. 2018 Sep 5;8(20):10094–10112. doi: 10.1002/ece3.4483

Table A4.

General linear mixed‐effect model (GLMM) results for biomass production as a function of several fixed factors and a hierarchical random factor

Model	LL	k	AIC_c	ΔAIC_c	wAIC_c	R _m ²	R _c ²
S + IAC + LN + C + T	57.115	13	−85.145	0.000	0.291	91.8	99.9
S + IAC + LN + T	55.664	12	−84.706	0.439	0.234	91.6	99.9
S + IAC + LN + N + T	56.336	13	−83.588	1.557	0.134	91.7	99.9
S + IAC + C + T	54.529	12	−82.437	2.708	0.075	91.4	99.9
S + IAC + T	53.195	11	−82.189	2.955	0.066	91.3	99.9
S + IAC + FDis + C + T	55.010	13	−80.934	4.210	0.035	91.5	99.9
S + IAC + N + T	53.732	12	−80.843	4.302	0.034	91.3	99.9
S + IAC + FDis + T	53.725	12	−80.829	4.316	0.034	91.3	99.9
S + IAC + RaoQ + C + T	54.906	13	−80.726	4.418	0.032	91.5	99.9
S + IAC + RaoQ + T	53.642	12	−80.661	4.483	0.031	91.3	99.9
S + IAC + FDis + N + T	54.336	13	−79.588	5.556	0.018	91.4	99.9
S + IAC + RaoQ + N + T	54.255	13	−79.425	5.719	0.017	91.4	99.9
IAC + NND + LN + C + T	20.838	13	−12.592	72.553	<0.001	78.2	98.3
IAC + NND + LN + N + T	19.234	13	−9.383	75.762	<0.001	77.9	98.2
IAC + NND + LN + T	17.491	12	−8.360	76.785	<0.001	77.1	98.2
IAC + NND + RaoQ + C + T	17.236	13	−5.386	79.758	<0.001	78.5	98.4
IAC + NND + FDis + C + T	16.871	13	−4.657	80.487	<0.001	78.8	98.3
IAC + NND + RaoQ + N + T	15.996	13	−2.907	82.238	<0.001	78.5	98.3
IAC + NND + C + T	14.646	12	−2.670	82.475	<0.001	78.3	98.1
IAC + NND + FDis + N + T	15.593	13	−2.101	83.043	<0.001	78.7	98.2
IAC + NND + RaoQ + T	14.180	12	−1.737	83.407	<0.001	77.6	98.1
IAC + NND + FDis + T	13.832	12	−1.042	84.102	<0.001	77.9	98.1
IAC + NND + N + T	13.113	12	0.396	85.541	<0.001	78.0	98.1
IAC + NND + T	11.641	11	0.918	86.062	<0.001	77.2	98.0
IAC + LN + pH + T	6.846	12	12.929	98.074	<0.001	82.3	99.9
IAC + RaoQ + pH + T	6.242	12	14.139	99.283	<0.001	81.8	99.9
IAC + FDis + pH + T	5.845	12	14.932	99.9.077	<0.001	82.1	99.9
IAC + LN + C + T	2.756	12	21.109	106.254	<0.001	69.0	99.9
IAC + pH + T	1.462	11	21.276	106.420	<0.001	80.8	99.9
IAC + RaoQ + C + T	2.402	12	21.818	106.962	<0.001	70.3	99.9
IAC + FDis + C + T	1.676	12	23.270	108.414	<0.001	70.6	99.9
IAC + LN + P + C + T	2.859	13	23.367	108.511	<0.001	67.5	99.9
IAC + RaoQ + P + C + T	2.428	13	24.229	109.373	<0.001	69.5	99.9
IAC + RaoQ + N + T	0.789	12	25.045	110.189	<0.001	70.2	99.9
IAC + FDis + P + C + T	1.745	13	25.594	110.739	<0.001	69.3	99.9
IAC + LN + N + T	0.252	12	26.118	111.262	<0.001	68.7	99.1
IAC + FDis + N + T	−0.088	12	26.797	111.942	<0.001	70.6	99.9
IAC + RaoQ + P + N + T	0.794	13	27.497	112.642	<0.001	69.9	99.9
IAC + RaoQ + T	−1.812	11	27.824	112.968	<0.001	68.9	99.9
IAC + LN + P + N + T	0.308	13	28.468	113.613	<0.001	67.3	98.6
IAC + LN + T	−2.241	11	28.682	113.827	<0.001	67.1	98.1
IAC + FDis + P + N + T	−0.058	13	29.200	114.345	<0.001	69.7	99.9
IAC + FDis + T	−2.728	11	29.656	114.800	<0.001	69.2	99.9
