This problematic behavior is not apparent, however, when accuracy is measured only as the correspondence between the proportion of replicates in which some topology is true and the proportion of replicates from which it is inferred.
Four females from each genotype were used in each replicate, rather then a single female, to increase the proportion of replicates with large numbers of eggs.
The proportion of replicates where rs in the resampled data was equal to or greater than zero indicates the probability of this outcome given these sequence data.
Both type I error rate and power were defined as the proportion of replicates in which the p-value was equal to or smaller than the significance threshold.
In 10,000 replicates of this simulation, the proportion of replicates yielding a prediction rate exceeding that obtained in the actual data using the posterior expectations of the θi was only 0.0236.
Both type-I error rates and power are estimated on 10,000 replicates, where power is defined as the proportion of replicates in which the association is detected at the predefined significance level 1.0E-6.
We then calculated the probability of observing a lack of rainforest-ecotone divergence, as the proportion of replicates where the absolute morphological divergence between rainforest and ecotone was less than or equal to that observed in West Africa.
Essentially, we calculate πrj as the proportion of replicates where prj is equal to or less than min(Prj,.≤Prm), with a possible modification required to ensure monotonicity of the {πrj} [32], [33].
For each simulation, these type I error rates are the proportion of replicates for which the computed LRTS exceeds 0.2157, 6.25, 7.81, 9.348 or 11.34, which correspond to the 0.975, 0.10, 0.05, 0.025 and 0.01 significance level cutoffs for a central chi-square distribution with 3 degrees of freedom (the asymptotic null distribution for each simulation).
For each simulation, these powers are the proportion of replicates for which the computed LRTS exceeds 16.27, 21.11, or 25.90, which correspond to the 10−3, 10−4, and 10−5 cutoffs for a central chi-square distribution with 3 degrees of freedom (the asymptotic null distribution for each simulation).
