Table 1 Model selection criteria procedures

From: Model selection may not be a mandatory step for phylogeny reconstruction

Criterion

Procedure

AIC

ML is computed for every candidate model and the model with minimal \(\left\{ { - 2\ell + 2K} \right\}\) is selected

AICc

Based on AIC but penalizes also for the data size. Namely, the model with minimal \(\{ {AIC + \frac{{2K\left( {K + 1} \right)}}{{n - K - 1}}} \}\) is selected; advised to be used instead of AIC when \(\frac{n}{K} < 40\)29

BIC

ML is computed for every candidate model and the model with minimal \(\left\{ { - 2\ell + K\ln n} \right\}\) is selected

DT

Based on BIC but incorporates relative branch-length error as a performance measure

hLRT/dLRT

Sequential likelihood ratio tests between pairs of nested models until one cannot be rejected. Topologies are fixed to allow nesting. While in hLRT the order in which parameters are added is defined a priori, in dLRT all models that differ in one parameter are compared in parallel and the hierarchy proceeds with the model that maximizes the log-likelihood difference. Thus, dLRT enables a different order of hypotheses testing for different datasets

BF

The ratio between the marginal likelihood of two models. A ratio above 10 implies strong support for the model at the numerator

  1. \(\ell\), the maximum log-likelihood of model M is computed as \(\log P(D|M,\theta )\); D, M, θ represent the data, the model, and the parameters estimates (i.e., the model parameters, branch lengths, and tree topology), respectively. K is the number of parameters; n is the data size (usually defined as the number of sites in the alignment33). The marginal likelihood is computed as \(P\left( {D{\mathrm{|}}M} \right) = \mathop {\int }\nolimits P\left( {D{\mathrm{|}}M,\theta } \right)P\left( {\theta {\mathrm{|}}M} \right)d\theta\)
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