Pierre Legendre, Daniel Borcard, and Pedro Peres-Neto. 2005. Analyzing beta diversity: partitioning the spatial variation of community composition data. Ecological Monographs 75:435–450.

Appendix C. Simulation results: portions of variation produced by the partitioning methods.

TABLE C1. Simulation results: portion of the species variation in the fractions shown in Fig. 1 (means after 1000 simulations). Fraction [d], which contains the residuals, is 1 – [a+b+c]. S = species; E = environmental variables; XY = geographic coordinates of the sites. Range = range parameter of the variogram for generation of autocorrelation; the size of the simulation field was 100 × 100 (arbitrary units).

	Species presence-absence							Species abundance
Partitioning method
	[a+b+c]	[a+b]	[b+c]	[a]	[b]	[c]		[a+b+c]	[a+b]	[b+c]	[a]	[b]	[c]
A) S unrelated to E (β = 0), S autocorrelated (range = 15), E = N(0,1)
RDA, XY	.0756	.0502	.0255	.0501	.0001	.0254		.0757	.0500	.0260	.0497	.0002	.0258
RDA, polynomial	.1586	.0502	.1092	.0494	.0008	.1084		.1603	.0500	.1114	.0489	.0011	.1103
RDA, PCNM	.1630	.0502	.1162	.0468	.0034	.1128		.1743	.0500	.1285	.0458	.0042	.1243
Mantel, D(XY)	.0028	.0015	.0013	.0015	.0000†	.0013		.0018	.0009	.0009	.0009	.0000†	.0009
Mantel, D(polyn.)	.0043	.0015	.0028	.0015	.0000†	.0028		.0024	.0009	.0015	.0009	.0000†	.0015
Mantel, ln(D(XY))	.0027	.0015	.0012	.0015	.0000†	.0012		.0019	.0009	.0010	.0009	.0000†	.0010
B) S related to E (β = 0.5), S autocorrelated (range = 15), E autocorrelated (range = 15)
RDA, XY	.1322	.1091	.0252	.1070	.0021	.0231		.1389	.1151	.0259	.1130	.0021	.0238
RDA, polynomial	.2090	.1091	.1085	.1005	.0086	.0999		.2165	.1151	.1107	.1058	.0093	.1014
RDA, PCNM	.2123	.1091	.1174	.0949	.0142	.1032		.2260	.1151	.1277	.0983	.0168	.1109
Mantel, D(XY)	.0059	.0046	.0013	.0046	.0000†	.0013		.0052	.0044	.0008	.0044	.0000†	.0008
Mantel, D(polyn.)	.0075	.0046	.0029	.0046	.0000†	.0029		.0058	.0044	.0014	.0044	.0000†	.0014
Mantel, ln(D(XY))	.0057	.0046	.0011	.0046	.0000†	.0011		.0053	.0044	.0009	.0044	.0000†	.0009
C) S related to E (β = 0.25), S autocorrelated (range = 15), E autocorrelated (range = 15)
RDA, XY	.0933	.0689	.0253	.0680	.0009	.0244		.0955	.0703	.0260	.0695	.0009	.0251
RDA, polynomial	.1742	.0689	.1088	.0654	.0035	.1053		.1773	.0703	.1108	.0665	.0038	.1070
RDA, PCNM	.1778	.0689	.1159	.0618	.0071	.1089		.1897	.0703	.1275	.0622	.0081	.1194
Mantel, D(XY)	.0032	.0020	.0012	.0020	.0000†	.0012		.0021	.0013	.0008	.0013	.0000†	.0008
Mantel, D(polyn.)	.0046	.0020	.0026	.0020	.0000†	.0026		.0027	.0013	.0014	.0013	.0000†	.0014
Mantel, ln(D(XY))	.0030	.0020	.0010	.0020	.0000†	.0010		.0022	.0013	.0009	.0013	.0000†	.0009
D) S related to E (β = 0.5), S autocorrelated (range = 15), E with deterministic gradient
RDA, XY	.1343	.1129	.0578	.0765	.0364	.0214		.1412	.1197	.0609	.0803	.0395	.0214
RDA, polynomial	.2117	.1129	.1378	.0739	.0390	.0988		.2198	.1197	.1426	.0772	.0425	.1001
RDA, PCNM	.2241	.1129	.1487	.0754	.0374	.1113		.2360	.1197	.1581	.0781	.0416	.1163
Mantel, D(XY)	.0110	.0090	.0054	.0056	.0034	.0020		.0112	.0096	.0055	.0057	.0039	.0016
Mantel, D(polyn.)	.0115	.0090	.0037	.0078	.0012	.0025		.0109	.0096	.0029	.0080	.0015	.0014
Mantel, ln(D(XY))	.0111	.0090	.0054	.0057	.0034	.0020		.0113	.0096	.0055	.0058	.0038	.0017
E) S related to E (β = 0.25), S autocorrelated (range = 15), E with deterministic gradient
RDA, XY	.0928	.0705	.0347	.0581	.0124	.0223		.0952	.0729	.0361	.0591	.0137	.0224
RDA, polynomial	.1750	.0705	.1182	.0568	.0137	.1045		.1787	.0729	.1210	.0577	.0152	.1058
RDA, PCNM	.1860	.0705	.1286	.0574	.0131	.1155		.1951	.0729	.1373	.0578	.0151	.1222
Mantel, D(XY)	.0040	.0025	.0019	.0021	.0004	.0015		.0032	.0021	.0017	.0015	.0006	.0011
Mantel, D(polyn.)	.0052	.0025	.0028	.0024	.0002	.0026		.0036	.0021	.0018	.0018	.0003	.0015
Mantel, ln(D(XY))	.0039	.0025	.0019	.0020	.0005	.0014		.0034	.0021	.0019	.0015	.0007	.0012

 

† In Mantel partitioning results, [b] fractions often had their first non-zero digits at the 5th or 6th decimal place.