Table 1.

The 27 mixed-effects models fitted by restricted maximum likelihood and ranked by AIC. Models could have random effects on either intercept (I) or slope and intercept (S & I), at each of the taxonomic levels order, family and species. K is the number of model parameters. is the restricted maximum likelihood. ΔAIC is the difference between the best model’s AIC and the AIC of the model in question. w is the Akaike weight; ∑w = 1

Rank	Random effects				K	log()	AIC	ΔAIC	w	∑(w)
	Order	Family	Species
1	S & I	I	S & I	15	1011·832	−1993·665	0·000	0·4003	0·4003
2	I	I	S & I	13	1009·811	−1993·622	0·043	0·3919	0·7922
3	I	S & I	S & I	15	1010·024	−1990·049	3·616	0·0657	0·8578
4	S & I	S & I	S & I	17	1011·845	−1989·689	3·975	0·0549	0·9127
5	S & I		S & I	14	1008·400	−1988·801	4·864	0·0352	0·9479
6	I		S & I	12	1005·875	−1987·751	5·914	0·0208	0·9687
7	S & I	I	I	13	1006·683	−1987·366	6·299	0·0172	0·9858
8	S & I		I	12	1005·082	−1986·163	7·501	0·0094	0·9952
9	S & I	S & I	I	15	1006·684	−1983·368	10·297	0·0023	0·9976
10	I	S & I	I	13	1003·915	−1981·831	11·834	0·0011	0·9986
11	I	I	I	11	1001·898	−1981·796	11·869	0·0011	0·9997
12	I		I	10	999·302	−1978·604	15·061	0·0002	0·9999
13		I	S & I	12	1000·279	−1976·559	17·106	<0·0001	1·0000
14		S & I	S & I	14	1000·658	−1973·316	20·349	<0·0001	1·0000
15		S & I	I	12	994·610	−1965·221	28·444	<0·0001	1·0000
16		I	I	10	990·907	−1961·814	31·850	<0·0001	1·0000
17	S & I	I		12	987·596	−1951·192	42·472	<0·0001	1·0000
18	S & I	S & I		14	988·379	−1948·758	44·907	<0·0001	1·0000
19	I	S & I		12	985·285	−1946·570	47·095	<0·0001	1·0000
20	I	I		10	982·851	−1945·701	47·964	<0·0001	1·0000
21	S & I			11	983·157	−1944·314	49·351	<0·0001	1·0000
22			S & I	11	979·395	−1936·790	56·874	<0·0001	1·0000
23	I			9	975·638	−1933·275	60·389	<0·0001	1·0000
24		S & I		11	976·514	−1931·028	62·637	<0·0001	1·0000
25		I		9	974·104	−1930·208	63·456	<0·0001	1·0000
26			I	9	973·479	−1928·957	64·708	<0·0001	1·0000
27				8	928·908	−1841·815	151·849	<0·0001	1·0000