Table 3. Log-likelihood values and parameter estimates under random-site models for P. toxostoma and C. nasus.

Fish species	Model Code	log-likelihood	Estimates of parameters	Number of PSS
P. toxostoma	M0: one ratio (1)	−2751.964	ω = 2.198
	M3: discrete (5)	−2500.823	p0 = 0.489, p1 = 0.437 , (p2 = 0.074), ω0 = 0.305, ω1 = 4.229, ω2 = 26.915
	M1a: nearly neutral (1)	−2651.110	p0 = 0.509, (p1 = 0.491), (ω0 = 0.080), (ω1 = 1)
	M2a: positive selection (3)	−2527.360	p0 = 0.357, p1 = 0.477, (p2 = 0.166), ω0 = 0.073, (ω1 = 1), ω2 = 7.929	9**, 3*
	M7: beta (2)	−2652.738	p = 0.244, q = 0.261
	M8: beta and ω (4)	−2528.900	p0 = 0.831, (p1 = 0.169), p = 0.033, q = 0.019, ω = 8.265	12**,2*
C. nasus	M0: one ratio (1)	−2597.715	ω = 2.028
	M3: discrete (5)	−2369.902	p0 = 0.526, p1 = 0.347, (p2 = 0.127), ω0 = 0.375, ω1 = 3.838, ω2 = 17.439
	M1a: nearly neutral (1)	−2495.173	p0 = 0.536, (p1 = 0.464), (ω0 = 0.093), (ω1 = 1)
	M2a: positive selection (3)	−2385.959	p0 = 0.33, p1 = 0.465, (p2 = 0.205), ω0 = 0.071, (ω1 = 1), ω2 = 7.524	13**, 4*
	M7: beta (2)	−2500.285	p = 0.234, q = 0.228
	M8: beta and ω (4)	−2386.939	p0 = 0.792, (p1 = 0.208), p = 0.034, q = 0.020, ω = 7.761	15**, 2*

The number following the model code given in parentheses represents the number of free parameters for the ω ratios. Parameters in parentheses are presented for clarity only but are not free parameters; for example, under M8 p1 = 1-p0; PSS are the positive selected sites identified using the BEB method at.

^*: P>95%;

^**: P>99%;

ω is the selection parameter; p_n is the proportion of sites that fall into the ω_n site class; p and q are the shape parameters of the β function (for M7 and M8 models).