panDecay: Phylogenetic Analysis using Decay Indices

panDecay is a Python command-line tool for calculating phylogenetic decay indices across multiple analysis frameworks. It can compute parsimony-based decay indices (traditional Bremer support), Maximum Likelihood (ML)-based decay indices, and Bayesian decay indices using MrBayes

Background

What are Decay Indices / Bremer Support?

In phylogenetics, assessing the support for individual branches (clades) in a tree is crucial. Traditional bootstrap methods resample characters to estimate support. Decay indices, originally developed for parsimony (Bremer, 1988; Bremer, 1994), measure how much worse a tree must be (e.g., how many extra steps in parsimony) to lose a particular clade. A higher decay value indicates stronger support for that clade.

Why ML-based Decay Indices?

While parsimony decay indices are well-established, maximum likelihood (ML) is a statistically robust framework for phylogenetic inference. ML-based decay indices extend this concept to the likelihood framework. Instead of "extra steps," we look at the difference in log-likelihood scores between the optimal ML tree and the best tree where a specific clade is constrained to be non-monophyletic (i.e., the branch defining that clade is collapsed).

panDecay automates this process by:

Finding the optimal ML tree and its likelihood score.
For each internal branch in the ML tree: a. Defining a constraint that forces the taxa in that clade to not form a monophyletic group (using PAUP*'s converse=yes constraint). b. Searching for the best ML tree under this reverse-constraint and recording its likelihood.
Calculating the difference in log-likelihood between the unconstrained ML tree and each constrained tree.
Performing an Approximately Unbiased (AU) test (Shimodaira, 2002) to statistically compare the unconstrained ML tree against all the constrained alternative trees. The p-value from the AU test indicates the significance of the support for the original clade.

A significantly worse likelihood for the constrained tree (and a low AU test p-value for that constrained tree) provides strong evidence in favor of the monophyly of the original clade.

Bayesian Decay Indices

panDecay now supports Bayesian phylogenetic decay indices, extending the decay index concept to Bayesian inference. Instead of comparing log-likelihoods, Bayesian decay indices compare marginal likelihoods between:

An unconstrained Bayesian analysis where all topologies are explored
Constrained analyses where specific clades are forced to be non-monophyletic

The Bayesian decay index for a clade is calculated as:

Bayesian Decay = ln(ML_unconstrained) - ln(ML_constrained)

Where ML represents the marginal likelihood (not to be confused with maximum likelihood). A positive Bayesian decay value indicates support for the clade, with larger values indicating stronger support.

Important Note on Interpretation: In phylogenetic applications, Bayesian decay values tend to closely approximate ML log-likelihood differences. This occurs because:

The compared models differ only in topological constraints, not in substitution models or parameters
When data strongly support a topology, the marginal likelihood is dominated by the likelihood component
Traditional interpretation scales were developed for comparing fundamentally different models and do not apply well to phylogenetic topology testing

Interpreting Bayesian decay values:

BD values should be interpreted comparatively across branches rather than using absolute thresholds
Compare BD values with other support metrics (ΔlnL, AU test p-values, bootstrap, parsimony decay)
BD values may scale with alignment size and sequence diversity
Strong support is best identified when multiple metrics concordantly indicate robust clade support

Note that BD values of 30-50 or higher are common when data strongly support a clade and should not be considered anomalous.

panDecay can perform Bayesian analyses using:

MrBayes: Currently supported with stepping-stone sampling (default) or harmonic mean marginal likelihood estimation

Features

Analysis Types

Parsimony Analysis: Calculates traditional Bremer support values (parsimony decay indices)
ML Analysis: Calculates ML-based decay values using log-likelihood differences
Bayesian Analysis: Calculates Bayesian decay indices using marginal likelihood comparisons
Combined Analysis: Performs multiple analysis types in a single run (e.g., ML+Bayesian, or all three)
Bootstrap Analysis: Optional bootstrap support values alongside decay indices

Core Capabilities

Performs the Approximately Unbiased (AU) test for statistical assessment of ML branch support
Supports DNA, Protein, and binary discrete morphological data
Optional site-specific likelihood analysis to identify which alignment positions support or conflict with each branch
Clean model specification system: --nst for DNA (1/2/6 = JC/HKY/GTR-like), --protein for proteins (jtt, wag, lg, etc.), automatic Mk for discrete data, with options for gamma-distributed rate heterogeneity (+G) and proportion of invariable sites (+I)
Allows fine-grained control over model parameters (gamma shape, pinvar, base frequencies, etc.)
Option to provide a custom PAUP* block for complex model or search strategy definitions
Option to provide a starting tree for the initial ML search

Bayesian Features

Support for MrBayes with automatic constraint generation
Marginal likelihood estimation using:
- Stepping-stone sampling (recommended, more accurate)
- Harmonic mean (faster but less reliable)
Improved Bayesian reporting:
- Primary focus on Bayes Decay for interpretability
- Clear warnings about model dimension effects for extreme values
MCMC Convergence Diagnostics:
- Automatic checking of ESS (Effective Sample Size)
- PSRF (Potential Scale Reduction Factor) monitoring
- ASDSF (Average Standard Deviation of Split Frequencies) tracking
- Configurable convergence thresholds with strict mode option
Flexible MCMC parameters (generations, chains, burnin, sampling frequency)
MPI support: Run chains in parallel with MPI-enabled MrBayes
BEAGLE support: GPU/CPU acceleration for likelihood calculations

Output Files

Tab-delimited results file with ML and/or Bayesian support values
Multiple Newick trees annotated with different support values
Detailed Markdown report summarizing the analysis and results
Comprehensive trees combining all support metrics when multiple analyses are performed
Optional static visualization (requires matplotlib and seaborn):
- Distribution of support values
- Site-specific support visualizations

Technical Features

Multi-threaded PAUP* execution (configurable)
Parallel execution of constraint analyses
Debug mode and option to keep temporary files
Robust error handling and recovery

