# Table 4 Proportions of simulations in which the most likely BiSSE model included asymmetry in $$\widehat{\uplambda}$$ versus simulations in which the most likely model included asymmetry in $$\widehat{\upmu}$$

Focal parameter Covariate parameter Ratio Proportion
A.
Asymmetry in Speciation Asymmetry in Extinction 26/121 0.21
No Asymmetry in Speciation Asymmetry in Extinction 13/479 0.03
Asymmetry in Extinction Asymmetry in Speciation 26/39 0.67
No Asymmetry in Extinction Asymmetry in Speciation 95/561 0.17
B.
Asymmetry in Speciation Asymmetry in Extinction 244/468 0.52
No Asymmetry in Speciation Asymmetry in Extinction 71/1332 0.05
Asymmetry in Extinction Asymmetry in Speciation 244/315 0.77
No Asymmetry in Extinction Asymmetry in Speciation 224/1485 0.15
1. The numerator in the ratio is the number of runs in which the most likely BiSSE model includes asymmetry as described for both the focal parameter and the covariate parameter. The denominator in the ratio represents the total number of runs for which the most likely BiSSE model includes asymmetry in the focal parameter only. For instance, in the second row of (A), there were 13 runs in which the best model included the character states having an effect on $$\widehat{\upmu}$$ but not on $$\widehat{\uplambda}$$, and 479 total runs in which the best model did not include the character states having an effect on $$\widehat{\upmu}$$ but not on $$\widehat{\uplambda}$$. Proportions are the decimal values of the respective ratios. Most likely BiSSE models are more likely to include rate asymmetry in both $$\widehat{\upmu}$$ and $$\widehat{\uplambda}$$ together in the same run than expected by chance in both of our simulation models (Fisher’s Exact Test P < 0.0001). In all of these runs, there was no effect of the character states on either λ or μ. (A) tabulates results from a punctuated equilibrium simulation of character evolution. (B) tabulates results from a continuous-time simulation of character evolution.