Table 4.

False positive rates (null scenarios) and true positive rates (alternative scenarios) for three LRTs when the evolutionary process includes DT nucleotide substitutions between codons, ω variability among sites, and MNRs

				SNR ($e^{{\beta }_{\mathit{HI}}}$ = 1)			High MNR ($e^{{\beta }_{\mathit{HI}}}$ = 0.05)
	ω 0	ω 1	ω 2	LRT-1	LRT-2	LRT-3	LRT-1	LRT-2	LRT-3
Null scenarios				False positives
3a	0.05	1.0	1.0	0.55	0.02	0.03	0.0	0.06*	0.10*
Alternative scenarios				True positives
3b	0.05	0.5	2.0	0.95	0.87	0.92	0.01	0.44	0.26
3c	0.05	1.0	2.0	0.99	0.47	0.46	0.0	0.27	0.18

LRT-1 compares M1a to M2a (under-fit models). LRT-2 compares G1a^x to G2a^x (perfect-fit models). LRT-3 compares G1a¹³ to G2a¹³ (over-fit models). The asterisk symbol (*) indicates that the results are based on < 100 replicates due to convergence problems with some datasets when there was high MNRs. For LRT-2 case 3a is based on 99 replicates. LRT-3 case 3a is based on 91 replicates