*4.5.3. Mixed Effects Model of Evolution (MEME)*

**Principle:** MEME is categorized under the 'branch-site random effects' phylogenetic methods [112]. Though this method is a generalization of FEL method, it differs from FEL and IFEL, by accounting for episodic positive selection that particularly affects a subset of lineages. MEME uniquely allows the distribution of *dN/dS (ω)* to vary from site to site (the fixed effect) and also from branch to branch at a site (the random effect).

#### **Algorithm steps:**


#### **4.6. Methods for reconstruction of molecular phylogeny**

Molecular phylogenetic analyses are the most commonly performed studies in virology with major applications in viral taxonomy, systematics and genotyping. Methods for reconstruction of phylogenetic tree are broadly classified into three main categories, *viz.* distance-based, character-based and Bayesian-based and are reviewed earlier [113, 114]. Distance-based methods use pairwise distance matrix as an input for tree building. Neighbour-joining [115], minimum evolution [116] and least square [117, 118] methods are widely used methods under this category. These methods are computationally efficient and suitable for the analysis of large datasets with low levels of sequence divergence. However, these methods do not perform equally well in case of highly divergent sequences with low levels of sequence similarity. Moreover, uncertainties can be introduced due to positioning of gaps in the MSA. Characterbased methods assume each site in MSA to evolve independently. The two classical methods under this category are maximum parsimony and maximum likelihood [119], which estimate the tree score based on the minimum number of changes and the log-likelihood value respec‐ tively. However, it needs to be mentioned that alignment-based phylogenetic methods are observed to misclassify taxa with mixed ancestry and/or recombination [91, 92].

The alignment-free methods have been developed as an alternative and can be classified into four categories based on the underlying principles employed. They are *k*-mer/word composi‐ tion, substring theory, information theory and graphical representation [120].

Whole genome-based phylogenetic trees are widely used for various viruses owing to their small genome sizes and conservation of genomic structure. Phylogenomics field has gained importance as whole genome data became available enabling the study of evolution in general and epidemiology and disease surveillance, in particular. This field when analysed in the context of spatio-temporal data helps to understand the disease spread and progression during outbreaks. The program such as Bayesian Evolutionary Analysis by Sampling Trees (BEAST) has been exclusively designed for phylogeography studies [121] and is used widely to study spatio-temporal dynamics of viruses at population scale.

BEAST software provides a Bayesian Markov chain Monte Carlo (MCMC) framework for parameter estimation and hypothesis testing of evolutionary models from molecular sequence data. It brings together a large number of evolutionary models into a single coherent frame‐ work for evolutionary inference. Available evolutionary models include substitution, inser‐ tion–deletion, demographic, tree shape priors, node calibration and relaxed clock models. This combinatorial principle is advantageous as it provides a flexible system to specify models to understand various aspects of virus evolution. BEAST uniquely incorporates the time-scale data to explicitly model the rate of molecular evolution on each branch in the tree. Under the uniform rate assumption over the entire tree, the molecular clock model becomes applicable. It is the first software to incorporate the relaxed molecular clock model that does not assume constant rate across lineages.
