Fig. 1

Risk of misinterpreting BiSSE results to incorrectly infer evolutionary rate asymmetry on simulated trees when no asymmetry exists. Simulation length is the amount of time the simulation ran to generate the simulated clade, with one unit being roughly the time necessary for the λ to drop below the μ (see Fig. 3). a, b λ and μ both decline, but at different rates such that μ eventually overtakes λ, as in Fig. 3a. c λ declines while μ is constant, so that eventually extinction dominates, as in Fig. 3b. d λ decreases while μ increases, as in Fig. 3c. The relative rates of speciation and extinction are the same as those described in the corresponding graph in Fig. 3. a Character evolution follows a punctuated equilibrium simulation, whereby character evolution only occurs during speciation events. b, c, d Character evolution is continuous with time and proceeds irrespective of speciation. Misinference rate represents the results of an AIC-based likelihood ratio test on BiSSE model fits in which the character states had or did not have an effect on \( \widehat{\uplambda} \), \( \widehat{\upmu} \), or \( \widehat{\mathrm{q}} \), respectively. Each combination of parameters and simulation length represents 100 simulated trees. The blue bars represent differences in \( \widehat{\uplambda} \), the red bars \( \widehat{\upmu} \), and the green bars \( \widehat{\mathrm{q}} \). Error bars represent the 95% confidence limits on the actual rate of misinference based on the size of the sample. In these simulations, the true evolutionary rates associated with ancestral and derived states are equal. Abbreviations of rates and symbols are in Table 5