An autoregressive model for global vertebrate richness rankings: long-distance dispersers may have stronger spatial structures

Zoological Studies

Table 1 Comparison of autoregressive models with different W for assessing global patterns of spatial autocorrelations

W	Mammals				Amphibians				Birds
	ρ	AIC _C	R ²	Moran'sI	ρ	AIC _C	R ²	Moran'sI	ρ	AIC _C	R ²	Moran'sI
Distance matrix
a = 1	0.118	7,443.883	0.914	0.184	0.126	8,034.76	0.784	0.206	0.117	8,693.137	0.862	0.153
a = 1.1	0.17	7,414.297	0.916	0.213	0.182	7,972.835	0.797	0.238	0.169	8,664.672	0.866	0.18
a = 1.2	0.242	7,382.141	0.919	0.243	0.261	7,906.554	0.81	0.27	0.241	8,631.682	0.87	0.208
a = 1.3	0.341	7,347.771	0.921	0.274	0.369	7,836.91	0.822	0.304	0.341	8,594.431	0.874	0.237
a = 1.4	0.476	7,311.783	0.924	0.306	0.516	7,765.194	0.834	0.338	0.478	8,553.433	0.879	0.268
a = 1.5	0.658	7,274.965	0.927	0.338	0.714	7,692.925	0.846	0.372	0.662	8,509.428	0.884	0.299
Binary matrix
Class = 2	0.003	9,385.66	0.441	−0.031	0.003	9,273.898	0.274	−0.021	0.004	10,170.65	0.442	0.016
Class = 4	0.003	9,385.66	0.441	−0.031	0.003	9,273.898	0.274	−0.021	0.004	10,170.65	0.442	0.016
Class = 6	0.003	9,305.439	0.483	0.011	0.003	9,211.798	0.316	0.03	0.003	10,094.25	0.481	0.045
Class = 8	0.003	9,305.439	0.483	0.011	0.003	9,211.798	0.316	0.03	0.003	10,094.25	0.481	0.045
Class = 10	0.003	9,305.439	0.483	0.011	0.003	9,211.798	0.316	0.03	0.003	10,094.25	0.481	0.045

ρ, autoregressive parameter; AIC_c, modified Akaike information criterion; R², the proportion of explained variation; a, the parameter in Equation 5.