) Bayesian phylogenetic trees.

Fig. A2. The effect of number of removed groups on the biomass of each taxonomic group.

Fig. A3. Bivariate plots of the raw species (S and H'), phylogenetic (PD), evolutionary distinctiveness (H_ed), mean pairwise distance (MPD) and multivariate functional diversity (FD, FAD) indices.

Fig. A4. Correlation between phylogenetic diversity (PD) determined via maximum likelihood and Bayes theorem (Spearman's ρ = 0.999).

Literature cited

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Petchey, O. L., and K. J. Gaston. 2002. Functional diversity (FD), species richness and community composition. Ecology Letters 5:402–411.

Tilman, D., D. Wedin, and J. Knops. 1996. Productivity and sustainability influenced by biodiversity in grassland ecosystems. Nature 379:718–720.

Villéger, S., N. W. H. Mason, and D. Mouillot. 2008. New multidimensional functional diversity indices for a multifaceted framework in functional ecology. Ecology 89:2290–2301.

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