Table 1.

Coverage summary for simulation study

	Site	Rate coverage						Mean	Subst. Model
Freqs	model	AC	AG	AT	CG	CT	GT	rate	coverage
Equal	plain	93	97	94	96	95	95	95	98
Equal	+G	91	95	93	93	95	93	93.3	97
Equal	+I	92	94	94	95	93	94	93.6	96
Equal	+G+I	89	96	95	94	95	95	94	98
Unequal	plain	96	95	96	97	93	96	95.5	96
Unequal	+G	95	94	94	94	96	96	94.8	98
Unequal	+I	89	94	95	95	93	95	93.5	93
Unequal	+G+I	97	94	94	93	93	96	94.5	97
Mean		94.25	94.25	94.75	94.75	93.75	95.75	94.6	96
	Site	Site model			Frequency	Frequency coverage
Freqs	model	coverage	α	p inv	coverage	A	C	G	T
Equal	plain	100			100	100	100	100	100
Equal	+G	96	94		100	100	100	100	100
Equal	+I	98		95	100	100	100	100	100
Equal	+G+I	99	89	88	100	100	100	100	100
Unequal	plain	100			100	92	95	97	96
Unequal	+G	97	94		100	97	92	92	98
Unequal	+I	98		92	100	95	94	94	89
Unequal	+G+I	100	93	91	100	99	96	96	98
Mean		98.75	93.50	91.50	100.00	97.38	97.88	97.13	97.38

The first column lists the frequency and site models used to generate the data, and the last row is the mean coverage over all 800 runs. Coverage for rate parameters and frequencies is defined as the number of replicate simulations in which the true parameter value was contained in the estimated 95% HPD interval. The mean rate column contains the coverage averaged over all six rate coverage columns (i.e. the proportion of the 600 parameter estimates whose values were contained in their respective 95% HPD intervals. For details of substitution model coverage see text. The site model coverage is the number of replicate simulations that contained the correct model specification for rate heterogeneity across sites in the 95% credible set of models. Columns α and p _inv are coverages of the shape and proportion invariable parameter conditioned on sampling from the true site model