Question: Interpretation of MEME Table Output (FEL Metrics, Beta Values, LRT Calculation) + Total Branch Length = 0 (No Runtime Errors)

[wxijia03]

Hi HyPhy team/community,
I am using the MEME method in HyPhy to detect episodic positive selection across ~50 species. I ran the analysis via [hyphy meme --alignment ace2_aln.fas --tree ace2_tree.nwk] and did not receive any runtime errors; however, I have several critical questions about the output table and unexpected results, and would greatly appreciate your guidance:

Context for Reference

Input data: CDS alignment (FASTA, ~1000bp, 50 species) + phylogenetic tree (Newick format, unrooted)

Key observations:

All "total branch length" values in the MEME table are 0 (no errors during run).
LRT values in the table do not match manual calculations using the LogL values from MEME/FEL.

Specific Questions

1. FEL-related metrics in the MEME table
   I noticed the MEME output table includes metrics associated with FEL (Fixed Effects Likelihood), even though I only executed the MEME workflow.
   What is the purpose of including FEL metrics in the MEME table (e.g., comparison, model component, validation)?
   What are the statistical hypotheses for these FEL metrics in the MEME output context?
2. Two beta values in MEME and model hypotheses
   I am unclear about the meaning of the two beta values reported in the MEME table:
   What do these two beta values specifically represent in the MEME mixed-effects model?
   My current understanding of MEME’s hypotheses is below—could you confirm if this is accurate?
   Null hypothesis (H₀): Beta values can vary across branches, but β ≤ α (no positive selection, only neutral/purifying selection).
   Alternative hypothesis (H₁): Beta values can vary across branches, and β > α (episodic positive selection is allowed for some site-branch combinations).
   Additionally, what are the statistical hypotheses for the FEL metrics in the far-right column of the table?
   Is the FEL metrics same as the FEL method？What's the difference between them？I noticed the site10 above，which get FEL alpha 0.00 in MEME table with alpha 13.44 which identified as “purifying site” in FEL. That's so strange.
3. LRT value calculation discrepancy
   I attempted to calculate LRT values using the formula I assumed for MEME:
   LRT = -2 × (MEME LogL - FEL LogL)
   However, this produces inconsistent results with the table:
   For example, at site 114:
   MEME LogL = -33.38
   FEL LogL = -32.52
   Manual calculation: LRT = -2 × (MEME LogL - FEL LogL) ≈ 1.72
   Table-reported LRT for site 114: 6.81
   Is the formula I used incorrect? If so, what is the correct mathematical formula for MEME’s LRT value calculation (per site)?
   Why does this discrepancy occur?
4. All "total branch length" values = 0 (no runtime errors)
   All rows in the MEME table show "total branch length = 0", even though my phylogenetic tree has non-zero branch lengths (verified by visualizing the tree in FigTree).
   Could this indicate an input error (e.g., tree format, alignment formatting, species ID mismatch between alignment and tree)?
   What other factors might cause total branch length to be 0 in MEME output (despite no errors)?
   Are there checks I can run to validate the input data compatibility with MEME?

Additional Info (if applicable)

I have verified:
Species IDs in the alignment FASTA match exactly with the tree Newick file (no typos/extra spaces).
The alignment is a valid CDS (length is multiple of 3, no stop codons in the middle).
The tree is in standard Newick format (tested with other phylogenetic tools, e.g., IQ-TREE, which recognizes branch lengths).
Thank you very much for your time and expertise—your clarification will help me correctly interpret the MEME results and troubleshoot the unexpected branch length issue.
Best regards,
wxijia03

[spond]

Dear @wxijia03,

Thank you for the detailed breakdown and for looking closely at the likelihood values. Here is some clarification on the points you raised regarding MEME's behavior and output:

1. Total Branch Length = 0

The "0" values for total branch length in the MEME output are confusing but expected in current versions of HyPhy. This reporting feature was disabled (hardcoded to return 0) during our optimization work for very large-scale SARS-CoV-2 analyses (back in 2021-2022) to minimize computational overhead. It was never restored to the standard output.

Rest assured that the branch lengths from your input tree are being used correctly for all likelihood calculations and parameter estimations; the 0 is simply a reporting placeholder in the results table.

2. The Nature of the LRT in MEME

A common point of confusion is that MEME's LRT compares MEME to FEL. This is not the case.
The Likelihood Ratio Test (LRT) reported by MEME is an internal test between two nested models:

• MEME Null (H₀): A model where the β is constrained to be ≤α); the key difference from FEL is that there are still TWO values of β
• MEME Alternative (H₁): The mixed-effects model where a fraction of branches is allowed to evolve under positive selection (β > α).

The FEL-related metrics included in the MEME table are provided primarily for reference and initialization, but they do not form the basis of the reported p-value.

3. FEL Likelihoods vs. MEME Likelihoods

If you encounter cases where the FEL likelihood is greater than the MEME likelihood, this indicates numerical convergence issues. Because the models are nested, the MEME likelihood should theoretically always be ≥ the FEL likelihood. When it isn't, it usually points to a "difficult" data regime where the optimizer struggles to find the global maximum for the more complex MEME model. This is most common with:

• Very shallow trees: Where there is insufficient mutational signal to reliably partition the variance.
• Extremely divergent trees: Where the signal may be saturated.

4. Beta Values and Hypotheses

In the MEME mixed-effects model, we estimate two β values and the proportion of branches belonging to the "+" (positive selection, β ≥ α) category and the "-" (negative/neutral, β ≤ α). The test specifically looks for evidence that β₊ > α on a subset of branches. Your understanding of the hypothesis structure (H₀ restricting β ≤ α vs H₁ allowing β > α) is correct.

Best,
Sergei