User Interface Features

Professional Runtime Banner: Clean, professional parameter display at startup
- Fixed 80-character width for consistent appearance
- Organized sections (Analysis Configuration, Runtime Settings, Bayesian Parameters, etc.)
- Includes software citation: "McInerney, J.O. (2025) panDecay: Phylogenetic Analysis with Decay Indices"
- No jagged edges or complex table formatting
Enhanced Progress Display: Clean, non-verbose progress tracking
- Unicode spinner animations with dynamic updates
- Consolidated messaging without repetitive output
- Progress indicators that overwrite cleanly
Comprehensive Output Reports: Enhanced markdown reports with complete analysis summaries
- Embedded site analysis summary tables
- Integrated parsimony analysis statistics
- PNG visualization embedding with relative links
- Complete file navigation and cross-references
Clean Console Output: Minimal, professional terminal output
Informative Error Messages: Clear error reporting with helpful troubleshooting suggestions

Installation

Dependencies

panDecay requires Python 3.8 or higher and has several dependencies that can be easily installed using pip.

PAUP*: Required for ML analysis. You must have a working PAUP* command-line executable installed and accessible in your system's PATH, or provide the full path to it. PAUP* can be obtained from phylosolutions.com.
MrBayes (optional): Required for Bayesian analysis. Install MrBayes and ensure it's accessible as mb in your PATH, or specify the path with --mrbayes-path. MrBayes can be obtained from nbisweden.github.io/MrBayes/.
Python Dependencies: All Python dependencies can be installed using the provided requirements.txt file:
```
pip install -r requirements.txt
```
This will install all required packages including BioPython, NumPy, and the optional visualization packages Matplotlib and Seaborn.

Installing panDecay

Option 1: Install from PyPI (Recommended)

pip install pandecay

Option 2: Install from GitHub (Latest Development Version)

pip install git+https://github.com/mol-evol/panDecay.git

Option 3: Development Installation

For developers or if you want to modify the code:

Clone the Repository:

git clone https://github.com/mol-evol/panDecay.git
cd panDecay

Install in Development Mode:
```
pip install -e .
```

This installs panDecay in "editable" mode, so changes to the source code are immediately available.

Usage

Basic Command

For DNA data:

pandecay <alignment_file> --nst <1|2|6> [options...]

For protein data:

pandecay <alignment_file> --data-type protein --protein <model_name> [options...]

For discrete morphological data:

pandecay <alignment_file> --data-type discrete [options...]

Command-Line Arguments

usage: pandecay [-h] [--format FORMAT] [--gamma] [--invariable] [--paup PAUP]
          [--output-dir OUTPUT_DIR] [--project-name PROJECT_NAME]
          [--output OUTPUT] [--tree TREE] [--site-analysis]
          [--data-type DATA_TYPE] [--nst {1,2,6}]
          [--protein {jtt,wag,lg,dayhoff,mtrev,cprev,blosum62,hivb,hivw}]
          [--gamma-shape GAMMA_SHAPE] [--prop-invar PROP_INVAR]
          [--base-freq {equal,estimate,empirical}]
          [--parsmodel | --no-parsmodel] [--threads THREADS]
          [--starting-tree STARTING_TREE] [--paup-block PAUP_BLOCK]
          [--temp TEMP] [--keep-files] [--debug]
          [--analysis {ml,bayesian,parsimony,ml+parsimony,bayesian+parsimony,ml+bayesian,all}]
          [--bootstrap] [--bootstrap-reps BOOTSTRAP_REPS]
          [--bayesian-software {mrbayes}] [--mrbayes-path MRBAYES_PATH]
          [--bayes-ngen BAYES_NGEN] [--bayes-burnin BAYES_BURNIN]
          [--bayes-chains BAYES_CHAINS] [--bayes-sample-freq BAYES_SAMPLE_FREQ]
          [--marginal-likelihood {ss,ps,hm}] [--ss-alpha SS_ALPHA]
          [--ss-nsteps SS_NSTEPS] [--use-mpi] [--mpi-processors MPI_PROCESSORS]
          [--mpirun-path MPIRUN_PATH] [--use-beagle] [--beagle-device {cpu,gpu,auto}]
          [--beagle-precision {single,double}] [--beagle-scaling {none,dynamic,always}]
          [--check-convergence | --no-check-convergence] [--min-ess MIN_ESS]
          [--max-psrf MAX_PSRF] [--max-asdsf MAX_ASDSF] [--convergence-strict]
          [--visualize]
          [--viz-format {png,pdf,svg}] [--annotation {au,lnl}]
          [--output-style {unicode,ascii}] [--constraint-mode {all,specific,exclude}]
          [--test-branches TEST_BRANCHES] [--constraint-file CONSTRAINT_FILE]
          [--config CONFIG] [--generate-config GENERATE_CONFIG]
          [alignment]

panDecay v1.1.1: Calculate phylogenetic decay indices (ML, Bayesian, and parsimony).

positional arguments:
  alignment             Input alignment file path (can also be provided via config file).

options:
  -h, --help            show this help message and exit
  --format FORMAT       Alignment format. Use 'auto' for automatic detection from file extension and content, or specify: fasta, nexus, phylip, clustal, embl, genbank. (default: auto)
**Model Specification (REQUIRED - no defaults):**
  --nst {1,2,6}         Substitution types for DNA data (REQUIRED for DNA).
                        1=JC-like (equal rates & frequencies), 2=HKY-like (ti/tv ratio, estimated frequencies), 
                        6=GTR-like (all rates different, estimated frequencies)
  --protein {jtt,wag,lg,dayhoff,mtrev,cprev,blosum62,hivb,hivw}
                        Amino acid model for protein data (REQUIRED for protein)
  --gamma               Add Gamma rate heterogeneity (+G) to model. (default: False)
  --invariable          Add invariable sites (+I) to model. (default: False)
  --paup PAUP           Path to PAUP* executable. (default: paup)
  --output OUTPUT       Output file for summary results. (default: pan_decay_indices.txt)
  --tree TREE           Base name for annotated tree files. Three trees will be generated with suffixes: _au.nwk (AU p-values), 
                        _delta_lnl.nwk (likelihood differences), and _combined.nwk (both values). (default: annotated_tree)
  --data-type {dna,protein,discrete}
                        Type of sequence data. (default: dna)
  --site-analysis       Perform site-specific likelihood analysis to identify supporting/conflicting sites for each branch. (default: False)
  -v, --version         show program's version number and exit

