Phylogenetic trees were then computed by maximum likelihood (Figure 4) and Bayesian analysis (Figure 5).
We then plot the best fitting exponential distribution with parameter λ estimated using the Maximum Likelihood Estimator, computed as the inverse of the sample mean (λ = 1/μ = 0.13).
This is a statistical estimation problem for which the standard method used is a maximum likelihood estimate computed by an algorithm known as the Baum-Welch algorithm [48].
Base calls were made by a maximum likelihood calculation, computed as the product of the probabilities for each base at each position using uncertainties estimated during image analysis.
σ u 2 and σ e 2 are estimated using restricted maximum likelihood and computed p values using the standard F test to test the null hypothesis b = 0. Thresholds reported in Rau et al. 2015 (P < 4.1E-6 suggestive, P < 4.1E-7 significant) were used in this study as well.
Consequently, a common approach consists of first estimating these variance parameters using a non-Bayesian algorithm, usually restricted maximum likelihood, and subsequently computing BLUP of genetic effects from standard mixed-model equations (see Equation 4).
A maximum likelihood tree was computed using phyml-alrt (JTT matrix, six rate categories, gamma parameter 1.0), which also computes aLRT branch support in computing time compatible with very large trees [ 35].
A maximum likelihood tree was computed using RAxML with the same options as for the global phylogenomic analysis (see above), and a Neighbor-Joining tree was computed using Mega 5.1 (Tamura et al. 2011), with the JTT model of substitution, a gamma model of rate heterogeneity, a pairwise deletion comparison, and 500 bootstrap iterations.
The maximum likelihood estimation is computed through the well-known EM algorithm [22].
Maximum likelihood training is computed by evaluating equation which takes linear time while other classifiers take expensive iterative approximation.
Maximum Likelihood trees were computed with the general time reversible model (gamma distributed with invariant sites) and 1000 bootstrap replicates.
