Skip to main content

Advertisement

Table 2 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 μ = 0 \( \widehat{\mathrm{q}} \)01 > \( \widehat{\mathrm{q}} \)10 \( \widehat{\mathrm{q}} \)10 > \( \widehat{\mathrm{q}} \)01
Punc. Eq., μ decreasing 0.25 32 68 50 48 2 36 64
0.5 45 55 52 48 0 42 58
0.75 49 51 56 44 0 42 58
1 54 46 47 52 1 51 49
1.5 56 44 48 46 6 50 50
2 60 40 15 13 72 63 37
Continuous, μ decreasing 0.25 54 46 34 56 10 59 41
0.5 56 44 44 46 10 49 51
0.75 48 52 52 48 0 50 50
1 49 51 52 48 0 49 51
1.5 49 51 46 54 0 48 52
2 49 51 56 44 0 46 54
Continuous, μ constant 0.25 45 55 38 59 3 55 45
0.5 49 51 43 56 1 57 43
0.75 49 51 46 54 0 48 52
1 47 53 50 50 0 46 54
1.5 48 52 51 49 0 50 50
2 60 40 60 40 0 62 38
Continuous, μ increasing 0.25 47 53 40 57 3 48 52
0.5 40 60 43 56 1 47 53
0.75 47 53 47 53 0 56 44
1 51 49 51 49 0 49 51
1.5 58 42 48 52 0 49 51
2 46 54 46 54 0 55 45
  1. The simulation specifies the model parameters we used to simulate the clade. The first (“Punc. Eq.”) set used a punctuated equilibrium simulation of character evolution wherein transitions between character states occur only during speciation events. The rest (“Continuous”) used a simulation 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 refers to the 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). λ, μ, and q refer to the parameters being estimated (Table 5) Speciation, extinction, and transition refer to the parameters being estimated. These results do not reflect whether our likelihood ratio tests found statistically significant differences between parameters, but only the sign of the difference between the estimated values