Table 1.

Testing for correlated evolution between rates of nucleotide substitution and symbiotic states as binary characters

Data set (nrDNA)	Independent analysis	Dependent analysis									Likelihood ratio	Simulation, P	q34 > q12 (P)	q13 > q12 (P)	q13 < q12 (P)
	Likelihood L(I)	Likelihood L(D)	q12 nm,s → nm,f	q13 nm,s → m,s	q21 nm,f → nm,s	q24 nm,f → m,f	q31 m,s → nm,s	q34 m,s → m,f	q42 m,f → nm,f	q43 m,f → m,s
25S	−33.34	−24.02	0.001074	0.091419	1.813253	2.161151	0.682283	1.180826	0.000065	0.568961	18.6	<0.001	<0.00001	<0.00001
ITS1+ITS2	−33.41	−29.50	0.136537	0.130906	0.310519	0.000194	1.023416	1.440970	0.000021	0.346760	7.8	0.05	0.05	not significant
5.8S	−31.61	−27.84	0.467298	0.079326	2.651783	0.130013	0.513440	0.782133	0.004209	0.391890	7.5	0.07	not significant		<0.01

q_ij represent all possible transitions of one binary character holding the state of the other constant. L(I) = likelihood value for the model of independent evolution (13), and L(D) = likelihood value for the model of correlated evolution. nm, nonmutualist; m, mutualist; s, slow rate of nucleotide substitution; f, fast rate of nucleotide substitution. To test the hypothesis that a shift in evolutionary rate is more likely to occur in a mutualist lineage, the rates of change from nm,s to nm,f (q₁₂) and from m,s to m,f (q₃₄) were constrained to be equal, and the likelihood of this model was compared to a model in which the rates were not constrained. To test whether a transitional change in a branch to mutualism occured first followed by an increase in evolutionary rate, a likelihood ratio test was implemented by constraining the rate of change from nm,s to nm,f (q₁₂) and the rate of change from nm,s to m,s (q₁₃) to be equal.