IAC + RaoQ + P + T	−1.670	12	29.961	115.106	<0.001	70.8	99.9
IAC + LN + P + T	−2.219	12	31.059	116.204	<0.001	68.0	98.3
IAC + C + T	−3.686	11	31.572	116.716	<0.001	68.6	99.9
IAC + FDis + P + T	−2.648	12	31.919	117.063	<0.001	70.7	99.9
IAC + P + C + T	−3.352	12	33.327	118.471	<0.001	65.7	99.9
IAC + N + T	−6.157	11	36.515	121.659	<0.001	68.2	99.9
IAC + P + N + T	−5.938	12	38.497	123.642	<0.001	65.7	98.6
IAC + T	−8.457	10	38.732	123.877	<0.001	66.7	97.9
IAC + P + T	−8.445	11	41.091	126.235	<0.001	66.1	97.9
H _max + LN + pH + T	−36.620	12	99.861	185.006	<0.001	65.3	99.9
H _max + pH + T	−38.365	11	99.9.930	186.075	<0.001	64.4	99.9
S + H _max + T	−38.574	11	101.347	186.492	<0.001	61.4	95.9
S + H _max + LN + T	−37.695	12	102.011	187.156	<0.001	60.4	96.4
S + H _max + C + T	−37.828	12	102.278	187.422	<0.001	61.2	96.0
S + H _max + LN + C + T	−36.857	13	102.798	187.943	<0.001	60.3	96.3
S + H _max + N + T	−38.205	12	103.032	188.177	<0.001	61.5	95.9
S + H _max + LN + N + T	−37.276	13	103.637	188.782	<0.001	60.4	96.5
NND + H _max + LN + C + T	−37.453	13	103.991	189.136	<0.001	56.3	96.3
NND + H _max + LN + T	−38.868	12	104.358	189.502	<0.001	55.6	96.3
NND + H _max + C + T	−39.270	12	105.162	190.307	<0.001	56.4	96.0
NND + H _max + LN + N + T	−38.097	13	105.278	190.422	<0.001	56.2	96.4
NND + H _max + T	−40.642	11	105.484	190.629	<0.001	55.7	95.9
NND + H _max + N + T	−39.902	12	106.425	191.570	<0.001	56.2	96.0
H _max + LN + C + T	−40.844	12	108.309	193.454	<0.001	51.6	99.9
H _max + LN + T	−42.684	11	109.567	194.712	<0.001	50.7	99.9
H _max + LN + N + T	−41.609	12	109.840	194.985	<0.001	51.5	99.9
H _max + C + T	−42.933	11	110.066	195.211	<0.001	51.3	97.2
H’ + H _max + LN + C + T	−40.551	13	110.187	195.332	<0.001	51.3	99.9
H _max + LN + P + C + T	−40.686	13	110.458	195.602	<0.001	53.8	99.9
H _max + LN + P + T	−42.179	12	110.980	196.125	<0.001	54.6	99.9
H _max + T	−44.775	10	111.367	196.512	<0.001	50.2	98.2
H _max + N + T	−43.679	11	111.558	196.702	<0.001	51.1	99.9
H + H _max + LN + T	−42.557	12	111.736	196.881	<0.001	50.4	99.9
H’ + H _max + LN + N + T	−41.403	13	111.891	197.036	<0.001	51.3	99.9
H _max + LN + P + N + T	−41.410	13	111.905	197.050	<0.001	54.0	99.9
H _max + P + C + T	−42.856	12	112.334	197.478	<0.001	52.9	96.9
H’ + H _max + C + T	−42.865	12	112.352	197.497	<0.001	51.1	97.5
H’ + H _max + LN + P + C + T	−40.477	14	112.544	197.688	<0.001	52.8	99.9
H _max + P + T	−44.432	11	113.065	198.209	<0.001	53.6	97.1
H’ + H _max + LN + P + T	−42.136	13	113.357	198.501	<0.001	54.1	99.9
H’ + H _max + T	−44.766	11	113.733	198.877	<0.001	50.1	98.3
H _max + P + N + T	−43.586	12	113.793	198.938	<0.001	52.8	98.4
H’ + H _max + N + T	−43.643	12	113.907	199.052	<0.001	50.9	99.9
H’ + H _max + LN + P + N + T	−41.283	14	114.157	199.301	<0.001	53.2	99.9
H’ + H _max + P + C + T	−42.821	13	114.727	199.871	<0.001	52.4	97.2
H’ + H _max + P + T	−44.429	12	115.480	200.624	<0.001	53.8	97.1
