Parsimony

Parsimony evaluates a tree by the minimum cost of explaining observed characters. It is a family of explicit cost models, reconstruction rules, and topology searches—not a single score. Bijux Phylogenetics exposes those parts separately so a result can be traced from character matrix to supported tree.

flowchart LR
    matrix["Character matrix<br/>and state coding"]
    costs["Weights · ordering<br/>cost matrix"]
    score["Character and<br/>tree scores"]
    search["Stepwise addition<br/>NNI · SPR · ratchet"]
    optima["Equal-best trees"]
    support["Consensus · bootstrap<br/>jackknife · Bremer"]
    artifacts["Trace · states · changes<br/>support tables"]

    matrix --> score
    costs --> score
    score --> search
    search --> optima
    optima --> support
    score --> artifacts
    search --> artifacts
    support --> artifacts

Keep Cost, Optimum, Topology, And History Separate

Parsimony answers several nested questions. Each answer has a different identity and a different evidentiary limit.

Result layer	Meaning	Does not by itself establish
cost model	the penalty assigned to every allowed state change	that the penalties describe the generating evolutionary process
tree score	the minimum cost attainable on one topology	that the topology is globally optimal
optimal score	the best score found under the declared search	that all tree space was exhausted
optimal topology set	all distinct equal-best trees retained by the search	one uniquely supported history
ancestral reconstruction	one or more minimum-cost state assignments	that reconstructed states or branch changes were observed
support summary	stability or extra-cost evidence under a named rule	a posterior probability or likelihood ratio

The result packet must preserve all six layers. Reporting only the best score erases topological multiplicity; reporting one resolved tree erases both search limits and ambiguity among minimum-cost histories.

Scoring Models

Model	Cost assumption	Appropriate interpretation
Fitch	unordered states with equal change cost	minimum number of state changes
Wagner	ordered states with distance-sensitive changes	minimum cost under the declared order
Sankoff	arbitrary state-to-state cost matrix	minimum cost under a fully explicit transition policy
Dollo	a derived state originates once but may be lost repeatedly	score under an asymmetric gain/loss history
Camin–Sokal	change is constrained in the declared irreversible direction	score under directional irreversibility

Ambiguous and polymorphic tip states must remain distinct from missing data. Character weights and cost matrices are part of the scientific model and must travel with the score. A lower tree length is comparable only when matrices, state encodings, weights, and cost rules are identical.

Reconstruction And Homoplasy

Minimum-score ancestral states are often non-unique. ACCTRAN resolves ambiguity toward earlier changes; DELTRAN delays changes toward descendant branches. The choice changes the placement of homoplasy without changing the minimum tree score, so branch-change tables must name the reconstruction rule.

Consistency, retention, and rescaled-consistency indices summarize different aspects of homoplasy. They depend on the character's attainable minimum and maximum as well as its observed steps. Report character-level values before aggregates; a single index can conceal a small set of strongly conflicting characters.

Searching Tree Space

Stepwise addition supplies starting trees. NNI explores local rearrangements; SPR reaches a broader neighborhood; the parsimony ratchet perturbs character weights to escape local optima. These searches are heuristic unless the declared problem is exhaustively enumerated.

A trustworthy search record retains:

• the starting-tree strategy and random seed;
• character weights and perturbation policy;
• move type, accepted moves, and score trajectory;
• stopping conditions and number of independent starts;
• every equal-best topology, not only the first encountered tree;
• a stable topology fingerprint for comparison across runs.

Repeated discovery of the same best score strengthens search evidence but does not prove global optimality.

The cross-method Search, Model Selection, And Support guide defines the candidate populations and tie discipline that a parsimony search shares with likelihood and Bayesian workflows without conflating their objectives.

Separate Score, Topology, And History Equivalence

Equal total scores establish only equality under the declared cost model. They do not establish that trees contain the same splits, that characters place changes on the same branches, or that the implied ancestral states are unique.

flowchart LR
    score["Equal minimum score"]
    trees["Distinct topology<br/>population"]
    states["Alternative minimum<br/>ancestral states"]
    histories["Alternative branch<br/>change histories"]
    decision["Consensus and ambiguity<br/>carried into interpretation"]

    score --> trees --> decision
    score --> states --> histories --> decision

Define the candidate population before summarizing it: all exhaustively enumerated trees, all equal-best trees discovered by a named search policy, or a bounded retained sample. A strict consensus over discovered optima is a property of that discovered set, not proof that every global optimum was found. Likewise, ACCTRAN and DELTRAN select resolutions within a score class; neither converts a non-unique minimum history into an observed event sequence.

Preserve a topology fingerprint, per-character score vector, reconstructed state ambiguity, and branch-change identity separately. Two results may agree on one of those projections and disagree on the others.

Support And Consensus

Strict or majority consensus describes agreement among a declared tree set. Bootstrap and jackknife support describe recovery under character resampling or deletion. Bremer support describes how much additional tree length is needed before a clade disappears. These quantities answer different questions and should never share an unlabeled “support” column.

Support does not establish model adequacy, absence of bias, or historical certainty. Report the resampling scheme, replicate count, search policy within each replicate, clade identity rule, and unresolved consensus structure.

Public Surface Map

Decision	Public surface	Structured evidence
load characters and weights	load_parsimony_character_matrix, load_parsimony_character_weights	taxa, character/state coding, ambiguity, weights, exclusions
score unordered or custom-cost changes	score_fitch, score_sankoff	per-character scores, node state sets or costs, total score
score ordered or irreversible changes	score_wagner, score_dollo, score_camin_sokal	declared transition policy, branch changes, character totals
reconstruct one minimum history	reconstruct_acctran, reconstruct_deltran	node states, branch changes, ambiguity-resolution policy
find lower-scoring topologies	build_parsimony_stepwise_addition_tree, search_parsimony_nni, search_parsimony_spr, run_parsimony_ratchet	starts, moves, score trajectory, termination, equal optima
assess homoplasy	consistency_index, retention_index, rescaled_consistency_index	character-level numerator, denominator, undefined cases, aggregate
assess clade stability	bootstrap_parsimony, jackknife_parsimony, compute_parsimony_bremer_support	replicate or score-decay population, failures, clade support
summarize equal optima	summarize_equal_best_parsimony_trees	topology identities, score equality, consensus and unresolved clades

These functions expose separate scientific contracts. A search report is not a score report, a reconstruction is not proof of a unique history, and a support table cannot recover characters or replicates that were omitted upstream.

Minimum Parsimony Result Packet

Publish the source matrix and taxon order, state vocabulary and ambiguity policy, weights or cost matrix, scoring model, per-character decomposition, search configuration and trace, all equal-best topology identities, reconstruction policy where used, support denominator, warnings and failed replicates, plus structured run and artifact inventories. Link every consensus, tree, branch-change table, and figure back to that packet.

Refuse a global-optimum claim from heuristic search unless exhaustive coverage is established. Refuse an unqualified ancestral history when multiple minimum-cost states remain. Qualify aggregate support whenever incomplete replicates or unresolved equal-best trees affect its denominator.

Review Checklist

Before interpreting a parsimony result, confirm that:

1. taxa and characters were parsed without silent coercion;
2. state ordering, ambiguity, weights, and transition costs are explicit;
3. per-character scores sum to the reported tree length;
4. reconstruction policy is named wherever branch changes are shown;
5. search traces support the claimed degree of optimization;
6. equal-best trees and consensus ambiguity are preserved;
7. each support value names its method and replication contract;
8. structured run, score, state, trace, and support artifacts remain available.