It is shown that the sampling distribution of the log likelihood-ratio under the null model is not χ2(p) where p is the number of additional random effects parameters in the model with spatial dependence.
The resulting scaled supF statistics have more similar distributions across different gene lengths ng under the null model.
For example, a BF of 100 indicates that the association data are 100 times more likely under that model than under the null model.
In our experiments, we generated ten associations under the null model for each examined X Y pair to compute the expectation under the null.
The number of high-quality potential binding sites with a 6 7 nt region of perfect complementarity at their 5' end (i.e. a seed region) is substantially (1.34 1.87 times) greater than expected under the null model reflected in the MS control set, and slightly (1.06 1.33 times) greater than expected under the null model reflected by FOM.
We generated these expectations by simulating data under the null model (e.g., the phylogeny estimated with the molecular clock enforced) using the model of sequence evolution appropriate for our empirical data.
For each gene length ng, we estimated the distribution of the supF statistic under the null model of no transition points by calculating the supF statistic for 100,000 samples of ng independent standard normal random variables.
The distributions of ΔAIC were simulated under the null model.
Again the observed probabilities lie outside the distribution under the Null model.
Under the null model, the whole sample derives from a single population obeying a coalescent process.
So, under the null model, we expect to see a significant larger T compared with T0.
