MEME (Mixed Effects Model of Evolution)

MEME (Mixed Effects Model of Evolution) employs a mixed-effects maximum likelihood approach to test the hypothesis that individual sites have been subject to episodic positive or diversifying selection. In other words, MEME aims to detect sites evolving under positive selection under a proportion of branches.

For each site, MEME infers two $\omega$ rate classes and corresponding weights representing the probability that the site evolves under each respective $\omega$ rate class at a given branch.

To infer $\omega$ rates, MEME infers a single $\alpha$ (dS) value and two separate $\beta$ (dN) values, $\beta^+$ and $\beta^-$. Both $\beta^+$ and $\beta^-$ share the same $\alpha$ per site.

Alternative Model Rate Parameter Constraints $$ \alpha\ unrestricted \ \beta^+\ unrestricted \ \beta^- \leq \alpha $$

Null Model Rate Parameter Constraints $$\alpha\ unrestricted \ \beta^+ \leq \alpha \ \beta^- \leq \alpha$$

The $\beta^+$ parameter is the key difference between the null and alternative models. In the null model, both $\beta^+$ and $\beta^-$ are constrained, but $\beta^+$ is unrestricted in the alternative model.

Positive selection for each site is inferred when $\beta^+ > \alpha$ and shown to be significant using the likelihood ratio test.

Citation

When using MEME in your analysis, please refer to the following publication:

Murrell, B et al. "Detecting individual sites subject to episodic diversifying selection." PLoS Genetics 8, e1002764 (2012).

Input Parameters

Required Inputs

• Alignment File: A file containing an in-frame codon alignment (supported formats include .fasta, .nex, etc.).
• Genetic Code: Indicates the genetic code to be used (default: "Universal").
• Phylogenetic Tree: A tree containing the phylogenetic tree structure (optionally annotated with branch lengths) appended to the end of the FASTA file or nestled within the NEXUS file.

Optional Inputs

• Multiple Hits: Allows the model to account for multiple nucleotide substitutions. Options include "None", "Double", or "Double+Triple" (default: "None").
• Site Multihit: Option to define how to handle multiple substitutions at the site level, with options "Estimate" or "Global".
• Rates: Defines the number of different categories of non-synonymous rates to include in the model (default value: 2).
• Resample: Specifies the number of bootstrapping replicates for hypothesis testing at each site (default: 0).
• Impute States: Option to impute likely character states for missing data (default: "No").

Outputs

Summary

MEME produces a detailed JSON output file which comprises:

• General analysis details including metadata and specified parameters.
• Per-site results summarizing selective pressures and evidence for diversifying selection.

Site-Level Output Details

Each site analyzed in the alignment contains:

• Alpha (α): The estimate of the synonymous substitution rate.
• Beta (β−): The estimate for the non-synonymous rate associated with negative selection.
• Beta (β+): The estimate for the non-synonymous rate associated with positive selection.
• Likelihood Ratio Test (LRT): Likelihood ratio test statistic for episodic diversification, i.e., p+ > 0 and β+ > α.
• P-value: Asymptotic p-value for episodic diversification, i.e., p+ > 0 and β+ > α
• Number of Branches Under Selection: An estimate for how many branches could be under selection at a given site.

Visualization

MEME includes an interactive visualization component that allows users to dynamically explore analysis outcomes. This can include:

• Detailed tables showing selection pressures per site.
• Graphical representations of rate estimates, LRT statistics, and p-values.
• Phylogenetic trees enhanced with information about select sites, facilitating easy interpretation of evolutionary relationships.

Example Workflow

1. Upload Data:

   • Begin by providing the necessary alignment file (.fasta, .nex, etc.) and associated phylogenetic tree.
   • Ensure to select the appropriate genetic code and set any optional parameters as needed for your specific analysis.

2. Run Analysis:

   • Click on the "Run Analysis" button to initiate the MEME analysis.
   • Optionally provide an email address to be notified upon completion.

3. Review Results:

   • Upon completion, review the generated summary statistics and visualizations using the analysis interface.
   • Adjust thresholds to explore different categories of selection based on your results.

