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Table 6 Schematic of the data analyses. Test type refers to whether the simulation was run to test for the propensity of BiSSE to indicate a most likely model with higher diversification rates in the ancestral state when the character has no effect (“asymmetry bias”) or to test the propensity of BiSSE to indicate a most likely model with higher diversification rates in the derived state when the character does have an effect (“Asymmetry detection”).

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

Test type Morphologic evolution model λ ratio Extinction rate change model
Asymmetry bias Test to determine if the best BiSSE model has evolutionary rates depending on character states (i.e. \( \widehat{\uplambda} \)0\( \widehat{\uplambda} \)1, when λ0 = λ1).
Asymmetry bias Punctuated 1.0 Decreasing
Asymmetry bias Continuous-time 1.0 Decreasing
Asymmetry bias Continuous-time 1.0 Constant
Asymmetry bias Continuous-time 1.0 Increasing
Asymmetry detection Test to determine if BiSSE correctly models evolutionary rates to depend on character states (i.e. \( \widehat{\uplambda} \)0 = \( \widehat{\uplambda} \)1, when λ0 = λ1).
Asymmetry detection Punctuated 1.33 Decreasing
Asymmetry detection Punctuated 1.05 Decreasing
Asymmetry detection Continuous-time 1.33 Decreasing
  1. Morphological evolution model refers to whether changes in character states were assumed to happen only during speciation events (“Punctuated”) or whether character states could evolve at any point in a species’ history, being independent of speciation events (“Continuous-time”). λ ratio signifies the ratio of λ10. The extinction rate change model represents what simulated long term trends existed in μ (in all runs, speciation rate was decreasing, and more rapidly than extinction). All combinations of models were run with six different simulation lengths of 0.25, 0.5, 0.75, 1.0, 1.5, and 2.0, where length 1 is the time required for speciation rate to decay to the point where speciation and extinction rates are equal. Each combination of parameters (including length of simulation) was run 100 times. Abbreviations of λ and μ are explained in Table 5