H’ + H _max + P + N + T	−43.573	13	116.231	201.375	<0.001	52.5	99.9
LN + pH + T	−57.526	11	139.252	224.396	<0.001	52.2	99.9
NND + LN + T	−58.903	11	142.006	227.150	<0.001	44.3	99.9
S + LN + T	−58.913	11	142.027	227.171	<0.001	48.2	99.9
NND + LN + C + T	−57.908	12	142.439	227.583	<0.001	44.9	97.7
S + LN + C + T	−58.424	12	143.471	228.615	<0.001	47.9	99.9
NND + LN + N + T	−58.753	12	144.128	229.273	<0.001	44.5	99.9
S + LN + N + T	−58.896	12	144.414	229.559	<0.001	48.2	99.9
LN + C + T	−62.205	11	148.611	233.755	<0.001	39.4	99.9
LN + T	−63.666	10	149.151	234.296	<0.001	38.3	99.9
RaoQ + pH + T	−62.497	11	149.193	234.338	<0.001	48.4	99.9
S + T	−63.748	10	149.315	234.459	<0.001	46.8	99.9
FDis + pH + T	−62.610	11	149.420	234.565	<0.001	48.5	99.9
H’ + LN + P + T	−61.491	12	149.605	234.749	<0.001	50.1	99.9
S + FDis + T	−62.862	11	149.923	235.068	<0.001	46.9	99.9
LN + P + T	−62.889	11	149.979	235.123	<0.001	49.1	99.9
S + RaoQ + T	−62.967	11	150.134	235.278	<0.001	46.6	99.9
H’ + LN + C + T	−61.896	12	150.414	235.558	<0.001	40.0	99.9
H’ + LN + T	−63.172	11	150.544	235.689	<0.001	39.1	99.9
LN + P + C + T	−62.024	12	150.671	235.815	<0.001	41.8	99.9
pH + T	−64.576	10	150.970	236.114	<0.001	47.1	99.9
LN + N + T	−63.394	11	150.988	236.133	<0.001	38.7	99.9
S + C + T	−63.454	11	151.108	236.253	<0.001	46.6	99.9
H’ + LN + P + C + T	−61.099	13	151.283	236.427	<0.001	50.4	99.9
S + N + T	−63.748	11	151.696	236.84	<0.001	46.8	99.9
S + FDis + C + T	−62.554	12	151.730	236.875	<0.001	46.7	99.9
NND + RaoQ + T	−63.844	11	151.888	237.033	<0.001	41.7	99.9
S + RaoQ + C + T	−62.660	12	151.942	237.087	<0.001	46.3	99.9
NND + FDis + T	−63.922	11	152.045	237.189	<0.001	42.0	99.9
H’ + LN + P + N + T	−61.490	13	152.064	237.209	<0.001	50.1	99.9
S + FDis + N + T	−62.854	12	152.330	237.475	<0.001	46.9	99.9
NND + T	−65.273	10	152.364	237.509	<0.001	41.1	99.9
LN + P + N + T	−62.874	12	152.369	237.513	<0.001	49.1	99.9
H’ + LN + N + T	−62.944	12	152.510	237.654	<0.001	39.4	99.9
S + RaoQ + N + T	−62.960	12	152.542	237.687	<0.001	46.6	99.9
NND + RaoQ + C + T	−63.067	12	152.757	237.901	<0.001	42.2	99.9
NND + FDis + C + T	−63.112	12	152.845	237.99	<0.001	42.5	99.9
NND + C + T	−64.367	11	152.934	238.078	<0.001	41.6	99.9
NND + RaoQ + N + T	−63.714	12	154.050	239.194	<0.001	41.9	99.9
NND + FDis + N + T	−63.784	12	154.190	239.334	<0.001	42.2	99.9
NND + N + T	−65.159	11	154.519	239.663	<0.001	41.3	99.9
H’ + RaoQ + P + T	−65.054	12	156.730	241.874	<0.001	47.4	99.9
RaoQ + P + T	−66.341	11	156.882	242.027	<0.001	46.3	99.9
H’ + FDis + P + T	−65.162	12	156.947	242.091	<0.001	47.3	99.9
RaoQ + T	−67.614	10	157.047	242.192	<0.001	36.3	99.9
RaoQ + C + T	−66.522	11	157.245	242.389	<0.001	37.2	99.9
FDis + P + T	−66.568	11	157.336	242.481	<0.001	46.1	99.9
FDis + T	−67.792	10	157.403	242.547	<0.001	36.5	99.9
FDis + C + T	−66.634	11	157.469	242.613	<0.001	37.4	99.9
H’ + RaoQ + T	−66.890	11	157.980	243.125	<0.001	37.4	99.9
