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Figure 4 Comparison between the maximum likelihood algorithm and the maximum method.
The likelihood ratio test between the maximum likelihood three-epoch and two-epoch models was highly significant (p = 4.52×10−11), showing that at least three periods of different population sizes must be considered to describe the data.
This region also features the most pronounced differences between the maximum likelihood and Bayesian trees.
The minimum log-likelihood difference between the maximum likelihood tree and trees not supporting the basal position of cartilaginous fishes is 18.3 ± 13.1.
We tested whether there were significant topological differences between the maximum likelihood trees of the four genes and a tree produced from the concatenated sequences of all four genes using the Shimodaira-Hasegawa test [ 86].
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Performance of the relatedness estimators was consistent between categories within populations and relatively consistent between populations: the maximum likelihood estimator rML performed best for all categories across all populations, rLR performed worst for BSS and CSA, rW performed worst for BASS, and rQG showed intermediate performance.
The data sets simulated under the static model were also evaluated under the duplication model, and the difference between the maximum likelihoods under each model for each data set were compared with our data set in order to confirm that the duplication model was a significantly better fit for the data.
City-specific estimates were included in a random-effects meta-analysis to assess between-city heterogeneity using the maximum likelihood method in the metareg procedure in Stata [ 27].
Plots were used to visualize the overlap between the results from the maximum likelihood and Bayesian approaches together.
As expected if allelic coalescence has occurred more recently than the split between the two species, the maximum likelihood genealogy for Co is consistent with reciprocal monophyly for H. melpomene and H. cydno, with 2.5 3.0% net divergence between species compared to < 1.3% uncorrected divergence within populations, and 0.4% net divergence between H. melpomene races (Table 2).
We first used the model A that enables ω (= dN/ dS) to vary both between sites and between lineages, and was implemented in the maximum likelihood framework [ 53].
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