Model Parameter Overrides (optional):
  --gamma-shape GAMMA_SHAPE
                        Fixed Gamma shape value (default: estimate if +G).
  --prop-invar PROP_INVAR
                        Fixed proportion of invariable sites (default: estimate if +I).
  --base-freq {equal,estimate,empirical}
                        Base/state frequencies (default: model-dependent). 'empirical' uses observed frequencies.
  --rates {equal,gamma}
                        Site rate variation model (overrides --gamma flag if specified).
**Model Parameters (optional):**
  --gamma-shape GAMMA_SHAPE     Fixed Gamma shape value (default: estimate if +G)
  --prop-invar PROP_INVAR       Fixed proportion of invariable sites (default: estimate if +I)
  --base-freq {equal,estimate,empirical}
                        Base/amino acid frequencies. equal=uniform, estimate=ML estimation, empirical=observed
  --parsmodel, --no-parsmodel
                        Use parsimony-based branch lengths (discrete data; default: yes for discrete). Use --no-parsmodel to disable. (default: None)

Runtime Control:
  --threads THREADS     Number of threads for PAUP* (e.g., 4, 'auto', or 'all'). 'auto' uses: total_cores - 2 (if cores > 2), 
                        total_cores - 1 (if cores > 1), or 1 core. Leaving some cores free is recommended for system stability. (default: auto)
  --starting-tree STARTING_TREE
                        Path to a user-provided starting tree file (Newick).
  --paup-block PAUP_BLOCK
                        Path to file with custom PAUP* commands for model/search setup (overrides most model args).
  --temp TEMP           Custom directory for temporary files (default: system temp).
  --keep-files          Keep temporary files after analysis. (default: False)
  --debug               Enable detailed debug logging (implies --keep-files). (default: False)

Analysis Mode:
  --analysis {ml,bayesian,parsimony,ml+parsimony,bayesian+parsimony,ml+bayesian,all}
                        Type of decay analysis to perform (default: ml). 
                        Options: ml, bayesian, parsimony, ml+parsimony, bayesian+parsimony, ml+bayesian, all

Bayesian Analysis Options:
  --bayesian-software {mrbayes}
                        Bayesian software to use (default: mrbayes)
  --mrbayes-path MRBAYES_PATH
                        Path to MrBayes executable (default: mb)
  --bayes-ngen BAYES_NGEN
                        Number of MCMC generations (default: 1000000)
  --bayes-burnin BAYES_BURNIN
                        Burnin fraction (0-1) (default: 0.25)
  --bayes-chains BAYES_CHAINS
                        Number of MCMC chains (default: 4)
  --bayes-sample-freq BAYES_SAMPLE_FREQ
                        Sample frequency for MCMC (default: 1000)
  --marginal-likelihood {ss,ps,hm}
                        Marginal likelihood estimation method: ss=stepping-stone, ps=path sampling, hm=harmonic mean (default: ss)
  --ss-alpha SS_ALPHA   Alpha parameter for stepping-stone sampling (default: 0.4)
  --ss-nsteps SS_NSTEPS Number of steps for stepping-stone sampling (default: 50)

Parallel Processing Options (MrBayes):
  --use-mpi             Use MPI version of MrBayes for parallel chains (default: False)
  --mpi-processors MPI_PROCESSORS
                        Number of processors for MPI (default: number of chains)
  --mpirun-path MPIRUN_PATH
                        Path to mpirun executable (default: mpirun)
  --use-beagle          Use BEAGLE library for likelihood calculations (default: False)
  --beagle-device {auto,cpu,gpu}
                        BEAGLE device type (default: auto)
  --beagle-precision {single,double}
                        BEAGLE precision level (default: double)
  --beagle-scaling {none,dynamic,always}
                        BEAGLE scaling frequency (default: dynamic)

Convergence Checking Options (MrBayes):
  --check-convergence/--no-check-convergence
                        Check MCMC convergence diagnostics (default: True)
  --min-ess MIN_ESS     Minimum ESS (Effective Sample Size) threshold (default: 200)
  --max-psrf MAX_PSRF   Maximum PSRF (Potential Scale Reduction Factor) threshold (default: 1.01)
  --max-asdsf MAX_ASDSF Maximum ASDSF (Average Standard Deviation of Split Frequencies) threshold (default: 0.01)
  --convergence-strict  Fail analysis if convergence criteria not met (default: warn only)

Bootstrap Analysis (optional):
  --bootstrap           Perform bootstrap analysis to calculate support values. (default: False)
  --bootstrap-reps BOOTSTRAP_REPS
                        Number of bootstrap replicates (default: 100)

Visualization Output (optional):
  --visualize           Generate static visualization plots (requires matplotlib, seaborn). (default: False)
  --viz-format {png,pdf,svg}
                        Format for static visualizations. (default: png)
  --annotation {au,lnl} Type of support values to visualize in distribution plots (au=AU p-values, lnl=likelihood differences). (default: lnl)
  --output-style {unicode,ascii,minimal}
                        Output formatting style: unicode (modern), ascii (compatible), minimal (basic). (default: unicode)

Configuration and Constraint Options:
  --config CONFIG       Read parameters from configuration file (INI format)
  --generate-config GENERATE_CONFIG
                        Generate a template configuration file at the specified path and exit
  --constraint-mode {all,specific,exclude}
                        Branch selection mode: all (test all branches), specific (test only specified), 
                        exclude (test all except specified) (default: all)
  --test-branches TEST_BRANCHES
                        Specify branches to test. Format: 'taxon1,taxon2,taxon3;taxon4,taxon5' for clades, 
                        '1,3,5' for branch IDs, or '@file.txt' to read from file
  --constraint-file CONSTRAINT_FILE
                        File containing constraint definitions (one per line)

Input Files

Sequence Alignment

A multiple sequence alignment file.

