Table 5.

Model specification: CAT analysis

Data set	Models		P-value	Conf. interval
	ML score	Parameters		Lower	Upper
Buckley	GTR+$\Gamma$	GTR+$\Gamma$	0.241	0.215	0.269
Buckley	GTR+$\Gamma$	CAT	0.013*	0.007	0.022
Dunn	GTR+I+$\Gamma$	GTR+I+$\Gamma$	<0.01**	<0.01	0.036
Dunn	GTR+I+$\Gamma$	CAT	0.080	0.035	0.152
Edwards	GTR+I+$\Gamma$	GTR+I+$\Gamma$	<0.01**	<0.01	0.036
Edwards	GTR+I+$\Gamma$	CAT	<0.01**	<0.01	0.036
Sullivan	GTR+I+$\Gamma$	GTR+I+$\Gamma$	0.290	0.204	0.389
Sullivan	GTR+I+$\Gamma$	CAT	0.030*	0.006	0.085
Liu	GTR+I+$\Gamma$	GTR+I+$\Gamma$	<0.01**	<0.01	0.036
Liu	GTR+I+$\Gamma$	CAT	<0.01**	<0.01	0.036
Wang	GTR+G	GTR+G	0.026*	0.014	0.044
Wang	GTR+G	CAT	0.020*	0.010	0.036

Notes: Model 1 and Model 2 are the same as described in Table 4. Using a model for simulation with a greater number of parameters free to vary, such as the CAT model of PhyloBayes, did not result in universally larger $\delta$ values and therefore a more conservative test, though this was true for one data set, Dunn. The outcome of two other tests also differed, for Buckley and Sullivan, but the result was a more liberal test. * indicates p-values less than 0.05; ** indicates less than 0.01.