H’ + FDis + T	−66.955	11	158.109	243.254	<0.001	37.7	99.9
H’ + RaoQ + C + T	−65.963	12	158.549	243.693	<0.001	38.1	99.9
H’ + FDis + C + T	−65.991	12	158.603	243.747	<0.001	38.4	99.9
RaoQ + P + C + T	−66.035	12	158.693	243.837	<0.001	46.6	99.9
H’ + RaoQ + P + C + T	−64.863	13	158.812	243.956	<0.001	47.5	99.9
H’ + P + T	−67.316	11	158.831	243.976	<0.001	45.5	99.9
RaoQ + N + T	−67.379	11	158.958	244.103	<0.001	36.6	99.9
H’ + FDis + P + C + T	−64.937	13	158.959	244.104	<0.001	47.5	99.9
FDis + P + C + T	−66.201	12	159.024	244.169	<0.001	46.4	99.9
H’ + RaoQ + P + N + T	−65.053	13	159.191	244.336	<0.001	47.4	99.9
FDis + N + T	−67.540	11	159.280	244.425	<0.001	36.8	99.9
RaoQ + P + N + T	−66.331	12	159.283	244.427	<0.001	46.3	99.9
H’ + FDis + P + N + T	−65.159	13	159.404	244.548	<0.001	47.3	99.9
H’ + T	−68.852	10	159.523	244.667	<0.001	36.1	99.9
FDis + P + N + T	−66.548	12	159.719	244.863	<0.001	46.2	99.9
H’ + C + T	−67.783	11	159.765	244.91	<0.001	37.0	99.9
H’ + RaoQ + N + T	−66.703	12	160.028	245.172	<0.001	37.7	99.9
C + T	−69.120	10	160.058	245.203	<0.001	35.1	99.9
H’ + FDis + N + T	−66.758	12	160.137	245.281	<0.001	38.0	99.9
H’ + P + C + T	−67.013	12	160.648	245.792	<0.001	45.8	99.9
H’ + P + N + T	−67.315	12	161.252	246.396	<0.001	45.5	99.9
H’ + N + T	−68.691	11	161.582	246.727	<0.001	36.4	99.9
P + T	−69.946	10	161.710	246.855	<0.001	43.3	99.9
P + C + T	−69.089	11	162.377	247.522	<0.001	36.2	99.9
N + T	−70.296	10	162.410	247.555	<0.001	34.3	99.9
P + N + T	−69.926	11	164.052	249.197	<0.001	43.3	99.9
1	−80.940	5	172.356	257.501	<0.001	0.0	91.1

Fixed factors are number of species (S), Shannon's evenness (H’), and phylogenetic diversity (IAC, imbalance of abundance at the clade; MNND, mean nearest neighbor distance), and community‐level mean of single functional traits (H _max, plot‐specific maximum plant height; LN, mean leaf nitrogen content value for individual species used for all plots where the species is found) or multivariate functional trait indices (RaoQ, Quadratic entropy; FDis, Functional dispersion: weighted distances from a weighted centroid in multitrait space), and experimental treatments (T: T _C = control, T _W = warming, T _N = nitrogen addition, T _WN = warming and nitrogen addition, and T _G = livestock‐grazing), and soil resources (C, soil carbon content; N, soil total nitrogen content; P, soil total phosphorus content). Hierarchical random factor is elevation (2700 m, 3200 m and 3400 m), treatment, and plot. Values are shown for the estimated number of model parameters (k), maximum log‐likelihood (LL), and the information‐theoretic Akaike's information criterion corrected for small samples (AIC_c), change in AIC_c relative to the top‐ranked model (ΔAIC_c), AIC_c weight (wAIC_c, model probability), and the marginal and total variance explained (R_m ², R_c ²) as a measure of the model's goodness of fit.