Formats: FASTA, NEXUS, PHYLIP, Clustal, EMBL, GenBank, etc. (any format BioPython's AlignIO can read).
Automatic Format Detection: panDecay automatically detects the format from file extensions:
- .fas, .fasta, .fa, .fna, .ffn, .faa, .frn → FASTA
- .nex, .nexus, .nxs → NEXUS
- .phy, .phylip, .phyl → PHYLIP
- .aln, .clustal, .clustalw → Clustal
- .embl → EMBL
- .gb, .gbk, .genbank → GenBank
Manual Override: Use --format <format> to specify format explicitly if needed.
Content: DNA, protein, or binary (0/1) discrete morphological characters. Use --data-type to specify.
- For discrete data, characters should be '0' or '1'. Missing data as '?' and gaps as '-' are also recognized.

Optional Starting Tree

A Newick tree file specified with --starting-tree <path_to_tree.nwk>.

If provided, PAUP* will use this tree as the initial tree for the ML search, potentially speeding up the search or helping to find a better likelihood peak. Branch lengths from the starting tree are typically re-optimized.

Optional PAUP* Block File

A text file specified with --paup-block <path_to_block.nex>.

This file should contain valid PAUP* commands that will be inserted into the PAUP* script.
It typically starts after execute <alignment_file>; and should define the model (lset), search strategy (hsearch), and potentially how trees/scores are saved.
This allows advanced users to have full control over PAUP*'s behavior for model setup and tree searching.
Format: The content should be the commands that would normally go between BEGIN PAUP; and END; in a PAUP block. For example:
```
lset nst=2 basefreq=empirical rates=gamma shape=estimate pinv=estimate;
hsearch nreps=100 swap=tbr multrees=yes;
savetrees file=my_custom_ml.tre replace=yes;
lscores 1 /scorefile=my_custom_scores.txt replace=yes;
```
panDecay will try to defensively add savetrees and lscores commands if they appear to be missing from the user's block when needed for its internal workflow.

Configuration File (INI format)

A configuration file specified with --config <path_to_config.ini>.

Format: Standard INI format with key-value pairs and optional sections
Purpose: Allows specifying all command-line parameters in a file for reproducibility and convenience
Template: Generate a fully-commented template with --generate-config template.ini
Sections:
- Main section (no header): Contains most parameters like alignment, model, output settings
- [constraints]: Define specific clades to test when using constraint_mode = specific

Example:

alignment = my_data.fas
nst = 6
gamma = true
constraint_mode = specific

[constraints]
clade1 = taxonA,taxonB,taxonC
clade2 = taxonD,taxonE

Note: Command-line arguments override configuration file values

Constraint File

A text file specified with --constraint-file <path> or --test-branches @<path>.

Format: One constraint per line, taxa separated by commas
Comments: Lines starting with # are ignored

Example:

# Primates clade
Homo_sapiens,Pan_troglodytes,Gorilla_gorilla
# Rodents clade  
Mus_musculus,Rattus_norvegicus

Output Files

Unless specified with --output, --tree, etc., output files are created in the current working directory.

Main Results File (`pan_decay_indices.txt` by default)

A tab-delimited text file containing:

The log-likelihood of the best ML tree found (for ML analyses).
For each internal branch tested:
- Clade_ID: An internal identifier for the branch.
- Num_Taxa: Number of taxa in the clade defined by this branch.
- ML Metrics (when ML analysis is performed):
  - Constrained_lnL: Log-likelihood of the best tree found when this clade was constrained to be non-monophyletic.
  - Delta_LnL: Log-likelihood difference (ΔlnL) between the constrained tree and the ML tree (constrained_lnL - ML_lnL).
  - AU_p-value: The p-value from the Approximately Unbiased test.
  - Significant_AU (p<0.05): "Yes" if AU p-value < 0.05, "No" otherwise.
- Bayesian Metrics (when Bayesian analysis is performed):
  - Bayes_ML_Diff: Marginal likelihood difference (unconstrained - constrained).
- Bootstrap (if bootstrap analysis performed): Bootstrap support value for the clade.
- Taxa_List: A comma-separated list of taxa in the clade.

Annotated Trees

panDecay generates several different annotated tree files:

<tree_base>_au.nwk: Tree with AU test p-values as branch labels
<tree_base>_delta_lnl.nwk: Tree with log-likelihood differences (ΔlnL) as branch labels
<tree_base>_combined.nwk: Tree with both values as branch labels in the format "AU:0.95|ΔlnL:2.34"

If bootstrap analysis is performed, additional tree files:

<tree_base>_bootstrap.nwk: Tree with bootstrap support values
<tree_base>_comprehensive.nwk: Tree with bootstrap values, AU test p-values, and log-likelihood differences combined in format "BS:80|AU:0.95|ΔlnL:2.34"

These trees can be visualized in standard tree viewers like FigTree, Dendroscope, iTOL, etc. The combined tree is particularly suited for FigTree which handles string labels well.

