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Table 3 Estimates of systematic bias in directionality of differences in evolutionary rates of most likely BiSSE models when no real (simulated) differences in evolutionary rates exist.

From: Binary-state speciation and extinction method is conditionally robust to realistic violations of its assumptions

Simulation Length Speciation Extinction Transition
\( \widehat{\uplambda} \)0 > \( \widehat{\uplambda} \)1 \( \widehat{\uplambda} \)1 > \( \widehat{\uplambda} \)0 \( \widehat{\upmu} \)0 > \( \widehat{\upmu} \)1 \( \widehat{\upmu} \)1 > \( \widehat{\upmu} \)0 \( \widehat{\mathrm{q}} \)01 > \( \widehat{\mathrm{q}} \)10 \( \widehat{\mathrm{q}} \)10 > \( \widehat{\mathrm{q}} \)01
Punc. Eq., μ decreasing 0.25 7 12 2 7 12 2
0.5 1 4 0 1 4 0
0.75 1 1 5 1 1 5
1 3 0 5 3 0 5
1.5 10 11 2 10 11 2
2 46 25 7 46 25 7
Continuous, μ decreasing 0.25 3 3 0 0 2 4
0.5 0 0 0 0 1 2
0.75 2 2 0 0 1 1
1 4 6 0 1 1 2
1.5 24 31 2 2 7 7
2 43 50 17 9 12 24
Continuous, μ constant 0.25 1 2 0 0 0 4
0.5 0 3 0 4 2 3
0.75 0 0 2 0 0 5
1 6 8 8 9 9 11
1.5 16 9 15 8 10 15
2 59 40 41 22 30 13
Continuous, μ increasing 0.25 1 1 0 0 3 3
0.5 1 3 0 2 3 1
0.75 3 4 1 2 2 2
1 7 1 4 2 5 2
1.5 21 15 35 34 38 39
2 46 53 45 50 23 22
  1. Unlike Table 2, this Table 3 counts only those runs in which the asymmetry in evolutionary rates was found to be statistically significant via a likelihood ratio test on the respective model fits. The simulation specifies the model parameters we used to simulate the clade. The first set used a punctuated equilibrium simulated of character evolution wherein transitions between character states occur only during speciation events. The rest used a simulated of character evolution wherein state changes are independent of speciation events. Our first two sets have both speciation and extinction rates declining with time as in Fig. 3a. The third has extinction rate constant and only speciation declining as in Fig. 3b. The final set has extinction rate increasing as in Fig. 3c. Length simulated time in the run: one unit is approximately the amount of time needed for speciation rate to decay below extinction rate (see Fig. 3). Speciation, extinction, and transition refer to the parameters being estimated (Table 5)