Table 1.

Model selection criteria procedures

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 $\left\{AIC+\frac{2K\left(K+1\right)}{n-K-1}\right\}$ 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 $\left\{-2\ell +Klnn\right\}$ 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

$\ell$, the maximum log-likelihood of model M is computed as $logP\left(D\mid M,\theta \right)$; 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 $P\left(D\mathrm{\mid }M\right)=\int P\left(D\mathrm{\mid }M,\theta \right)P\left(\theta \mathrm{\mid }M\right)d\theta$