Example Annotated Tree Visualization

The following example shows a comprehensive annotated tree from a combined analysis (ML + Bayesian + Parsimony + Bootstrap):

In this visualization:

Branch labels show multiple support metrics in the format: Clade_X - BS:XX|AU:X.XXXX|ΔlnL:XX.XX|BD:XX.XX|BF:X.XXe+XX|PD:XX
BS: Bootstrap support percentage (when available)
AU: Approximately Unbiased test p-value (lower values = stronger support)
ΔlnL: Log-likelihood difference (higher values = stronger support)
BD: Bayesian Decay (higher values = stronger support)
PD: Parsimony Decay (traditional Bremer support)
Branch colors and exact label formatting may vary by tree viewer; this example uses FigTree's visualization

Detailed Markdown Report (`<output_stem>.md`)

A Markdown file providing a more human-readable summary of the analysis parameters, summary statistics, and detailed branch support results in a table format. It also includes a brief interpretation guide. A good markdown viewer is Joplin or MarkdownLivePreview.

Site-Specific Analysis (Optional)

If --site-analysis is used, additional output files are generated in a directory named <output_stem>_site_analysis/:

site_analysis_summary.txt: A summary of supporting vs. conflicting sites for each branch.
site_data_Clade_X.txt: For each branch, detailed site-by-site likelihood differences.
site_plot_Clade_X.png: Visualization of site-specific support/conflict (if matplotlib is available).
site_hist_Clade_X.png: Histogram showing the distribution of site likelihood differences.

This feature allows you to identify which alignment positions support or conflict with each branch in the tree.

Visualizations (Optional)

If --visualize is used, static plots are generated (requires matplotlib and seaborn):

Support Distribution Plot (<output_stem>_dist_au.<viz_format> and <output_stem>_dist_delta_lnl.<viz_format>): Histograms showing the distribution of AU p-values and ΔlnL values across all tested branches.

Understanding the Site Analysis Plots in panDecay

What the Bar Colours Mean

In the site-specific likelihood plots generated by panDecay (such as site_plot_Clade_X.png):

Green bars represent sites that support the branch/clade being tested. These are alignment positions where the ML tree (with the clade present) has a better likelihood than the constrained tree (where the clade is forced to be non-monophyletic).
Red bars represent sites that conflict with the branch/clade being tested. These are alignment positions where the constrained tree (without the clade) actually has a better likelihood than the ML tree.

What "Delta lnL" Means

"Delta lnL" (ΔlnL) refers to the difference in site-specific log-likelihood between the ML tree and the constrained tree for each site in your alignment. Specifically:

Delta lnL = lnL_ML - lnL_constrained

Where:

lnL_ML is the log-likelihood of that specific site in the maximum likelihood tree (with the clade present)
lnL_constrained is the log-likelihood of that site in the constrained tree (where the clade is forced to be non-monophyletic)

Interpreting the Values

Negative Delta lnL (green bars):
- When Delta lnL is negative, it means the ML tree has a better (less negative) likelihood for that site than the constrained tree
- These sites provide evidence supporting the clade's existence in the tree
- The more negative the value, the stronger the support from that site
Positive Delta lnL (red bars):
- When Delta lnL is positive, it means the constrained tree has a better likelihood for that site than the ML tree
- These sites provide evidence against the clade's existence
- The more positive the value, the stronger the conflict
Values near zero:
- Sites with Delta lnL values very close to zero are effectively neutral regarding this particular branch
- They don't strongly support or conflict with the branch

Additional Information in the Plots

The site-specific analysis plots also contain a text box with summary statistics:

Supporting sites: Total number of sites with negative Delta lnL (green bars)
Conflicting sites: Total number of sites with positive Delta lnL (red bars)
Support ratio: The ratio of supporting sites to conflicting sites
Weighted ratio: The ratio of the sum of absolute values of supporting deltas to the sum of conflicting deltas

Practical Significance

These visualizations allow you to identify which specific positions in your alignment are driving the support or conflict for a particular branch. This can be useful for:

Detecting potential alignment errors or problematic regions
Identifying sites that might be under different selective pressures
Finding evidence of recombination or horizontal gene transfer
Understanding the strength of evidence for contentious branches in your phylogeny

A branch with many strong green bars and few red bars has robust evidence across many sites. A branch with a more balanced mix of green and red bars, or with only a few strong green bars, has more tenuous support and might be less reliable.

Temporary Files (Debug/Keep)

If --debug or --keep-files is used, a temporary directory (usually in debug_runs/mldecay_<timestamp>/ or a user-specified path) will be retained. This directory contains:

alignment.nex: The alignment converted to NEXUS format.
ml_search.nex, paup_ml.log: PAUP* script and log for the initial ML tree search.
ml_tree.tre, ml_score.txt: The best ML tree and its likelihood score file.
constraint_search_*.nex, paup_constraint_*.log: PAUP* scripts and logs for each constrained search.
constraint_tree_*.tre, constraint_score_*.txt: Constrained trees and their score files.
au_test.nex, paup_au.log: PAUP* script and log for the AU test.
au_test_results.txt: Score file from the AU test (though the log is primarily parsed).
bootstrap_search.nex, paup_bootstrap.log, bootstrap_trees.tre (if --bootstrap used): Bootstrap analysis files.
site_analysis_*.nex, site_lnl_*.txt (if --site-analysis used): Site-specific likelihood files.
mldecay_debug.log (in the main execution directory if --debug is on): Detailed script execution log.

Examples & Recipes

Let alignment.fas be a FASTA DNA alignment, proteins.phy be a PHYLIP protein alignment and morpho.nex be a morphological dataset.

