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Maximum likelihood (ML) trees were inferred with the selected model and ML-estimated substitution parameters.
Maximum likelihood (ML) trees were then inferred with the selected model (HKY+Γ, 8 categories, for all data sets) and ML-estimated substitution parameters.
They necessarily need to be coupled to numerical optimization methods to find maximum likelihood estimates of parameters such as insertion and deletion rates, substitution parameters, and branch lengths.
Proper mixing of chains, acceptance probabilities and convergence of likelihood values, tree topologies, branch lengths and model substitution parameters were checked in the four runs before the samples were pooled.
Ultrametric trees were obtained by enforcing a molecular clock on the inferred genealogy, and re-estimating the branch lengths and substitution parameters with maximum likelihood with the previously selected evolutionary model.
The approach is similar to one employed by Galtier and Boursot [40] except that the BASEML model does not include a rate heterogeneity parameter and calculates substitution parameters separately for first, second, and third codon positions (in our simulations, only the third codon position is variable).
The substitution parameters were estimated over a neighbor-joining tree.
This applies to incomplete data as well as gene-specific substitution parameters.
The substitution parameters were allowed to vary independently between each partition.
Maximum-likelihood (ML) trees were then inferred with the selected model and ML-estimated substitution parameters.
This is in turn equivalent to making the hypothesis that all LHT and substitution parameters scale allometrically with body size.
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