Fig. 2
Ability of BiSSE fits to enable detection of speciation rate asymmetry on simulated trees when asymmetry does exist (not \( \widehat{\upmu} \) or \( \widehat{\mathrm{q}} \), unlike Fig. 1). In (a), λ1 is 1.33 times λ0 at any given point in time, but both decline exponentially with time as in Fig. 3a. Moreover, changes between character states occur only during speciation events, as predicted by punctuated equilibrium. In (b), λ1 is 1.05 times λ0, and changes between character states occur only during speciation events, as predicted by punctuated equilibrium. In (c), λ1 is 1.33 times λ0, but character evolution occurs independently of speciation. The yellow bar represents the proportion of runs in which the most likely BiSSE model did not include a difference in λ values, even when one existed. The red bar signifies runs in which the best model included asymmetry in \( \widehat{\uplambda} \), but in the wrong direction, estimating \( \widehat{\uplambda} \)0 to be greater than \( \widehat{\uplambda} \)1. The blue bar indicates that that the best model is the most correct, incorporating the real difference between λ0 and λ and found a difference of the correct sign. All three sets of bars refer to estimation speciation rates. Proportion of runs represents the proportion (out of 100 runs) that each result for simulation length. Length of simulation is scaled such that one unit is approximately the time required for speciation rate to drop below extinction rate (see Fig. 3a). Error bars represent the 95% confidence limits on the actual frequency of the particular type of estimation being represented. Assessment of statistical significance is conducted using a likelihood ratio test