Example 1: Basic DNA Analysis

Analyze a DNA alignment with GTR+G+I model, automatically estimating parameters.

pandecay alignment.fas --nst 6 --gamma --invariable --data-type dna \
    --output dna_decay.txt --tree dna_annotated

Example 2: Parsimony Analysis (Traditional Bremer Support)

Calculate traditional Bremer support values using parsimony analysis.

pandecay alignment.fas --analysis parsimony \
    --output parsimony_bremer.txt --tree parsimony_annotated

Example 3: Protein Data with Specific Model

Analyze a protein alignment using the WAG model, fixed gamma shape, and estimating proportion of invariable sites. The PHYLIP format is auto-detected from the .phy extension.

pandecay proteins.phy --data-type protein \
    --protein wag --gamma --gamma-shape 0.85 --invariable \
    --output protein_decay.txt --tree protein_annotated --threads 8

Example 4: Discrete Morphological Data

Analyze a binary (0/1) discrete morphological dataset (e.g., in NEXUS format morpho.nex) using the Mk+G model.

pandecay morpho.nex --data-type discrete \
    --gamma \
    --output morpho_decay.txt --tree morpho_annotated

Note: For discrete data, ensure characters are '0' and '1'. --parsmodel (default for discrete) will use parsimony-like branch lengths.

Example 5: Using a Starting Tree

Perform a GTR+G analysis, but provide PAUP* with a starting tree to potentially speed up or refine the initial ML search.

pandecay alignment.fas --nst 6 --gamma \
    --starting-tree my_start_tree.nwk \
    --output results_with_start_tree.txt

Example 6: Advanced Control with PAUP* Block

Use a custom PAUP* block for complex settings. Assume my_paup_commands.txt contains:

lset nst=6 basefreq=empirical rates=gamma(categories=8) shape=estimate pinv=0.1;
hsearch nreps=50 swap=tbr addseq=random hold=1 multrees=yes;

Then run:

pandecay alignment.fas --paup-block my_paup_commands.txt \
    --output results_custom_block.txt

(panDecay will still handle the constraint generation and AU test logic around your block.)

Example 7: Site-Specific Analysis

Analyze which sites in the alignment support or conflict with each clade:

pandecay alignment.fas --nst 6 --gamma --site-analysis --visualize \
    --output site_analysis_results.txt

This will generate site-specific likelihood analyses in addition to the standard branch support results.

Example 8: Bootstrap Analysis

Perform bootstrap analysis (100 replicates by default) alongside ML decay indices:

pandecay alignment.fas --nst 6 --gamma --bootstrap \
    --output with_bootstrap.txt

For more bootstrap replicates:

pandecay alignment.fas --nst 6 --gamma --bootstrap --bootstrap-reps 500 \
    --output bootstrap500.txt

This will produce additional tree files with bootstrap values and a comprehensive tree that combines bootstrap values with ML decay indices.

Example 9: Bayesian Analysis Only

Perform only Bayesian decay analysis using MrBayes:

pandecay alignment.fas --nst 6 --analysis bayesian --bayesian-software mrbayes \
    --bayes-ngen 500000 --output bayesian_only.txt

Example 10: Combined ML and Bayesian Analysis

Run both ML and Bayesian analyses:

pandecay alignment.fas --nst 6 --gamma --analysis ml+bayesian --bayesian-software mrbayes \
    --bayes-ngen 1000000 --output combined_analysis.txt

Example 11: Combined ML and Parsimony Analysis

Run both ML and parsimony analyses to compare modern and traditional support values:

pandecay alignment.fas --nst 6 --gamma --analysis ml+parsimony \
    --output ml_parsimony_analysis.txt

Example 12: All Three Analysis Types

Run ML, Bayesian, and parsimony analyses in a single run:

pandecay alignment.fas --nst 6 --gamma --analysis all \
    --bayesian-software mrbayes --bayes-ngen 1000000 --output complete_analysis.txt

Example 13: Using MPI for Parallel MrBayes

If you have MPI-enabled MrBayes installed:

pandecay alignment.fas --analysis bayesian --bayesian-software mrbayes --use-mpi \
    --mpi-processors 8 --bayes-chains 4 --bayes-ngen 2000000

This runs 4 chains across 8 processors (2 chains per processor for better mixing).

Example 14: Using BEAGLE for GPU Acceleration

If MrBayes is compiled with BEAGLE support:

pandecay alignment.fas --analysis ml+bayesian --bayesian-software mrbayes --use-beagle \
    --beagle-device gpu --beagle-precision single --bayes-ngen 5000000

For CPU-based BEAGLE acceleration:

pandecay alignment.fas --analysis ml+bayesian --bayesian-software mrbayes --use-beagle \
    --beagle-device cpu --beagle-precision double

Example 15: Combined MPI and BEAGLE

For maximum performance with both MPI and BEAGLE:

pandecay large_alignment.fas --analysis bayesian --bayesian-software mrbayes \
    --use-mpi --mpi-processors 16 --use-beagle --beagle-device gpu \
    --bayes-chains 4 --bayes-ngen 10000000 --bayes-sample-freq 5000

Installation Requirements for Parallel Processing

For MPI Support

To use --use-mpi, you need MrBayes compiled with MPI support. Follow the MrBayes manual instructions to compile with --enable-mpi=yes.

For BEAGLE Support

To use --use-beagle, you need:

BEAGLE library installed (GPU or CPU version)
MrBayes compiled with --with-beagle flag

Example installation on macOS:

# Install BEAGLE
brew install beagle-lib

# Compile MrBayes with BEAGLE and MPI
./configure --with-beagle --enable-mpi=yes
make && sudo make install

Example 16: Quick Bayesian Test

For a quick test with minimal MCMC generations:

pandecay alignment.fas --analysis ml+bayesian --bayesian-software mrbayes \
    --bayes-ngen 10000 --bayes-sample-freq 100 \
    --output quick_test.txt

Example 17: Using Configuration Files

Generate a template configuration file and use it for analysis:

# Generate template
pandecay --generate-config my_analysis.ini

# Edit my_analysis.ini with your parameters, then run:
pandecay --config my_analysis.ini

# Override config file settings with command-line arguments
pandecay --config my_analysis.ini --threads 16 --output different_output.txt

Example 18: Testing Specific Branches

Test only specific clades of interest:

# Test only clades containing specific taxa (semicolon-separated)
pandecay alignment.fas --constraint-mode specific \
    --test-branches "Homo_sapiens,Pan_troglodytes;Mus_musculus,Rattus_norvegicus"