4. Export Results:

   • Download the detailed results generated in JSON format for further analysis or archival purposes.

References

• MEME Source Code and Documentation - Explore the method's implementation and additional functionality.
• PLOS Genetics article - Access the original publication detailing the MEME method and its applications.

Example CLI Usage

To run the MEME analysis using HyPhy, use the following command:

/path/to/hyphy/hyphy meme --alignment <alignment_file> --tree <tree_file> --code <genetic_code> --multiple-hits <multiple_hits> --site-multihit <site_multihit> --rates <rates> --resample <resample> --impute-states <impute_states>

Parameters

• --alignment: Path to the in-frame codon alignment file.
• --tree: Path to the phylogenetic tree file.
• --code: Genetic code to be used (default: "Universal").
• --multiple-hits: Options for including multiple substitutions; values can be "None", "Double", or "Double+Triple" (default: "None").
• --site-multihit: Option to handle multiple substitutions at the site level; choose "Estimate" or "Global".
• --rates: Number of different categories of non-synonymous rates to include in the model (default: 2).
• --resample: Number of bootstrapping replicates for hypothesis testing (default: 0).
• --impute-states: Impute likely character states for missing data (default: "No").

Full Example Usage

Here is a complete example command using default inputs for optimal parameters:

/path/to/hyphy/hyphy meme --alignment my_alignment.fasta --tree my_tree.nwk --code Universal --multiple-hits None --site-multihit Estimate --rates 2 --resample 0 --impute-states No

Minimal Example Command

The following command uses only required parameters without any default values:

/path/to/hyphy/hyphy meme --alignment my_alignment.fasta --tree my_tree.nwk --code Universal

FAQ

1. What do the results of MEME indicate?

Results from MEME report the sites that show evidence of episodic positive selection, along with empirical Bayes factors (EBFs) that indicate the strength of the evidence for selection on each site across branches. A significant p-value indicates positive selection, while the number of branches associated with that selection can highlight the locations within the phylogeny.

2. Why might there be significant p-values with 0 branches under selection?

This situation often arises when the variation at a site indicates divergence but does not correlate with specific branches being highly influential. It suggests diffuse support for selection; that is, multiple branches contribute to the signal for selection without any single branch being statistically significant on its own.

3. How should I interpret EBF (Empirical Bayes Factor) in the MEME output?

EBF is used to assess the strength of evidence for positive selection at a given site on specific branches. Higher EBF values suggest stronger evidence for selection. Generally, EBF values greater than 100 indicate strong support for positive selection.

4. What is the best strategy to analyze selection pressure across different branches?

Using tools such as BUSTED or aBSREL is recommended for branch-level analysis of selection pressure. After identifying positively selected genes, you can then apply MEME for site-specific analysis. It is not advisable to filter results based only on previously detected positive selection.

5. Can I run MEME and aBSREL on the same dataset?

Yes, you can run both tools on the same dataset. However, be cautious of interpreting results when using both methods, as they employ different approaches to testing for selection.

6. What if I have a limited sample size, such as fewer than 10 sequences?

For smaller sample sizes, the power to detect selection is inherently reduced. BUSTED is particularly useful for detecting selection at the gene level even with limited data. Methods like FEL and MEME may still be applied, but results should be interpreted with caution, keeping in mind the potential for false negatives or positives.

7. Is it important to provide an outgroup when analyzing selection?

While not strictly necessary, including an outgroup in your analysis can provide valuable context for identifying positive selection and establishing the evolutionary history of the genes of interest. An outgroup can help polarize the traits and infer the ancestral states more reliably.

8. How do I interpret my results across different methods (e.g. MEME vs. FEL)?

When interpreting results obtained from different methods, remember that:

• MEME focuses on episodic positive selection, while FEL analyzes pervasive selection.
• Results may vary; it’s essential to compare the significance of p-values and EBF values collectively rather than relying on one method exclusively.
• Use the findings to inform hypotheses, but approach conclusions conservatively, recognizing the potential for discrepancies.