The basal split within plethodontids has been dated at ∼ 40 to ∼130 Myr, depending on data set and analytical technique; divergence time estimates for our six focal taxa are similarly varied, but all are ≥25 Myr (Mueller 2006; Marjanovic and Laurin 2007; Kozak et al. 2009; Zhang and Wake 2009; Zheng et al. 2011).
It uses a Normal-Gaussian model to approximate the Boltzmann distribution, hence, formulae for computing the mean and variance parameters of the Gaussian model are derived from the analytical minimization of the Kullback Leibler divergence.
Again, only a small divergence between the analytical and simulative solutions is noticeable.
We now study the symmetrized divergence between the analytical and limiting distributions of for some moderate values of and under different and.
Owing to the concern that assumptions of particular analytical methods may systematically bias divergence time estimates, we compare several methods for accommodating among-lineage rate heterogeneity for the purpose of estimating the divergence times of modern avian lineages.
This is in qualitative agreement with experimental results, and it is at variance with previous analytical studies where fluid viscosity was neglected and divergence instability was predicted.
Furthermore, in this case there exists an analytical solution for modified Jensen-Rényi divergence, which reduces the computational burden of the algorithm and improves the accuracy of the solution.
Two ensembles are then compared using an analytical expression of the Kullback-Leibler divergence between two normal distributions.
As a result, multiple independent phylogenetic markers with sufficient sequence divergence are necessary, and analytical approaches from population genetics may in some cases be more appropriate than traditional phylogenetic methods [ 5, 6].
Additionally, we note that many other factors, including fossil data and analytical tools used, affect the accuracy of divergence date estimation [[ 12, 50, 51], e.g. [ 52, 53]].
Thus, our results validated our experiment and suggested that our analytical procedures are suitable for studying expression divergence in exon transcripts.