# Test specific branch IDs from a previous analysis
pandecay alignment.fas --constraint-mode specific \
    --test-branches "1,3,5,7"

# Read constraints from a file
pandecay alignment.fas --constraint-mode specific \
    --test-branches "@my_constraints.txt"

# Test all branches EXCEPT specified ones
pandecay alignment.fas --constraint-mode exclude \
    --test-branches "Drosophila_melanogaster,Anopheles_gambiae"

Example 19: Combined Config File with Constraints

Create a configuration file with constraint definitions:

# my_analysis.ini
alignment = vertebrates.fas
nst = 6
gamma = true
analysis = all
constraint_mode = specific

[constraints]
primates = Homo_sapiens,Pan_troglodytes,Gorilla_gorilla
rodents = Mus_musculus,Rattus_norvegicus
birds = Gallus_gallus,Taeniopygia_guttata

Then run:

pandecay --config my_analysis.ini

Interpreting Results

ML Tree Log-Likelihood: The baseline score for your optimal tree.
Constrained Log-Likelihood (Constrained_lnL): The score of the best tree found when a particular clade was forced to be non-monophyletic. This score will typically be worse (more positive, since they are -lnL) than the ML tree's score.
Log-Likelihood Difference (Delta_LnL or ΔlnL):
- Calculated as Constrained_lnL - ML_lnL.
- A larger positive value (i.e., the constrained tree has much worse likelihood) indicates stronger support for the original clade. This is the "decay" value in the likelihood sense.
AU p-value:
- Tests the null hypothesis that the ML tree is not significantly better than the constrained alternative tree (where the clade is broken).
- A low p-value (e.g., < 0.05) leads to rejecting the null hypothesis. This means the constrained tree is significantly worse, providing statistical support for the original clade's monophyly.
- A high p-value (e.g., > 0.05) means we cannot reject the null hypothesis; the data do not provide strong statistical evidence to prefer the ML tree (with the clade) over the alternative (clade broken). This implies weaker support for that specific clade.
Bootstrap Value (if bootstrap analysis performed):
- Percentage of bootstrap replicates in which the clade appears.
- Higher values (e.g., > 70%) indicate stronger support.
- Bootstrap is a widely-used and well-understood method, providing a complementary measure of support to the AU test and ΔlnL values.
Bayesian Decay (BD):
- The primary metric for Bayesian support: marginal log-likelihood difference (unconstrained - constrained)
- Key insight: In phylogenetic topology testing, BD values typically closely approximate ML log-likelihood differences
- Interpretation: BD values should be interpreted comparatively rather than using absolute thresholds:
  - Compare BD values across branches to identify relatively well-supported vs poorly-supported clades
  - Evaluate BD values alongside other metrics (ΔlnL, AU test, bootstrap, parsimony decay)
  - Consider that BD values may scale with alignment properties (size, diversity)
  - The strongest evidence for clade support comes from concordance across multiple metrics
- Note: BD values of 30-50 or higher are common when data strongly support a clade and should not be considered anomalous
- Why traditional BF scales don't apply: Traditional Bayes factor thresholds were developed for comparing fundamentally different models, not for topology testing where models differ only by a single constraint
- Negative values suggest potential issues:
  - Poor MCMC convergence (check convergence diagnostics)
  - Marginal likelihood estimation problems
  - Genuine lack of support for the clade

Site-Specific Analysis Interpretation:

Negative delta lnL values indicate sites that support the branch (they become less likely when the branch is constrained to be absent).
Positive delta lnL values indicate sites that conflict with the branch (they become more likely when the branch is removed).
Values near zero indicate sites that are neutral regarding this branch.

Generally, clades with large positive ΔlnL values, low AU_p-values, high bootstrap values, and many supporting sites are considered well-supported.

Troubleshooting

"PAUP* not found": Ensure PAUP* is installed and either in your system PATH or you are providing the full path via --paup /path/to/paup.
"I/O operation on closed file" / PAUP* crashes for some constraints:
- This can occur if PAUP* or the system is under extreme load. Ensure you are not using all CPU cores for PAUP*. Use --threads auto (default) or specify a number of threads less than your total core count (e.g., total_cores - 2).
- Check the PAUP* logs in the temporary directory (if kept with --keep-files or --debug) for specific PAUP* error messages.
Low Support Values / Unexpected Results:
- Ensure your chosen evolutionary model is appropriate for your data.
- The heuristic search in PAUP* (hsearch) may not always find the global optimum. More intensive search settings (e.g., more nreps, different swap algorithms) might be needed, potentially by using a custom --paup-block.
- The data itself may not contain strong signal for certain relationships.
Python Errors: Ensure all Python dependencies (BioPython, NumPy) are correctly installed for the Python interpreter you are using.
Site-specific analysis errors: If the site analysis fails but the main analysis succeeds, try running the analysis again with --keep-files and check the site-specific likelihood files in the temporary directory.
Bootstrap fails but ML analysis succeeds: Bootstrap analysis can be computationally intensive. Try using fewer bootstrap replicates (--bootstrap-reps 50) or allocate more processing time by increasing the timeout value in the code.
MrBayes errors:
- "Command not found": Ensure MrBayes is installed and accessible. Use --mrbayes-path /path/to/mb if it's not in your PATH.
- "Error in command 'Ss'": Your version of MrBayes doesn't support stepping-stone sampling. The program will automatically use harmonic mean estimation instead.
- Path errors with spaces: panDecay handles paths with spaces automatically by using relative paths for MrBayes execution.
- No Bayesian output: Check the debug log for specific errors. Ensure your alignment is compatible with MrBayes (e.g., taxon names without special characters).
Bayesian analysis takes too long: Reduce the number of generations (--bayes-ngen 50000) or increase sampling frequency (--bayes-sample-freq 500) for testing. Production runs typically need at least 1 million generations.

