Table 1. Model description, model parameter estimates, log-likelihood, log(L), and AIC for one homogeneous and seven heterogeneous rate or correlation multivariate Brownian evolution models fit to the centrarchid feeding morphology evolution data of Fig. 1.

${\sigma }_{i,j}^2$ gives the instantaneous variance of the Brownian process (evolutionary rate) for the ith trait and jth regime. Note that this is a different use of subscripts as compared to Eq. (1) in which only traits, and not regimes, were being indicated. r_j gives the evolutionary correlation between traits 1 and 2 for evolutionary regime j. In the table, regime 1 is non-piscivory and regime 2 is piscivorous feeding mode, while trait 1 is relative gape width and trait 2 is relative buccal length (Fig. 1). The best-supported model using AIC as our model selection criterion, highlighted in bold font, is model 3c: different rates for trait 2, different correlations.

Model description	${\sigma }_{1,1}^2$	${\sigma }_{1,2}^2$	${\sigma }_{2,1}^2$	${\sigma }_{2,2}^2$	r 1	r 2	log(L)	AIC
Common rates, common correlation [1]	0.11	–	0.056	–	0.41	–	72.2	−134.4
Different rates, common correlation [2]	0.18	0.05	0.02	0.09	0.45	–	78.0	−142.0
Different rates (trait 1), common correlation [2b]	0.20	0.04	0.06	–	0.55	–	76.0	−140.0
Different rates (trait 2), common correlation [2c]	0.11	–	0.02	0.10	0.33	–	75.3	−138.7
Common rates, different correlation [3]	0.10	–	0.06	–	0.16	0.68	73.6	−135.2
Different rates (trait 1), different correlation [3b]	0.17	0.05	0.06	–	0.36	0.65	76.5	−139.0
Different rates (trait 2), different correlation [3c]	0.11	–	0.01	0.16	0.00	0.85	80.7	−147.4
No common structure [4]	0.14	0.08	0.01	0.13	−0.05	0.80	81.2	−146.5