Tree Uncertainty And Sensitivity

Tree uncertainty is not one number. It can appear as competing topology modes, unstable clades or taxa, disagreement between bootstrap and posterior support, gene-tree conflict, sensitivity to consensus thresholds, or dependence on burn-in and thinning. Each pattern has a different denominator and consequence for downstream claims.

flowchart LR
    population["Identified tree<br/>population"]
    structure["Clades · splits · quartets<br/>and tree distances"]
    patterns["Modes · instability<br/>conflict · sensitivity"]
    consequence["Stable · qualified<br/>unstable · not assessable"]
    claim["Bounded scientific claim"]

    population --> structure --> patterns --> consequence --> claim

Uncertainty Axes Are Not Interchangeable

An analysis can be stable on one axis and fragile on another. Name every axis that can reach the consumer instead of compressing them into “tree uncertainty.”

Axis	Population or alternative	Downstream quantity at risk
topology	posterior, bootstrap, gene-tree, or candidate topology population	clade identity, sister relationships, transition placement
root	admitted biological, temporal, or algorithmic roots	direction, ancestry, basal states, ingroup definition
branch length or node time	samples, intervals, calibrations, or fitted alternatives	rates, chronology, exposure, comparative covariance
taxon population	reconciled inclusions, missing taxa, rogue-taxon sensitivity	node correspondence, clade membership, available opportunities
model and analysis policy	substitution/trait models, burn-in, thinning, consensus thresholds	tree weights, retained modes, support and final classification

Propagate the axes that can materially change the downstream claim. A stable consensus topology does not discharge uncertainty in dates or branch lengths; a narrow date interval does not establish stable clade identity.

Diagnose The Uncertainty Source

Pattern	Relevant public surface	Interpretation boundary
several common topology modes	summarize_posterior_topology_diversity, cluster_trees_by_topology, detect_posterior_topology_multimodality	one consensus may conceal separated regions of tree space
clades or taxa change across trees	detect_unstable_clades, detect_unstable_taxa, detect_rogue_taxa	instability identifies dependence, not the biological cause
bootstrap and posterior support disagree	compare_bootstrap_and_posterior_uncertainty	methods have different sampling meanings and need aligned clade keys
two posterior samples differ	compare_posterior_tree_sets, compare_posterior_topological_diversity	chain/run populations must be independently identified and comparably selected
gene trees conflict	summarize_gene_tree_conflicts, compute_gene_tree_quartet_concordance_factors	discordance is an observation; incomplete lineage sorting or another cause requires separate evidence
conclusion changes with threshold or thinning	compare_consensus_thresholds, assess_tree_set_thinning_sensitivity	stability applies only to the declared alternatives and selection policy

The corresponding reports preserve row-level observations. A narrative such as “topology was uncertain” is not a substitute for mode frequencies, unstable clade keys, affected taxa, run comparisons, or failed members.

Retain The Analysis Population

For posterior trees, record chain and run identity, requested samples, burn-in, thinning, retained sample indices, parse failures, duplicate handling, and weights. For bootstrap trees, record requested, completed, failed, and admitted replicates. For gene trees, retain locus identity and taxon reconciliation.

Changing any of these creates a new uncertainty result. In particular, a thinned sample can be useful for resource control while supporting a weaker statement about rare modes or tail behavior than the full retained sample.

Distinguish Frequency, Conflict, And Instability

• frequency counts how often an identified clade, split, topology, or quartet appears in the admitted population;
• conflict records incompatible observations or mutually exclusive clades;
• instability records how a conclusion or identity changes across members, methods, runs, or policies.

A low-frequency clade is not automatically a conflict. A high-frequency clade can coexist with instability elsewhere in the tree. A rogue-taxon score does not authorize deleting that taxon; it identifies a sensitivity question that must be rerun with a declared population change.

Propagate Uncertainty To The Consumer

Consumer	Minimum propagation
ancestral reconstruction	node/clade identity across trees, state summary by member, missing nodes and conclusion stability
comparative model	coefficient/model summary across trees, failed fits, admitted taxa and direction/significance stability
biogeography or host history	event or transition observation across trees, opportunity denominator and unresolved placements
representative-tree figure	selection method, clade frequencies, omitted modes and unstable taxa/clades
publication claim	uncertainty population, sensitivity axes, outcome class and exact non-claim

If downstream analysis uses one selected tree, say so explicitly. The analysis result is conditional on that tree until a declared set of plausible trees is propagated through the method.

Compare Runs Without Pooling Them First

Keep run or chain identities separate long enough to compare topology frequencies, distance distributions, modes, branch lengths, node ages, and failed-member patterns. Pooling before comparison can make two disagreeing runs look like one broad posterior.

flowchart TB
    run_a["Run A retained trees"] --> compare["Run-level comparison"]
    run_b["Run B retained trees"] --> compare
    compare --> decision{"Comparable and<br/>acceptably consistent?"}
    decision -->|yes| pool["Declared pooled population"]
    decision -->|no| qualify["Preserve separate results<br/>and investigate"]

Pooling is a new population identity. Retain the run-level comparison even when pooling is accepted.

Classify The Consequence

Use stable only when the material conclusion survives the declared tree population and sensitivity policies. Use qualified when direction survives but magnitude, support, selected topology, or affected clades change. Use unstable when plausible alternatives reverse or remove the conclusion. Use not assessable when failures, missing runs, or non-comparable identities prevent the planned evaluation.

The classification must link to its population, thresholds, row-level observations, and failed members. Figures reveal modes and conflicts; the structured reports own the denominator and consequence.