Understanding Bayesian Decay Values in Phylogenetic Topology Testing

In phylogenetic applications, Bayesian decay values tend to closely approximate ML log-likelihood differences. This occurs because:

Why Bayesian Decay Values Behave Similarly to ML Differences

Minimal Model Complexity Differences
- In topology testing, we compare models that differ only by a single topological constraint
- All other model parameters (substitution model, rates, frequencies) remain identical
Likelihood Dominates Marginal Likelihood
- When data strongly support a topology, the posterior concentrates around the ML tree
- The marginal likelihood becomes dominated by the likelihood component
- This explains why Bayesian decay values closely approximate ML log-likelihood differences
Different Prior Effects
- In topology testing, the prior difference is only in tree space
- When data signal is strong, this prior difference has minimal impact

Key Insights for Phylogenetics

BD ≈ ΔlnL: The Bayesian decay value typically approximates the ML log-likelihood difference
- This is expected behavior, not an anomaly
- Both metrics primarily reflect the strength of data support for the topology
Large BD Values Are Normal:
- BD values of 30-50 or higher are common for well-supported clades
- They simply reflect strong data signal for the clade
Phylogenetic-Specific Interpretation:
- Focus on BD values for Bayesian interpretation
- Use phylogenetic-specific thresholds (BD: 0-2 weak, 2-5 moderate, 5-10 strong, >10 very strong)
- Compare BD values across clades in your tree for relative support assessment

Practical Implications

When interpreting panDecay results:

Compare BD and ML differences - similar values confirm proper analysis
Use BD values for interpretation with phylogenetic-appropriate thresholds
Consider relative support across branches rather than absolute thresholds

This understanding helps provide accurate assessment of phylogenetic support.

Citations

If you use panDecay in your research, please cite this GitHub repository. Additionally, consider citing the relevant methodological papers:

PAUP*:
- Swofford, D. L. (2003). PAUP*. Phylogenetic Analysis Using Parsimony (*and Other Methods). Version 4. Sinauer Associates, Sunderland, Massachusetts.
Bremer Support (Decay Index) - Original Concept (Parsimony):
- Bremer, K. (1988). The limits of amino acid sequence data in angiosperm phylogenetic reconstruction. Evolution, 42(4), 795-803.
- Bremer, K. (1994). Branch support and tree stability. Cladistics, 10(3), 295-304.
Approximately Unbiased (AU) Test:
- Shimodaira, H. (2002). An approximately unbiased test of phylogenetic tree selection. Systematic Biology, 51(3), 492-508.
General ML Phylogenetics:
- Felsenstein, J. (1981). Evolutionary trees from DNA sequences: a maximum likelihood approach. Journal of Molecular Evolution, 17(6), 368-376.
Site-specific likelihood methods:
- Goldman, N., Anderson, J. P., & Rodrigo, A. G. (2000). Likelihood-based tests of topologies in phylogenetics. Systematic Biology, 49(4), 652-670.
Bootstrap Methods:
- Felsenstein, J. (1985). Confidence limits on phylogenies: an approach using the bootstrap. Evolution, 39(4), 783-791.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Contributing

Contributions, bug reports, and feature requests are welcome! Please feel free to:

Open an issue on GitHub.
Submit a pull request with your changes.

Contact

For questions or support, please open an issue on the GitHub repository.

Project Maintainer: James McInerney

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panDecay: Phylogenetic Analysis using Decay Indices

Table of Contents

Background

What are Decay Indices / Bremer Support?

Why ML-based Decay Indices?

Bayesian Decay Indices

Features

Analysis Types

Core Capabilities

Bayesian Features

Output Files

Technical Features

User Interface Features

Installation

Dependencies

Installing panDecay

Option 1: Install from PyPI (Recommended)

Option 2: Install from GitHub (Latest Development Version)

Option 3: Development Installation

Usage

Basic Command

Command-Line Arguments

Input Files

Sequence Alignment

Optional Starting Tree

Optional PAUP* Block File

Configuration File (INI format)

Constraint File

Output Files

Main Results File (pan_decay_indices.txt by default)

Annotated Trees

Example Annotated Tree Visualization

Detailed Markdown Report (<output_stem>.md)

Site-Specific Analysis (Optional)

Visualizations (Optional)

Understanding the Site Analysis Plots in panDecay

What the Bar Colours Mean

What "Delta lnL" Means

Interpreting the Values

Additional Information in the Plots

Practical Significance

Temporary Files (Debug/Keep)

Examples & Recipes

Example 1: Basic DNA Analysis

Example 2: Parsimony Analysis (Traditional Bremer Support)

Example 3: Protein Data with Specific Model

Example 4: Discrete Morphological Data

Example 5: Using a Starting Tree

Example 6: Advanced Control with PAUP* Block

Example 7: Site-Specific Analysis

Example 8: Bootstrap Analysis

Example 9: Bayesian Analysis Only

Example 10: Combined ML and Bayesian Analysis

Example 11: Combined ML and Parsimony Analysis

Example 12: All Three Analysis Types

Example 13: Using MPI for Parallel MrBayes

Example 14: Using BEAGLE for GPU Acceleration

Example 15: Combined MPI and BEAGLE

Installation Requirements for Parallel Processing

For MPI Support

For BEAGLE Support

Example 16: Quick Bayesian Test

Example 17: Using Configuration Files

Example 18: Testing Specific Branches

Example 19: Combined Config File with Constraints

Interpreting Results

Troubleshooting

Understanding Bayesian Decay Values in Phylogenetic Topology Testing

Why Bayesian Decay Values Behave Similarly to ML Differences

Key Insights for Phylogenetics

Practical Implications

Citations

License

Contributing

Contact

About

Main Results File (`pan_decay_indices.txt` by default)

Detailed Markdown Report (`<output_stem>.md`)

Packages